Structure Elucidation in Organic Chemistry: The Search for the Right Tools 9783527333363

Table of contents :
Cover
Half Title
Structure Elucidation in Organic Chemistry: The Search for the Right Tools
Copyright
Contents
Preface
List of Contributors
Preface
List of Contributors
1. Interaction of Radiation with Matter
1.1 Introduction
1.2 Spectroscopy: A Definition
1.3 Electromagnetic Radiation
1.4 Electromagnetic Spectrum
1.5 Interaction of Radiation with Matter
1.6 Magnetic Spectroscopies
1.7 Pulse Techniques in NMR Spectroscopy
1.8 Line Widths
1.9 Selection Rules
1.10 Summary of Spectroscopic Techniques
1.10.1 Absorption-Based Methods
1.10.2 Emission-Based Methods
1.10.3 Scattering and Diffraction Methods
References
2. Computational Spectroscopy Tools for Molecular Structure Analysis
2.1 Introduction
2.2 Potential Energy Surface and Molecular Structure
2.2.1 Minima and Conformational Analysis
2.2.2 Spectroscopic Tools for Structure Determination
2.3 Computational Aspects for Spectroscopic Techniques
2.3.1 DFT and Hybrid Approaches for Spectroscopic Applications
2.3.2 Rotational Spectroscopy
2.3.3 Vibrational Spectroscopy: Infrared (IR), Vibrational Circular Dichroism (VCD), Raman
2.3.4 Electronic Spectroscopy: One-Photon Absorption (OPA) and Electronic Circular Dichroism (ECD)
2.3.5 Magnetic Resonance Spectroscopy: Electronic Spin Resonance (ESR)
2.4 Application and Case Studies
2.4.1 Semi-Experimental Equilibrium Structure
2.4.2 Identification of Conformers/Tautomers
2.4.2.1 Rotational Spectrum of Proteinogenic Glutamic Acid
2.4.2.2 IR Spectrum of Glycine
2.4.2.3 Vibrational (IR/VCD) and Electronic (OPA/ECD) Spectra of (Z)-8-Methoxy-4-Cyclooctenone
2.4.2.4 ESR Spectra of Uracil Anion
2.4.3 3D Structure: Molecular Complexes and Flexible Macromolecules
2.4.3.1 Molecular Structure of Anisole Complexes
2.4.3.2 ESR Spectrum of Peptides
Acknowledgments
References
3. Absolute Configuration and Conformational Analysis of Chiral Compounds via Experimental and Theoretical Prediction of Chiroptical Properties: ORD, ECD, and VCD
3.1 Introduction
3.2 Chirality
3.3 What is a Chiroptical Method?
3.4 Quantum Mechanical (Ab Initio) Methods for Predicting Chiroptical Properties
3.5 Electronic Circular Dichroism (ECD)
3.5.1 Advantages of ECD
3.5.2 Limitations of ECD
3.5.3 Applications of ECD
3.5.3.1 Empirical Methods
3.5.3.2 Exciton Coupling
3.5.3.3 ECD Simulation via Ab Initio Methods: Conformational Analysis and Determination of AC
3.5.4 Challenge due to Vibronic Coupling
3.6 Vibrational Circular Dichroism (VCD)
3.6.1 Advantages of VCD
3.6.2 Limitations of VCD
3.6.3 Application of VCD
3.6.3.1 AC Assignment of Moderately Flexible Molecules with One Chiral Center
3.6.3.2 AC Assignment of Flexible Molecules with More Than One Chiral Center
3.6.3.3 Establishing Solute-Solvent and Solute-Solute Intermolecular Interactions of Chiral Molecules
3.6.3.4 AC Assignment via VCD Exciton Coupling Methodology-The Future Perspective
3.7 Optical Rotatory Dispersion (ORD)
3.7.1 Advantages of ORD
3.7.2 Limitations of ORD
3.8 When More than One Method is Needed
3.8.1 Combination of ECD and VCD
3.8.2 Combination of ECD and ORD
3.8.3 Combination of VCD and ORD
3.9 Concluding Remarks
References
4. Mass Spectrometry Strategies in the Assignment of Molecular Structure: Breaking Chemical Bonds before Bringing the Pieces of the Puzzle Together
4.1 Introduction
4.2 Instrumentation and Technology
4.2.1 Ionization Techniques
4.2.2 Mass Analyzers
4.2.3 Tandem Mass Spectrometry Technologies
4.2.4 Data Acquisition Strategies in Tandem Mass Spectrometry
4.3 Breaking Chemical Bonds-Fragmentation Reactions
4.3.1 Fragmentation of Odd-Electron Ions
4.3.2 Fragmentation of Even-Electron Ions
4.3.3 Additional Strategies and Tools
4.4 Confirmation of Identity
4.4.1 Retrieving Compound Identity by Library Searching
4.4.2 Multiple SRM Transitions in Residue Screening
4.4.3 Confirming the Identity of Synthetic Products
4.5 Putting the Puzzle Together-Structure Elucidation of Unknowns
4.5.1 Strategies for Identification of Related Substances
4.5.2 Identification of Unknowns
4.6 Conclusions and Perspectives
Abbreviations
References
5. Basic Principles of IR/Raman: Applications in Small Molecules Structural Elucidation
5.1 Introduction
5.2 Characteristic Vibrational Modes: Diatomics and Chemical Bonds
5.2.1 The Diatomic Example
5.2.2 Equilibrium Properties: Dipole Moment and Polarizability
5.3 Fundamental Vibrational Modes and Molecular Structure
5.4 Selection Rules and Finding the Number of Normal Modes in Each Symmetry Species
5.5 The Vibrational Assignment of Raman and Infrared Spectra
5.6 Conclusions
References
6. Solid-State NMR Applications in the Structural Elucidation of Small Molecules
6.1 Introduction
6.2 Line-Narrowing and Sensitivity Enhancement Methods in ssNMR Spectroscopy
6.3 Probing Dynamics in Solids
6.4 Application of ssNMR Spectroscopy to Small Molecules
6.4.1 Hydrogen Bonding
6.4.2 Guest Molecules Adsorbed in Porous Materials
6.4.2.1 Probe Molecules to Study the Acidity of Catalysts
6.4.2.2 Other Molecules Anchored on Materials
6.4.2.3 The Special Case of CO2
6.4.3 Energy-Related Compounds
6.4.4 Pharmaceuticals
6.4.5 Biomolecules
6.5 NMR of Molecules on Surfaces (DNP)
6.6 NMR Crystallography
Acronyms
References
7. Simplified NMR Procedures for the Assignment of the Absolute Configuration
7.1 Introduction
7.2 Single Derivatization Methods for Mono- and Polyfunctional Compounds
7.2.1 Low Temperature
7.2.2 Selective Complexation
7.2.3 Esterification Shifts
7.3 Resin-Bound Chiral Derivatizing Agents (Mix and Shake Method)
7.4 Non-resin in Tube Assignment (BPG and BINOL Borates)
7.5 Tandem HPLC-NMR: Simultaneous Enantioresolution and Configurational Assignment
7.6 Assignment Based on the Chemical Shifts from the Auxiliaries
7.7 Scope and Conclusions
References
8. Structural Elucidation of Small Organic Molecules Assisted by NMR in Aligned Media
8.1 Introduction
8.2 Aligning Media
8.2.1 Magnetic Susceptibility
8.2.2 Paramagnetic Systems
8.2.3 Mechanically Strained Polymer Gels
8.2.3.1 Strained Gels for Polar Solvents
8.3 Measurement of RDCs
8.3.1 Measurement of 1DCH RDCs
8.3.1.1 13C Detected Experiments
8.3.1.2 1H Detected Experiments
8.3.2 1H-1H Couplings E.COSY and P.E.HSQC Experiments
8.4 Computational Methodology
8.4.1 Determination of the Alignment Tensor
8.4.2 Symmetrical Rotors
8.5 Data Analysis: Use of RDCs as Structural Constraints in Small Molecules
8.5.1 Determination of Configuration for Rigid Molecules
8.5.2 Assignment of Diastereotopic Groups
8.5.3 RC Assignment in Molecules with Conformational Flexibility
8.5.3.1 Multitensor Approaches to the Flexibility Problem
8.5.3.2 Multiple-Tensors Analysis: Dimers and Pseudo-Dimers
8.6 RDCs and Determination of Absolute Configuration
8.6.1 Assignment of the Absolute Configuration: Combination of Residual Dipolar Couplings and Chiroptical Techniques
8.7 Conclusions and Perspectives
Acknowledgments
References
9. NMR Techniques for the Study of Transient Intermolecular Interactions
9.1 Introduction
9.2 Nuclear Overhauser Effect
9.2.1 Introduction to NOE-Based Methods
9.2.2 Transferred NOE
9.2.3 CORCEMA: Relaxation Matrix
9.2.4 Transfer-NOE Applications
9.2.5 Transfer-NOE: Quantitative Applications
9.3 Saturation Transfer Difference NMR
9.3.1 STD NMR Applications
9.3.1.1 Ligand Screening
9.3.1.2 Epitope Mapping
9.3.1.3 Quantitative Structural Analysis: CORCEMA-ST
9.3.1.4 Binding Constants from STD NMR
9.4 Diffusion NMR
9.4.1 Diffusion and Molecular Structure
9.4.2 Measuring Diffusion with NMR
9.4.3 Diffusion Coefficient in the Presence of Chemical Exchange
9.4.4 Diffusion NMR Applications
9.4.4.1 Diffusion NMR Screening
9.4.4.2 Diffusion NMR in the Study of Non-covalent Transient Intermolecular Interactions
9.4.4.3 Diffusion NMR in the Study of Self-aggregation
9.4.4.4 Diffusion NMR to Determine the Equilibrium Binding Constant
9.5 Conclusions
References
10. Analysis of Molecular Interactions by Surface Plasmon Resonance Spectroscopy
10.1 Introduction
10.2 General Aspects of the Surface Plasmon Resonance Principle
10.3 The SPR Experiment
10.3.1 Sensor Surface Design and Preparation
10.3.1.1 Covalent Immobilization
10.3.1.2 Non-covalent Immobilization
10.3.2 The Binding Experiment
10.4 The Information Contained in the SPR Experiment
10.4.1 Qualitative Information
10.4.2 Binding Affinity and Kinetics
10.4.3 Concentration Analysis
10.4.4 Thermodynamics
10.5 SPR Applications: From Large to Small Molecules
10.5.1 Working with SPR and Large Molecules
10.5.1.1 Protein-Protein/Peptide Interactions
10.5.1.2 Antibody-Antigen Interactions
10.5.1.3 Oligonucleotides
10.5.1.4 Larger Structures
10.5.2 Working with SPR and Small Molecules
10.5.2.1 Starting Up
10.5.2.2 Steric Hindrance
10.5.2.3 Mass Transport Limitation
10.5.2.4 Matrix Effects
10.5.2.5 Refractive Index Jumps and Baseline Drifting
10.5.2.6 Limited Solubility and Use of Organic Solvents
10.5.2.7 Changes of Refractive Index Increments
10.6 Beyond SPR-Orthogonal Interaction Biosensor Technologies
References
11. Determination of Absolute Configurations by Electronic CD Exciton Chirality, Vibrational CD, 1H NMR Anisotropy, and X-ray Crystallography Methods-Principles, Practices, and Reliability
11.1 Introduction
11.2 Reliability in the AC Determination and Selection of Method
11.3 Non-empirical Method: AC Determination by the X-ray Bijvoet Method
11.4 Non-empirical Method: AC Determination by the ECD Exciton Chirality Method
11.4.1 Outline of the ECD Exciton Chirality Method
11.4.2 Molecular Exciton Theory of the CD Exciton Chirality Rule and Application to Steroidal Dibenzoate
11.4.3 The Most Ideal Exciton CD of (6R,15R)-(+)-6, 15-Dihydro-6,15-ethanonaphtho[2,3-c]pentaphene
11.4.4 Illustrative Cases: Application of the CD Exciton Chirality Rule
11.4.4.1 Acyclic 1,2-Glycols
11.4.4.2 Acetylene Alcohols
11.5 Non-empirical Method: AC Determination by VCD Spectroscopy and DFT MO Simulation
11.6 Empirical Method: AC Determination by 1H NMR Anisotropy Method Using MαNP Acid
11.6.1 Enantioresolution of Racemic Aliphatic Alcohols Using MαNP Acid and Simultaneous Determination of Their ACs
11.6.2 Application of the MαNP Acid Method to cis-2-Butyl-2-methyl-1-tetralol
11.6.3 Verification of the AC of cis-2-Butyl-2-methyl-1-tetralol by X-ray Crystallography
11.6.4 Verification of the AC of (S)-(-)-[VCD(+)984]-4-Ethyl-4-methyloctane by Chemical Correlation
11.7 Relative Method: X-ray Crystallography Using Camphorsultam Dichlorophthalic Acid (CSDP Acid)
11.7.1 Application of the CSDP Acid Method to Other Racemic Alcohols
11.7.2 Application of the CSDP Acid Method to Asymmetric Reaction Products
11.8 Relative Method: X-ray Crystallography Using of MαNP Group as Internal Reference
11.8.1 Alternative Preparation of Enantiopure MαNP Acid
11.8.2 AC Determination of Other MαNP Esters by X-ray Crystallography
11.9 Conclusion
Acknowledgments
References
12. An Integrated Approach to Structure Verification Using Automated Procedures
12.1 Introduction
12.1.1 Setting the Scene: The Need for an Automatic Structure Verification (ASV) Platform
12.1.2 Automatic Structure Verification: What It Is and What It Is Not
12.1.3 Background and Existing ASV System
12.2 Practical Aspects of NMR Automatic Verification
12.2.1 Digital Resolution
12.2.1.1 Zero Filling
12.2.2 Window Functions
12.2.2.1 Sensitivity Enhancement
12.2.2.2 Resolution Enhancement
12.2.2.3 Weighting Functions and Integration
12.2.3 Linear Prediction
12.2.4 Relaxation Times and Delays
12.2.5 Alignment of 1H and HSQC Spectra
12.2.6 General Recommendations for the Choice of NMR Acquisition and Processing Parameters
12.2.6.1 1H-NMR Spectra
12.2.6.2 Single Bond 1H-13C 2D Heterocorrelation
12.3 The Architecture of the Automatic Verification Expert System
12.3.1 Introduction
12.3.2 The Scoring System
12.3.2.1 Score
12.3.2.2 Significance
12.3.2.3 Quality
12.3.3 NMR Prediction and Spectral Synthesis
12.3.3.1 13C-NMR Prediction
12.3.3.2 1H-NMR Prediction
12.3.3.3 1H Spectral Synthesis
12.3.4 Automatic Importing and Processing of NMR Data Sets
12.3.5 Automatic Analysis: Spectral Deconvolution and Peaks Labeling
12.3.6 ASV Tests
12.3.6.1 Number of Nuclides Test (NN)
12.3.6.2 1H Prediction Bounds Metrics
12.3.6.3 Automatic Assignments Test
12.4 Performance of the Automated Structure Verification Systems
12.4.1 Basic Definitions
12.4.2 Tests of Performance
12.5 Conclusions
Acknowledgments
References
13. On the Search for the Appropriate Techniques for Structural Elucidation of Small Molecules
13.1 Introduction
13.2 The Challenge of Structural Determination
13.3 Tools: Mass Spectrometry (MS)
13.4 Tools: Solution NMR Spectroscopy
13.5 Tools: Solid-State NMR Spectroscopy
13.6 Chiroptical Spectroscopies
13.7 Theoretical Calculations: Ab initio Calculations of NMR Shifts
13.8 Theoretical Calculations: Computer-Assisted Structure Elucidation
13.9 Summary
Acknowledgments
References
Index

Citation preview

Edited by María-Magdalena Cid and Jorge Bravo Structure Elucidation in Organic Chemistry

Related Titles Silverstein, R.M., Webster, F.X., Kiemle, D.

Gauglitz, G., Moore, D.S. (eds.)

The Spectrometric Identification of Organic Compounds

Handbook of Spectroscopy

7th Edition 2013 Print ISBN: 978-1-118-51735-2 (Also available in a variety of electronic formats)

Grunenberg, J.

Computational Spectroscopy Methods, Experiments and Applications

2nd Edition 2013 Print ISBN: 978-3-527-32150-6 (Also available in a variety of electronic formats)

Berger, S., Sicker, D.

Classics in Spectroscopy Isolation and Structure Elucidation of Natural Products 2009 Print ISBN: 978-3-527-32617-4

2010 Print ISBN: 978-3-527-32649-5

Findeisen, M., Berger, S.

50 and More Essential NMR Experiments A Detailed Guide 2013 Print ISBN: 978-3-527-33483-4

Pregosin, P.S.

NMR in Organometallic Chemistry 2012 Print ISBN: 978-3-527-33013-3 (Also available in a variety of electronic formats)

Edited by María-Magdalena Cid and Jorge Bravo

Structure Elucidation in Organic Chemistry The Search for the Right Tools

The Editors Prof. Dr. Maria-Magdalena Cid

University of Vigo Organic Chemistry Department Lagoas-Marcosende 36310 Vigo Spain

All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.

Prof. Dr. Jorge Bravo

University of Vigo Inorganic Chemistry Department Campus Universitario Lagoas Marcosende 36310 Vigo Spain

Library of Congress Card No.: applied for British Library Cataloguing-in-Publication Data

A catalogue record for this book is available from the British Library. Bibliographic information published by the Deutsche Nationalbibliothek

The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at . © 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Boschstr. 12, 69469 Weinheim, Germany All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law. Print ISBN: 978-3-527-33336-3 ePDF ISBN: 978-3-527-66464-1 ePub ISBN: 978-3-527-66463-4 Mobi ISBN: 978-3-527-66462-7 oBook ISBN: 978-3-527-66461-0 Cover Design Grafik-Design Schulz,

Fußgönheim, Germany Typesetting Laserwords Private Limited,

Chennai, India Printing and Binding Markono Print

Media Pte, Singapore Printed on acid-free paper

V

Contents Preface XV List of Contributors XVII 1

Interaction of Radiation with Matter 1 Ignacio Pérez-Juste and Olalla Nieto Faza

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.10.1 1.10.2 1.10.3

Introduction 1 Spectroscopy: A Definition 1 Electromagnetic Radiation 2 Electromagnetic Spectrum 4 Interaction of Radiation with Matter 6 Magnetic Spectroscopies 12 Pulse Techniques in NMR Spectroscopy 14 Line Widths 15 Selection Rules 17 Summary of Spectroscopic Techniques 18 Absorption-Based Methods 19 Emission-Based Methods 20 Scattering and Diffraction Methods 21 References 23

2

Computational Spectroscopy Tools for Molecular Structure Analysis 27 Cristina Puzzarini and Malgorzata Biczysko

2.1 2.2 2.2.1 2.2.2 2.3 2.3.1 2.3.2 2.3.3

Introduction 27 Potential Energy Surface and Molecular Structure 29 Minima and Conformational Analysis 29 Spectroscopic Tools for Structure Determination 31 Computational Aspects for Spectroscopic Techniques 32 DFT and Hybrid Approaches for Spectroscopic Applications 32 Rotational Spectroscopy 33 Vibrational Spectroscopy: Infrared (IR), Vibrational Circular Dichroism (VCD), Raman 34

VI

Contents

2.3.4 2.3.5 2.4 2.4.1 2.4.2 2.4.2.1 2.4.2.2 2.4.2.3 2.4.2.4 2.4.3 2.4.3.1 2.4.3.2

Electronic Spectroscopy: One-Photon Absorption (OPA) and Electronic Circular Dichroism (ECD) 36 Magnetic Resonance Spectroscopy: Electronic Spin Resonance (ESR) 38 Application and Case Studies 40 Semi-Experimental Equilibrium Structure 40 Identification of Conformers/Tautomers 42 Rotational Spectrum of Proteinogenic Glutamic Acid 43 IR Spectrum of Glycine 43 Vibrational (IR/VCD) and Electronic (OPA/ECD) Spectra of (Z)-8-Methoxy-4-Cyclooctenone 47 ESR Spectra of Uracil Anion 48 3D Structure: Molecular Complexes and Flexible Macromolecules 50 Molecular Structure of Anisole Complexes 50 ESR Spectrum of Peptides 53 Acknowledgments 55 References 55

3

Absolute Configuration and Conformational Analysis of Chiral Compounds via Experimental and Theoretical Prediction of Chiroptical Properties: ORD, ECD, and VCD 65 Ana G. Petrovic, Nina Berova, and José Lorenzo Alonso-Gómez

3.1 3.2 3.3 3.4

Introduction 65 Chirality 65 What is a Chiroptical Method? 66 Quantum Mechanical (Ab Initio) Methods for Predicting Chiroptical Properties 71 Electronic Circular Dichroism (ECD) 73 Advantages of ECD 73 Limitations of ECD 73 Applications of ECD 74 Empirical Methods 74 Exciton Coupling 75 ECD Simulation via Ab Initio Methods: Conformational Analysis and Determination of AC 77 Challenge due to Vibronic Coupling 82 Vibrational Circular Dichroism (VCD) 82 Advantages of VCD 85 Limitations of VCD 86 Application of VCD 86 AC Assignment of Moderately Flexible Molecules with One Chiral Center 86 AC Assignment of Flexible Molecules with More Than One Chiral Center 88

3.5 3.5.1 3.5.2 3.5.3 3.5.3.1 3.5.3.2 3.5.3.3 3.5.4 3.6 3.6.1 3.6.2 3.6.3 3.6.3.1 3.6.3.2

Contents

3.6.3.3 3.6.3.4 3.7 3.7.1 3.7.2 3.8 3.8.1 3.8.2 3.8.3 3.9

Establishing Solute–Solvent and Solute–Solute Intermolecular Interactions of Chiral Molecules 90 AC Assignment via VCD Exciton Coupling Methodology–The Future Perspective 94 Optical Rotatory Dispersion (ORD) 95 Advantages of ORD 96 Limitations of ORD 96 When More than One Method is Needed 97 Combination of ECD and VCD 97 Combination of ECD and ORD 97 Combination of VCD and ORD 99 Concluding Remarks 100 References 100

4

Mass Spectrometry Strategies in the Assignment of Molecular Structure: Breaking Chemical Bonds before Bringing the Pieces of the Puzzle Together 105 Wilfried M.A. Niessen and Maarten Honing

4.1 4.2 4.2.1 4.2.2 4.2.3 4.2.4 4.3 4.3.1 4.3.2 4.3.3 4.4 4.4.1 4.4.2 4.4.3 4.5

Introduction 105 Instrumentation and Technology 106 Ionization Techniques 107 Mass Analyzers 109 Tandem Mass Spectrometry Technologies 111 Data Acquisition Strategies in Tandem Mass Spectrometry 115 Breaking Chemical Bonds–Fragmentation Reactions 116 Fragmentation of Odd-Electron Ions 116 Fragmentation of Even-Electron Ions 118 Additional Strategies and Tools 123 Confirmation of Identity 125 Retrieving Compound Identity by Library Searching 126 Multiple SRM Transitions in Residue Screening 126 Confirming the Identity of Synthetic Products 127 Putting the Puzzle Together–Structure Elucidation of Unknowns 128 Strategies for Identification of Related Substances 128 Identification of Unknowns 131 Conclusions and Perspectives 136 Abbreviations 136 References 137

4.5.1 4.5.2 4.6

5

Basic Principles of IR/Raman: Applications in Small Molecules Structural Elucidation 145 Ricardo F. Aroca

5.1

Introduction 145

VII

VIII

Contents

5.2 5.2.1 5.2.2 5.3 5.4 5.5 5.6

Characteristic Vibrational Modes: Diatomics and Chemical Bonds 148 The Diatomic Example 150 Equilibrium Properties: Dipole Moment and Polarizability 153 Fundamental Vibrational Modes and Molecular Structure 158 Selection Rules and Finding the Number of Normal Modes in Each Symmetry Species 159 The Vibrational Assignment of Raman and Infrared Spectra 163 Conclusions 169 References 169

6

Solid-State NMR Applications in the Structural Elucidation of Small Molecules 173 Mariana Sardo, João Rocha, and Luís Mafra

6.1 6.2

Introduction 173 Line-Narrowing and Sensitivity Enhancement Methods in ssNMR Spectroscopy 174 Probing Dynamics in Solids 175 Application of ssNMR Spectroscopy to Small Molecules 178 Hydrogen Bonding 178 Guest Molecules Adsorbed in Porous Materials 180 Probe Molecules to Study the Acidity of Catalysts 181 Other Molecules Anchored on Materials 188 The Special Case of CO2 191 Energy-Related Compounds 194 Pharmaceuticals 197 Biomolecules 206 NMR of Molecules on Surfaces (DNP) 214 NMR Crystallography 217 Acronyms 228 References 229

6.3 6.4 6.4.1 6.4.2 6.4.2.1 6.4.2.2 6.4.2.3 6.4.3 6.4.4 6.4.5 6.5 6.6

7

Simplified NMR Procedures for the Assignment of the Absolute Configuration 241 José Manuel Seco, Emilio Quiñoá, and Ricardo Riguera

7.1 7.2

Introduction 241 Single Derivatization Methods for Mono- and Polyfunctional Compounds 243 Low Temperature 243 Selective Complexation 252 Esterification Shifts 254 Resin-Bound Chiral Derivatizing Agents (Mix and Shake Method) 257 Non-resin in Tube Assignment (BPG and BINOL Borates) 260

7.2.1 7.2.2 7.2.3 7.3 7.4

Contents

7.5 7.6 7.7

Tandem HPLC-NMR: Simultaneous Enantioresolution and Configurational Assignment 262 Assignment Based on the Chemical Shifts from the Auxiliaries Scope and Conclusions 272 References 273

264

8

Structural Elucidation of Small Organic Molecules Assisted by NMR in Aligned Media 279 Roberto R. Gil, Christian Griesinger, Armando Navarro-Vázquez, and Han Sun

8.1 8.2 8.2.1 8.2.2 8.2.3 8.2.3.1 8.3 8.3.1 8.3.1.1 8.3.1.2 8.3.2 8.4 8.4.1 8.4.2 8.5

Introduction 279 Aligning Media 284 Magnetic Susceptibility 284 Paramagnetic Systems 288 Mechanically Strained Polymer Gels 290 Strained Gels for Polar Solvents 290 Measurement of RDCs 291 Measurement of 1 DCH RDCs 292 13 C Detected Experiments 292 1 H Detected Experiments 292 1 H–1 H Couplings E.COSY and P.E.HSQC Experiments 296 Computational Methodology 297 Determination of the Alignment Tensor 297 Symmetrical Rotors 299 Data Analysis: Use of RDCs as Structural Constraints in Small Molecules 300 Determination of Configuration for Rigid Molecules 300 Assignment of Diastereotopic Groups 303 RC Assignment in Molecules with Conformational Flexibility 305 Multitensor Approaches to the Flexibility Problem 307 Multiple-Tensors Analysis: Dimers and Pseudo-Dimers 308 RDCs and Determination of Absolute Configuration 311 Assignment of the Absolute Configuration: Combination of Residual Dipolar Couplings and Chiroptical Techniques 312 Conclusions and Perspectives 316 Acknowledgments 316 References 316

8.5.1 8.5.2 8.5.3 8.5.3.1 8.5.3.2 8.6 8.6.1 8.7

9

NMR Techniques for the Study of Transient Intermolecular Interactions 325 Jesús Angulo, Ana Ardá, Eurico J. Cabrita, Manuel Martín-Pastor, Jesús Jiménez-Barbero, and Pedro M. Nieto

9.1 9.2 9.2.1 9.2.2

Introduction 325 Nuclear Overhauser Effect 326 Introduction to NOE-Based Methods Transferred NOE 328

326

IX

X

Contents

9.2.3 9.2.4 9.2.5 9.3 9.3.1 9.3.1.1 9.3.1.2 9.3.1.3 9.3.1.4 9.4 9.4.1 9.4.2 9.4.3 9.4.4 9.4.4.1 9.4.4.2 9.4.4.3 9.4.4.4 9.5

CORCEMA: Relaxation Matrix 331 Transfer-NOE Applications 332 Transfer-NOE: Quantitative Applications 334 Saturation Transfer Difference NMR 335 STD NMR Applications 337 Ligand Screening 337 Epitope Mapping 338 Quantitative Structural Analysis: CORCEMA-ST 339 Binding Constants from STD NMR 341 Diffusion NMR 345 Diffusion and Molecular Structure 345 Measuring Diffusion with NMR 345 Diffusion Coefficient in the Presence of Chemical Exchange Diffusion NMR Applications 349 Diffusion NMR Screening 349 Diffusion NMR in the Study of Non-covalent Transient Intermolecular Interactions 349 Diffusion NMR in the Study of Self-aggregation 350 Diffusion NMR to Determine the Equilibrium Binding Constant 351 Conclusions 354 References 354

348

10

Analysis of Molecular Interactions by Surface Plasmon Resonance Spectroscopy 361 Eva Muñoz and Daniel Ricklin

10.1 10.2 10.3 10.3.1 10.3.1.1 10.3.1.2 10.3.2 10.4 10.4.1 10.4.2 10.4.3 10.4.4 10.5 10.5.1 10.5.1.1 10.5.1.2 10.5.1.3 10.5.1.4 10.5.2

Introduction 361 General Aspects of the Surface Plasmon Resonance Principle 362 The SPR Experiment 363 Sensor Surface Design and Preparation 364 Covalent Immobilization 364 Non-covalent Immobilization 366 The Binding Experiment 367 The Information Contained in the SPR Experiment 369 Qualitative Information 369 Binding Affinity and Kinetics 370 Concentration Analysis 372 Thermodynamics 373 SPR Applications: From Large to Small Molecules 373 Working with SPR and Large Molecules 373 Protein–Protein/Peptide Interactions 373 Antibody–Antigen Interactions 376 Oligonucleotides 377 Larger Structures 378 Working with SPR and Small Molecules 378

Contents

10.5.2.1 10.5.2.2 10.5.2.3 10.5.2.4 10.5.2.5 10.5.2.6 10.5.2.7 10.6

Starting Up 379 Steric Hindrance 380 Mass Transport Limitation 381 Matrix Effects 382 Refractive Index Jumps and Baseline Drifting 383 Limited Solubility and Use of Organic Solvents 384 Changes of Refractive Index Increments 385 Beyond SPR–Orthogonal Interaction Biosensor Technologies 386 References 387

11

Determination of Absolute Configurations by Electronic CD Exciton Chirality, Vibrational CD, 1 H NMR Anisotropy, and X-ray Crystallography Methods–Principles, Practices, and Reliability 393 Nobuyuki Harada

11.1 11.2 11.3

Introduction 393 Reliability in the AC Determination and Selection of Method 394 Non-empirical Method: AC Determination by the X-ray Bijvoet Method 395 Non-empirical Method: AC Determination by the ECD Exciton Chirality Method 396 Outline of the ECD Exciton Chirality Method 396 Molecular Exciton Theory of the CD Exciton Chirality Rule and Application to Steroidal Dibenzoate 398 The Most Ideal Exciton CD of (6R,15R)-(+)-6, 15-Dihydro-6,15-ethanonaphtho[2,3-c]pentaphene 400 Illustrative Cases: Application of the CD Exciton Chirality Rule 401 Acyclic 1,2-Glycols 401 Acetylene Alcohols 403 Non-empirical Method: AC Determination by VCD Spectroscopy and DFT MO Simulation 403 Empirical Method: AC Determination by 1 H NMR Anisotropy Method Using MαNP Acid 408 Enantioresolution of Racemic Aliphatic Alcohols Using MαNP Acid and Simultaneous Determination of Their ACs 411 Application of the MαNP Acid Method to cis-2-Butyl-2-methyl-1-tetralol 411 Verification of the AC of cis-2-Butyl-2-methyl-1-tetralol by X-ray Crystallography 414 Verification of the AC of (S)-(−)-[VCD(+)984]-4-Ethyl-4-methyloctane by Chemical Correlation 415 Relative Method: X-ray Crystallography Using Camphorsultam Dichlorophthalic Acid (CSDP Acid) 416 Application of the CSDP Acid Method to Other Racemic Alcohols 418

11.4 11.4.1 11.4.2 11.4.3 11.4.4 11.4.4.1 11.4.4.2 11.5 11.6 11.6.1 11.6.2 11.6.3 11.6.4

11.7 11.7.1

XI

XII

Contents

11.7.2 11.8 11.8.1 11.8.2 11.9

Application of the CSDP Acid Method to Asymmetric Reaction Products 430 Relative Method: X-ray Crystallography Using of MαNP Group as Internal Reference 432 Alternative Preparation of Enantiopure MαNP Acid 432 AC Determination of Other MαNP Esters by X-ray Crystallography 433 Conclusion 438 Acknowledgments 439 References 439

12

An Integrated Approach to Structure Verification Using Automated Procedures 445 Juan Carlos Cobas Gómez, Michael Bernstein, and Stanislav Sýkora

12.1 12.1.1

Introduction 445 Setting the Scene: The Need for an Automatic Structure Verification (ASV) Platform 445 Automatic Structure Verification: What It Is and What It Is Not 449 Background and Existing ASV System 451 Practical Aspects of NMR Automatic Verification 453 Digital Resolution 453 Zero Filling 454 Window Functions 457 Sensitivity Enhancement 458 Resolution Enhancement 459 Weighting Functions and Integration 460 Linear Prediction 462 Relaxation Times and Delays 464 Alignment of 1 H and HSQC Spectra 465 General Recommendations for the Choice of NMR Acquisition and Processing Parameters 466 1 H-NMR Spectra 466 Single Bond 1 H-13 C 2D Heterocorrelation 466 The Architecture of the Automatic Verification Expert System 471 Introduction 471 The Scoring System 472 Score 473 Significance 473 Quality 473 NMR Prediction and Spectral Synthesis 474 13 C-NMR Prediction 474 1 H-NMR Prediction 475 1 H Spectral Synthesis 476 Automatic Importing and Processing of NMR Data Sets 476

12.1.2 12.1.3 12.2 12.2.1 12.2.1.1 12.2.2 12.2.2.1 12.2.2.2 12.2.2.3 12.2.3 12.2.4 12.2.5 12.2.6 12.2.6.1 12.2.6.2 12.3 12.3.1 12.3.2 12.3.2.1 12.3.2.2 12.3.2.3 12.3.3 12.3.3.1 12.3.3.2 12.3.3.3 12.3.4

Contents

12.3.5 12.3.6 12.3.6.1 12.3.6.2 12.3.6.3 12.4 12.4.1 12.4.2 12.5

Automatic Analysis: Spectral Deconvolution and Peaks Labeling 478 ASV Tests 483 Number of Nuclides Test (NN) 483 1 H Prediction Bounds Metrics 483 Automatic Assignments Test 484 Performance of the Automated Structure Verification Systems Basic Definitions 485 Tests of Performance 488 Conclusions 490 Acknowledgments 490 References 490

13

On the Search for the Appropriate Techniques for Structural Elucidation of Small Molecules 493 María Magdalena Cid and Jorge Bravo

13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8

Introduction 493 The Challenge of Structural Determination 495 Tools: Mass Spectrometry (MS) 497 Tools: Solution NMR Spectroscopy 499 Tools: Solid-State NMR Spectroscopy 501 Chiroptical Spectroscopies 507 Theoretical Calculations: Ab initio Calculations of NMR Shifts Theoretical Calculations: Computer-Assisted Structure Elucidation 514 Summary 515 Acknowledgments 516 References 516

13.9

Index

521

485

512

XIII

XV

Preface The correct structural determination of a given molecule is not only a matter of building up a puzzle with more or less academic interest but also a complex exercise with aftermaths that sometimes go well beyond. A well-documented example is the repercussions at different levels that the resolution of the DNA structure in 1954 had, a landmark that merited the Nobel Prize for Medicine in 1962. However, it is not necessary to go back to those years to be aware of the importance of correct structure determination. In this regard, a recent article published by C&EN, reports on the first legal case in which a structural reassignment puts in trouble a patent and clinical trials of the promising anticancer agent TIC10. In this article Nick Levinson, the Stanford University postdoc who discovered the bosutinib problem, says, “I find it astonishing that a drug candidate can get this far through regulatory controls and into trials without the key players actually having done the proper quality control. It points to a serious hole in the whole process.” The application of spectroscopy for structure determination and analysis has seen a big growth during the last decades and is now an important part of every chemistry course, as spectroscopic methods are nowadays used at some point in the solution of almost all problems in chemistry, including those at the frontier of life sciences. Besides, determining the molecular structure of materials is an essential step in understanding their properties and how they are formed. This book is intended to provide the readers with the advantages of the synergy among all the involved techniques in structural elucidation to solve a particular target, bridging the gap among mass spectrometry, optical and X-ray spectroscopies, and nuclear magnetic and surface plasmon resonances (SPRs) by providing the needed knowledge and applicability of all of them. Because most of the advances in these techniques required the use of computational tools, computational spectroscopy is another subject included in the book. This book provides the advanced student or practicing chemist with a comprehensive and up-to-date perspective on structural elucidation studies of pure substances and mixtures, in molecular or supramolecular architectures. It starts with an introductory chapter describing the different manifestations of light-matter interactions. Chapter 2 is devoted to computational spectroscopy, providing an overview of the theoretical background and computational requirements needed for molecular structure analysis by means of spectroscopic techniques. Chapters

XVI

Preface

about the use of mass spectrometry (Chapter 4) and infrared/Raman spectroscopy (Chapter 5) for characterizing, identifying, or determining a structure provide qualitative and quantitative information not available from any other techniques. Several chapters are devoted to nuclear magnetic resonance (NMR), because, since its discovery, it is the analytical method that has had the greatest impact, particularly in chemistry. In fact, developments in NMR have been the motive behind the award of two Nobel prizes for chemistry. NMR is used in all branches of science in which precise structural determination is required and in which the nature of interactions and reactions in solution are being studied. Thus, part of the book focuses on topics of current interest in solid and solution NMR in isotropic and anisotropic media. Transfer nuclear Overhauser effect and saturation transfer difference (STD) allowing the detection of transient binding of small molecules to macromolecular receptors is also treated along with automatic verification system (ASV) applied to assess the correctness of a proposed structure. Two separate chapters are devoted to optical spectroscopy (electronic and vibrational circular dichroism and optical rotatory dispersion) (Chapter 3) and X-ray analysis (Chapter 11), as they are essential techniques for determination of relative and absolute configuration of natural products. The book also aims at introducing the reader to the applications of SPR technology (Chapter 10), emphasizing on a practical point of view since SPR sensors have become a central tool for the study of biomolecular interactions and the detection of chemical and biological species. Finally, Chapter 13 tries to emphasize that the structural determination of chemical compounds is commonly a difficult task and frequently entails the combined use of several tools. To illustrate the power of this combination, randomly chosen representative cases of misassigned structures are discussed. We hope this book provides experts and untrained researchers with the needed tools to solve structural problems and also with the current state of development in other not so common techniques. We thank those who made this book a reality either by proofreading the manuscripts or by giving interesting suggestions to improve them. We would like to make a special mention of all the authors for their commitment in this project and also to Dr. Carlos Silva for his invaluable assistance in the design of the cover and Dr. Reinhold Weber for all his support without which this project would not have reached the end. Vigo, December 2014

Mar´ıa Magdalena Cid Jorge Bravo

XVII

List of Contributors José Lorenzo Alonso-Gómez

Ricardo F. Aroca

Universidade de Vigo Departamento de Quimica Orgánica Edificio de Ciencias Experimentais Campus Lagoas-Marcosende 36310 Vigo Spain

University of Windsor Department of Chemistry and Biochemistry Windsor, N9B 3P4 Ontario Canada

Jesús Angulo

Instituto de Investigaciones Quimicas CSIC-US Glycosystems Laboratory Avenida Americo Vespucio 49 41092 Sevilla Spain Ana Ardá

Centro de Investigaciones Biológicas Chemical and Physical Biology Ramiro de Maeztu 9 28040 Madrid Spain

Michael Bernstein

Mestrelab Research S.L., Feliciano Barrera 9 Baixo 15706 Santiago de Compostela Spain Nina Berova

Columbia University Department of Chemistry Havemeyer Hall MC 3114 3000 Broadway New York 10027 USA

XVIII

List of Contributors

Malgorzata Biczysko

Juan Carlos Cobas Gómez

Istituto Italiano di Tecnologia Center for Nanotechnology Innovation @NEST Piazza San Silvestro 12 56127 Pisa Italy

Mestrelab Research S.L., Feliciano Barrera 9 Baixo 15706 Santiago de Compostela Spain

and

Roberto R. Gil

Scuola Normale Superiore Piazza dei Cavalieri 7 56126 Pisa Italy Jorge Bravo

Universidade de Vigo Departamento de Quimica Inorganica Edificio de Ciencias Experimentais Campus Lagoas-Marcosende 36310 Vigo Spain Eurico J. Cabrita

Universidade Nova de Lisboa Departamento de Quimica Faculdade de Ciencias e Tecnologia 2829-516 Caparica Portugal María Magdalena Cid

Universidade de Vigo Departamento de Quimica Organica Edificio de Ciencias Experimentais Campus Lagoas-Marcosende 36310 Vigo Spain

Carnegie Mellon University Department of Chemistry Mellon Institute Room 302 4400 Fifth Avenue Pittsburgh PA 15213-3890 USA Christian Griesinger

Max-Planck-Institut für Biophysikalische Chemie Abteilung 030 Am Fassberg 11 37077 Göttingen Germany Nobuyuki Harada

Tohoku University Institute for Multidisciplinary Research for Advanced Materials 2-1-1 Katahira Aoba Sendai 980-8577 Japan Maarten Honing

VU University Amsterdam Department of BioMolecular Analysis De Boelelaan 1083 1081 HV Amsterdam The Netherlands

List of Contributors

Jesús Jiménez-Barbero

Wilfried M.A. Niessen

Centro de Investigaciones Biológicas C/Ramiro de Maeztu 9 28040 Madrid Spain

VU University Amsterdam Department of BioMolecular Analysis De Boelelaan 1083 1081 HV Amsterdam The Netherlands

Luís Mafra

University of Aveiro Department of Chemistry CICECO 3810-193 Aveiro Portugal Manuel Martín-Pastor

Universidade de Santiago de Compostela Unidade de RMN.RIAIDT Edificio CACTUS Campus Vida s/n 15782 Santiago de Compostela Spain Eva Muñoz

Universidade de Santiago de Compostela Departamento de Quimica Organica Facultade de Quimica y Centro Investigacion en Quimica Bilogica y Materiales Moleculares (CIQUS) Campus Vida s/n 15782 Santiago de Compostela Spain

Pedro M. Nieto

Instituto de Investigaciones Quimicas CSIC-US Glycosystems Laboratory Avenida Americo Vespucio 49 41092 Sevilla Spain Olalla Nieto Faza

Universidade de Vigo Departamento de Química Física Facultad de Química Edificio de Ciencias Experimentais Campus Lagoas-Marcosende 36310 Vigo Spain Ignacio Pérez-Juste

Universidade de Vigo Departamento de Química Física Facultad de Química Edificio de Ciencias Experimentais Campus Lagoas-Marcosende 36310 Vigo Spain

Armando Navarro-Vázquez

Universidade de Vigo Departamento de Quimica Organica Edificio de Ciencias Experimentais Campus Lagoas-Marcosende 36310 Vigo Spain

Ana G. Petrovic

New York Institute of Technology 1855 Broadway Office 405A New York NY 10023-7692 USA

XIX

XX

List of Contributors

Cristina Puzzarini

Ricardo Riguera Vega

Universitá di Bologna Dipartimento di Chimica “Giacomo Ciamician” Via Selmi 2 40126 Bologna Italy

Universidade de Santiago de Compostela Departamento de Quimica Organica Facultade de Quimica y Centro Investigacion en Quimica Bilogica y Materiales Moleculares (CIQUS) Campus Vida s/n 15782 Santiago de Compostela Spain

Emilio Quiñoá Cabana

Universidade de Santiago de Compostela Departamento de Quimica Organica Facultade de Quimica y Centro Investigacion en Quimica Bilogica y Materiales Moleculares (CIQUS) Campus Vida s/n 15782 Santiago de Compostela Spain

João Rocha

University of Aveiro Department of Chemistry CICECO 3810-193 Aveiro Portugal Mariana Sardo

Daniel Ricklin

University of Pennsylvania Department of Pathology and Laboratory Medicine 401 Stellar Chance Laboratories 422 Curie Boulevard Philadelphia PA 19104 USA

University of Aveiro Department of Chemistry CICECO 3810-193 Aveiro Portugal José Manuel Seco

Universidade de Santiago de Compostela Departamento de Quimica Organica Facultade de Quimica y Centro Investigacion en Quimica Bilogica y Materiales Moleculares (CIQUS) Campus Vida s/n 15782 Santiago de Compostela Spain

List of Contributors

Han Sun

Stanislav Sýkora

Abteilung NMR-basierte Strukturbiologie Max-Planck-Institut für biophysikalische Chemie Am Fassberg 11 37077 Göttingen Germany

Extra Byte Via Raffaello Sanzio 22C Castano Primo Italy

XXI

1

1 Interaction of Radiation with Matter Ignacio Pérez-Juste and Olalla Nieto Faza

1.1 Introduction

The interaction of light with matter is at the basis of one of the primary participants in human perception, because a significant part of the cerebral cortex is dedicated to visual processing. This complex mechanism starts with the lightinduced isomerization of a retinal molecule that triggers a messenger cascade to produce the transmission of a nerve impulse from the retina. And it is through sight that we gather most of our knowledge of our environment (sizes, colors, shapes, etc.). However, the chemical properties of the visual pigments in our retinas, together with the structure of the eye, limit our perceptions to light wavelengths between 390 and 750 nm and objects larger than 0.1 mm. Application of our knowledge about the interaction of light with matter and the development of optical instruments allowed us very early to use optical devices to immensely expand the range of objects accessible to our study, from the organelles in cells to faraway galaxies. In parallel, the discovery of electromagnetic radiation outside of the visible range provided incentives and tools for the elaboration of unifying concepts about light and for a myriad of technological applications. In this chapter, we summarize the main laws that govern the interaction of electromagnetic radiation with matter, and the way in which these laws can be applied to the different phenomena that can arise from this interaction. This information is necessarily limited, and will be developed in more detail as needed in each of the following chapters on specific techniques.

1.2 Spectroscopy: A Definition

Spectroscopy is the study of the interaction of electromagnetic radiation with matter involving either absorption, emission, or scattering of radiation by the system under study. Atomic and molecular spectra can provide detailed Structure Elucidation in Organic Chemistry: The Search for the Right Tools, First Edition. Edited by María-Magdalena Cid and Jorge Bravo. © 2015 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2015 by Wiley-VCH Verlag GmbH & Co. KGaA.

2

1 Interaction of Radiation with Matter

information about the structure and chemical properties of the system. Spectroscopic techniques are one of the main sources of molecular geometries, that is, bond lengths, bond angles, and torsion angles, and can also yield, as will be seen, significant information about molecular symmetry, energy level distributions, electron densities, or electric and magnetic properties [1–15]. Spectroscopy has been an essential tool in the development of models for atomic and molecular structure, prompting scientists to refine existing models to accurately reproduce the experimentally observed spacing between energy states. A dramatic example of this is the birth of quantum theory (to explain the discrete nature of electronic transitions in atoms) or the discovery of the element helium in the spectrum of the Sun, well before it was found on Earth [16–19]. Nowadays, spectroscopic tools are routinely used in quantitative and qualitative chemical analysis and in the characterization of new molecules and materials, and play an essential role in such diverse fields as the elaboration and testing of theoretical models, synthetic chemistry, the study of reaction mechanisms, or biochemistry and materials science [20–23]. Atomic and molecular spectroscopies are mainly related to the absorption or emission of electromagnetic radiation and the changes taking place in those systems as a consequence of the energy of the radiation. Diffraction methods, however, involve the wave nature of the radiation, and rely on the interpretation of the interference patterns between waves upon their encounter with obstacles of dimensions roughly close to their wavelength. When these waves correspond to electromagnetic waves in the X-ray region of the spectrum or particles such as electrons or neutrons, their wavelengths are similar to the spacing between atoms in condensed phases such as liquids or crystals and they can be employed to obtain useful information about the atomic positions in these materials. X-ray diffraction produced the key images for unraveling the double-helix structure of DNA, and is routinely used to elucidate the structure of large biomolecules, surfaces, or materials [24–26].

1.3 Electromagnetic Radiation

According to elementary physics, a charge is surrounded by an electric field, and a moving charge, that is, an electrical current, also generates a magnetic field. Besides this, accelerated charges emit electromagnetic radiation, while radiation accelerates charged particles. Maxwell’s equations condense all these phenomena describing the dynamics of free charges and currents and providing the foundation of classical electromagnetic theory and the interaction of light and matter. These equations describe macroscopically the behavior of charges in electric and/or magnetic fields, both in vacuum and in materials. Among these, propagation of light in vacuum is easier to describe, since light in matter is constantly absorbed and re-emitted, so that the solution of Maxwell’s equations in matter requires detailed knowledge about the structure of the material, a simplified model

1.3

Electromagnetic Radiation

for the material, or some empirical information about the interaction between light and matter. Solution of Maxwell’s equations without sources (charges or currents) leads to the equation of a propagating electromagnetic wave [27]. Thus, electromagnetic radiation can be described as a wave phenomenon formed by the combination of electric (E) and magnetic (H) fields, which oscillate in phase orthogonal to each other and orthogonal to the direction of propagation as well. For a given direction of propagation, these two orthogonal fields can be oriented in any direction in the plane perpendicular to it. However, if restrictions are imposed on the oscillation planes of the wave, polarized radiation can be obtained. Thus, for a plane-polarized (also known as linearly polarized) wave traveling in the x direction, the electric and magnetic fields of the electromagnetic radiation given by )] [ ( x − 𝜈t (1.1) E = E0 sin 2π 𝜆 )] [ ( x E = H 0 sin 2π − 𝜈t (1.2) 𝜆 are always in the same two orthogonal planes. The plane of polarization is conventionally taken to be the plane containing the electric field (the xy plane in Figure 1.1) because, as seen below, radiation and matter usually interact through the electric component. E0 and H 0 in the previous equations correspond to the amplitudes, that is, the maximum values of the electric and magnetic fields, respectively. The radiation wavelength, 𝜆, can be defined as the distance between adjacent crests at a given point in time, and the frequency, 𝜈, is the number of oscillations passing by a point in a given time (that is, the inverse of the wave period), usually with units of s−1 or Hz. The relation between frequency and wavelength is given by c (1.3) ν= 𝜆 where c is the velocity of propagation of the wave. In vacuum, c equals the speed of light (c0 ), but in general c = c0 /n where n is the index of refraction of the propagation medium. For historical reasons, the use of the inverse of the wavelength is y

x E = E0 sin[2π (– - νt)] λ λ

x z x H = H0 sin[2π(– - νt)] λ Figure 1.1 Plane-polarized electromagnetic radiation.

3

4

1 Interaction of Radiation with Matter

also very common in spectroscopy; 1 (1.4) 𝜆 It is known as wavenumber and is usually given in units of cm−1 . Ondulatory and corpuscular theories of light coexisted and replaced each other since the seventeenth century, but the wave nature of the electromagnetic radiation was firmly established by Maxwell in the nineteenth century. However, at the beginning of the twentieth century Planck and Einstein showed that radiation also presents the properties of a particle. According to the corpuscular theory, electromagnetic radiation can be described as quantum energy packets named photons that possess an energy given by ̃ ν=

E = hν

(1.5)

where 𝜈 is the radiation frequency and h is Planck’s constant. Later, in 1924 de Broglie stated that if electromagnetic waves present properties associated with particles, the particles can also display wavelike properties and proposed that the wavelength of a particle behaving as a wave depends on its linear momentum, p, according to the expression 𝜆=

h h = p mv

(1.6)

where m is the particle mass and v is its velocity. Further experiments of diffraction with electron beams confirmed the wavelike properties of particles, and nowadays neutron and electron diffraction techniques, such as X-ray diffraction, are used in laboratories all over the world for the characterization of materials. According to the previous 1.6, electromagnetic radiation is considered to have a dual nature, as a wave and as a particle, which manifests in different phenomena. As will be seen below, the description of the interaction of light and matter in spectroscopic methods where radiation is absorbed or emitted is based on the corpuscular behavior of the radiation since photons are absorbed or emitted depending on their energy. Diffraction methods, however, are based on the wave behavior of radiation or on the wavelike properties of particles.

1.4 Electromagnetic Spectrum

Depending on its frequency or wavelength, an electromagnetic wave is included in one of the several regions in which the electromagnetic spectrum is divided. As can be seen in Table 1.1, the electromagnetic spectrum covers a large range of radiation frequencies, of which the visible region is only a small part. The traditional division of the electromagnetic spectrum into regions is artificial because there are no fundamental differences between radiations in these regions beyond the energies involved. However, each region can be usually related to particular technological applications (from radio communications to gamma knife surgery) or a

Wavelength

300 m → 10 cm 10 cm → 0.1 mm 0.1 mm → 1 μm 700 nm → 400 nm 400 nm → 10 nm 100 Å → 0.3 Å 0.3 Å → 0.003 Å

106 → 3 × 109 3 × 109 → 3 × 1012

3 × 1012 → 3 × 1014

4.3 × 1014 → 7.5 × 1014 7.5 × 1014 → 3 × 1016 3 × 1016 → 1019

1019 → 1022

Radio Microwave

Infrared

a)

3 × 108 → 3 × 1010

14 300 → 25 000 25 000 → 106 106 → 3 × 108 104 → 109

1.7 → 3.1 3.1 → 120 120 → 4 × 104

0.012 → 1.2

4.1 × 10−9 → 1.2 × 10−5 1.2 × 10−5 → 0.012

3 × 10−5 → 0.1 0.1 → 100 100 → 10 000

Energy (eV)

Wavenumber (cm−1 )

Most commonly used spectroscopic units: Radio frequency radiation: MHz = 106 Hz (Hz = s−1 ). Microwave radiation: GHz = 109 Hz. Infrared radiation: cm−1 (wavenumbers). Visible and ultraviolet radiation: nm = 10−9 m. X-ray and 𝛾-ray radiation: nm = 10−9 m and Å = 10−10 m.

γ-rays

Visible Ultraviolet X-rays

Region

Frequency (s−1 )

Table 1.1 Electromagnetic spectrum.a)

Nuclear magnetic resonance Electron spin resonance and rotational spectroscopy Rotational spectroscopy and vibrational spectroscopy UV–visible UV–visible Electronic transition (internal electrons) Nuclear transitions

Spectroscopy

1.4 Electromagnetic Spectrum 5

6

1 Interaction of Radiation with Matter

certain spectroscopic method, the latter depending on the energy levels between which the radiation causes a transition or the processes that may occur in atoms or molecules exposed to that radiation. It must be noted, however, that the limits between regions are diffuse and that the type of energy transition associated with each spectroscopic region is only approximate.

1.5 Interaction of Radiation with Matter

The study of spectroscopic methods requires the use of quantum mechanics concepts [17–19]. From the early work of Bohr on atomic spectra, it could be established that absorption or emission of radiation is possible because of the quantization of atomic and molecular energy levels. Thus, Bohr’s frequency condition indicates that a system can experiment on a transition between two states 1 and 2 if the energy of the electromagnetic radiation absorbed equals the energy difference between the two states ΔE1→2 = E2 − E1 = hν

(1.7)

On the other hand, emission of radiation is due to the return of an atomic or molecular system from an excited state to a lower energy state, and the energy of the emitted radiation also corresponds to the energy difference between the states involved in the transition (Figure 1.2). The application of quantum mechanics to atoms and molecules shows that these systems display a large number of quantized energy levels. The energy of a molecule is then the result of the contributions from electronic configuration, vibration, rotation and translation, and various electron–electron, nuclear–nuclear and nuclear–electron interactions. Most often, these contributions can be considered independent and treated separately because their energies usually differ by several orders of magnitude. As a consequence, the energy differences between different types of levels in molecular systems (electronic and vibrational, for example) correspond to electromagnetic radiation of different frequency and, as seen above, this causes each region of the spectrum to be related with a characteristic type of spectroscopy. The occurrence of quantized energy levels together with electromagnetic radiation of proper energy is not, however, a sufficient condition for absorption or emission of radiation. The probability of a transition and the amount of radiation absorbed or emitted E2 hν

E2 hν

E1

E1

Figure 1.2 (a,b) Absorption and emission between quantized energy levels.

1.5

Interaction of Radiation with Matter

depends on the nature of the interaction between the molecular system and the radiation. The mechanism of interaction between electromagnetic radiation and matter relies on the interaction between the oscillating electric and magnetic fields of the radiation with the electric or magnetic dipole moment of an atom or molecule. Thus, a molecular system can experience a force as a consequence of the electrostatic interaction between its electric dipole moment and the oscillating electric field of the electromagnetic radiation. On the other hand, the interaction between the permanent magnetic moment of a nucleus or an electron and the magnetic field of the electromagnetic radiation is the foundation of nuclear magnetic resonance, electron spin resonance, and related spectroscopic techniques. According to this, the interaction between atoms or molecules and the electromagnetic radiation requires the existence of a permanent electric or magnetic dipole or the instantaneous creation of an electric dipole due to internal motions. As is shown below, the magnitude of this interaction depends on the size of the molecular dipole moment. The quantitative study of the interaction of electromagnetic radiation with matter can be done using a simple semi-classical model. In this model the electromagnetic radiation is treated classically, while the energy levels are obtained by solving the time-dependent Schrödinger equation. It is due to the time dependence of radiation shown in Equations 1.1 and 1.2 that the interaction of radiation with atoms and molecules requires solving the time-dependent Schrödinger equation. For a single particle described by means of a wave function depending on coordinates and time, Ψ(x, y, z; t), the form of the Schrödinger equation is ∂Ψ(x, y, z; t) h ∂Ψ(x, y, z; t) = iℏ Ĥ Ψ(x, y, z; t) = i 2π ∂t ∂t or

(

ℏ2 2 ̂ − ∇ +V 2m

) Ψ(x, y, z; t) = iℏ

∂Ψ(x, y, z; t) ∂t

(1.8)

(1.9)

where the Hamiltonian operator Ĥ is the combination of the Laplacian operator, 2 2 2 given by ∇2 ≡ ∂x∂ 2 + ∂y∂ 2 + ∂z∂ 2 , and the potential energy operator V̂ , which depends only on the spatial coordinates (x, y, z). If the potential energy is considered to be time independent, the wave function Ψ(x, y, z; t) can be written as the product of a time-independent function 𝜓(x, y, z) and a function of time 𝜙(t) Ψ(x, y, z; t) = 𝜓(x, y, z)𝜙(t)

(1.10)

From now on, to simplify the notation, explicit inclusion of coordinates and time is discontinued. Introducing the above function allows us to separate the Schrödinger equation into two equations. The first, ) ( ℏ2 2 ̂ ∇ + V 𝜓 = E𝜓 (1.11) − 2m

7

8

1 Interaction of Radiation with Matter

corresponds to the time-independent Schrödinger equation whose solution provides the energy of the particle in a state n (E = En ) and the wave function 𝜓(x, y, z), from which physical properties can be deduced. The second, iℏ

d𝜙 = E𝜙 dt

(1.12)

is a first order differential equation on time with a solution given by 𝜙(t) = e−iEn t∕ℏ

(1.13)

It must be noted here that this time-dependent factor in the solution of the Schrödinger equation always has the same form; therefore the total wave function for a single particle can be written as Ψn = 𝜓n e−iEn t∕ℏ

(1.14)

More complex quantum mechanical systems, such as atoms or molecules, usually possess several stationary states described by total wave functions Ψ0 , Ψ1 , Ψ2 , … , with discrete energies E0 , E1 , E2 , . . . . For a transition between two nondegenerate m and n states caused by a photon of adequate frequency, the Ψm and Ψn wave functions describing the states involved in the transition are solutions of the Schrödinger equation, and their linear combination Ψ = cm (t)Ψm + cn (t)Ψn

(1.15)

should be also a solution of the equation. Such a superposition of states is the general solution for systems in transition between two states. The initial state Ψm is described by cm = 1/cn = 0 and the final state Ψn is described by cm = 0/cn = 1. During an absorptive transition, the coefficients change from cm = 1 → 0 to cn = 0 → 1, while they change from cm = 0 → 1 and cn = 1 → 0 if radiation is emitted. Time enters this way into the solution of the problem, since the coefficients ci (t) are only functions of time. If we want to model how this radiation-induced transition between states Ψm and Ψn takes place, we can consider that the time-dependent radiation field associated to exposure to an electromagnetic radiation is a perturbation Ĥ ′ (x, y, z, t) that must be added to the Hamiltonian for the unperturbed system H0 Ĥ = Ĥ 0 + Ĥ ′

(1.16)

If the potential due to the electromagnetic radiation is small compared to the molecular potential, the Schrödinger equation during irradiation becomes (Ĥ 0 + Ĥ ′ ) Ψ = iℏ

∂Ψ ∂t

(1.17)

which can be solved by means of perturbation theory. After some algebra, the rate of increase of cn , that is, the rate of transition from initial state m to final state n can be obtained as dcn c = m Ψ∗n Ĥ ′ Ψm dv dt iℏ ∫

(1.18)

1.5

Interaction of Radiation with Matter

According to Equation 1.18, explicit forms for the Ψm and Ψn wave functions and the Ĥ ′ Hamiltonian are needed to evaluate the intensity of a transition. To obtain further insight into the form of the Ĥ ′ Hamiltonian, the interaction between the electromagnetic radiation and the system must be analyzed. As cited above, the electric and magnetic components of the radiation can interact with the electric or the magnetic dipole of the system. For the sake of brevity, in our analysis we will consider the system as an electric dipole moving only on one dimension x. Extension of this derivation to the three-dimensional case and to magnetic properties is straightforward. In this framework, the magnitude of the dipole moment (𝜇 x ) depends on the displacement of an electric charge (e) by a distance x from its equilibrium position 𝜇x = ex

(1.19)

The Hamiltonian representing the classical interaction between the electric dipole moment and the electric field of the electromagnetic radiation is Ĥ ′ = −𝝁E = −𝜇E cos 𝜃

(1.20)

where 𝜃 is the angle between the dipole and the electric field. For a polarized electromagnetic radiation traveling along the x direction, the amplitude of the electric field is Ex = 2Exo cos 2πνt = Exo (ei2πνt + e−i2πνt )

(1.21)

where Exo is the maximum amplitude of the electric field (Figure 1.1). If we assume that the dipole and the electric radiation field are parallel Ĥ ′ = −𝜇x Ex = −exEx and introducing the above expressions it can be shown that ) ( 1 − ei(En −Em +hν)t∕ℏ 1 − ei(En −Em −hν)t∕ℏ o ∗ + cn = Ex 𝜓n 𝜇x 𝜓m dv ∫ En − Em + hν En − Em − hν

(1.22)

(1.23)

𝜓 ∗ 𝜇 𝜓 dv is usually represented as 𝜇xnm = ⟨n|𝜇x |m⟩ and is ∫ n x m known as the transition dipole moment integral. According to the initial conditions, if the energy of the initial state m is lower than that of the final state n, the energy difference (En − Em ) will be positive for a transition Ψm → Ψn caused by absorption of radiation, and will be negative for a transition Ψm ← Ψn with emission of radiation. If we only consider now the absorption process, the above expression can be simplified because when the frequency of the radiation fulfills that where the integral

hν = En − Em

(1.24)

the denominator of the second term in the addition becomes very small and the entire second term can take large values, so that the first term containing

9

10

1 Interaction of Radiation with Matter

En − Em + hν can be neglected. Under these conditions, the probability of finding the system in the upper state n after irradiation is given by ( 2[ ( ) ]) sin πt En − Em − hν ∕h 2 ∗ o 2 nm 2 (1.25) |cn | = cn cn = 4(Ex ) (𝜇x ) (En − Em − hν)2 This expression applies only when the radiation is monochromatic. By integration over all the frequencies, the total transition probability, that is, the probability of finding the system in state n after interaction with the radiation, is |c2n | = c∗n cn = 4(Exo )2 (𝜇xnm )2

∞

∫−∞

(Exo )2 nm 2 sin2 [πt(En − Em − hν)∕h] dν = (𝜇x ) t (En − Em − hν)2 ℏ2 (1.26)

According to this, the probability of a system in state Ψm undergoing a transition to state Ψn due to irradiation is proportional to the transition dipole moment integral, the square of the incident electric field amplitude (the intensity of the radiation), and the time of irradiation. In order to compare with experimental results on the amount of radiation absorbed, it is convenient to rewrite the previous expression substituting the electric field strength by the energy density (𝜌), that is, the energy per unit volume that is irradiated by the electromagnetic radiation. These magnitudes are related by the expression (Exo )2 (1.27) 2π Further differentiation of the transition probability with respect to time and extension of the complete procedure for isotropic radiation (where the three x, y, z components of the radiation–dipole interactions are equal) gives the transition probability per unit time as 𝜌=

d[c∗n cn ] 8π3 2 = 2 𝜇nm 𝜌(ν) = Bnm 𝜌(ν) dt 3h where 2 = 𝜇nm

∑

(𝜇inm )2

(1.28)

(1.29)

i=x,y,z

and 8π3 2 𝜇 (1.30) 3h2 nm called Einstein’s coefficient of induced absorption. Expression (1.28) shows that the rate of the Ψm → Ψn transition depends on the square of the dipole moment integral and the energy density of the radiation. If we change the initial conditions in Equation 1.15 to those for a system in an upper energy state, that is, with cm = 0 and cn = 1, the previous treatment for induced absorption would be formally identical for the emission of radiation from an excited state Ψn to state Ψm induced by an electromagnetic radiation. Bnm =

1.5

Interaction of Radiation with Matter

Thus, the expression for induced emission from an excited state is identical to that for induced absorption with Bmn = Bnm . However, the procedure presented here has not considered the possibility of spontaneous emission from the upper state Ψn to the lower energy state Ψm , a process that can be of importance when the population of the upper energy state is significant. Following Equation 1.28, in the presence of radiation the population change of the upper state due to induced absorption must be proportional to the population of the lower state according to ( ) dNn = Nm→n = Nm Bmn 𝜌(ν) (1.31) dt absorption However, there is also a population change of the upper state n due to induced emission ) ( dNn = Nm←n = −Nn Bnm 𝜌(ν) (1.32) dt emission and the possibility of spontaneous emission ) ( dNn = Nm←n = −Nn Anm dt emission

(1.33)

where Anm is the Einstein coefficient for spontaneous emission. The relationship between the Anm and Bnm coefficients can be established using the radiative energy density given by the Planck radiation law 𝜌(ν) =

8πhν3mn c3 (ehνmn ∕kT − 1)

(1.34)

and the relationship between the upper and lower state populations given by the Boltzmann distribution law Nn = Nm e−(Em −En )∕kT = Nm ehνmn ∕kT

(1.35)

For a system in equilibrium, absorption and emission rates must be equal and the net change of the upper state population is zero: ) ( dNn = Nm→n + Nm←n = (Nm − Nn )Bmn 𝜌(ν) − Nn Anm = 0 (1.36) dt which gives the relation between spontaneous and induced Einstein’s coefficients 8πhν3mn Bnm (1.37) c3 According to Equation 1.36, when a system is irradiated there will be competitive induced and spontaneous emissions that reduce the intensity of the absorption lines. However, only induced emission is coherent with the incident radiation, that is, they travel in the same direction and have the same phase, so that the net absorption intensity equals the difference between the absorbed and induced emission intensities according to Anm =

Nn Bmn 𝜌(ν) − Nn Bnm 𝜌(ν) = Bmn 𝜌(ν)(Nm − Nn )

(1.38)

11

12

1 Interaction of Radiation with Matter

which states that the intensity for a given absorption depends on the population difference between the initial and final states. It must be also noted here that, due to the ν3mn factor, the importance of spontaneous emission increases as the radiation frequency increases (which is of importance in lasers). However, for transitions with frequencies below 1012 s−1 the magnitude of Anm compared to Bnm is insignificant and spontaneous emission can be neglected.

1.6 Magnetic Spectroscopies

All the above discussion is focused on the changes experienced by matter as a consequence of the electric field of the electromagnetic radiation. In addition, we will now comment briefly on some aspects of nuclear magnetic resonance methods and electron spin resonance methods that are instead related to the action of the magnetic field of the radiation. The phenomenon of magnetic resonance is due to the interaction of an external magnetic field with the magnetic moment associated with the spin of a nucleus or an electron. In the absence of an external magnetic field, the states of a spin system are degenerated, that is, they have the same energy, and no spectroscopic transitions can be observed. However, when the spin system interacts with an external magnetic field, the energy degeneracy is removed and absorption or emission of radiation can be observed [7, 28–30]. If we consider initially the nuclear magnetic resonance, the interaction energy between a nuclear magnetic moment, 𝝁m , and the external magnetic field, H, is given by E = −𝝁𝐦 ⋅ H

(1.39)

The nuclear magnetic moment is proportional to the nuclear spin angular momentum I 1 e 𝝁𝐦 = g N I = gN 𝛽N I (1.40) 2mp ℏ where the nuclear magneton, 𝛽 N , depends on the proton mass, mp , and the values of the nuclear gN factor must be determined experimentally for each nucleus. As a consequence of the effect of the magnetic field, the orientations of the nuclear magnetic moment along the z direction of the incident field are quantized and can only take values according to Iz = ℏMI

(1.41)

where the values of the magnetic quantum number are MI = −I, … ,0, … , I. For the common case of protons in 1 H-NMR and carbons in 13 C-NMR with I = 1∕2, the orientation with MI = +1/2 is parallel to the field direction and is energetically preferred, while the orientation with MI = −1/2 is antiparallel. Following the expressions above, the energies for these spin states are given by EMI = −gN 𝛽N Hz MI

(1.42)

1.6

Magnetic Spectroscopies

and the energy separation between two levels is ΔE = hν = E−1∕2 − E1∕2 = gN 𝛽N Hz

(1.43)

𝜔 = 2πν = 𝛾Hz

(1.44)

or where 𝛾 is called the magnetogyric ratio and includes a combination of factors given by g 𝛽 (1.45) 𝛾= N N ℏ It must be recalled here that the expression for the NMR quantum mechanical transition frequency 𝜔 is similar to that of the Larmor angular frequency obtained for the classical description of the precessional motion experimented by the nuclear magnetic moment around the direction of the external electromagnetic field. According to the above, the energies needed for transitions between nuclear magnetic levels depend both on the intensity of the applied magnetic field and on the value for the magnetogyric ratio for each nucleus (Figure 1.3). However, it must be noted that the energy separation between levels is very small compared with the average energy of thermal motion and, as a consequence, the populations of the separated energy levels are nearly equal and signal sensitivities are small. Some characteristic resonance frequencies and common magnetic fields are shown in Table 1.2. Quantitative treatment for electron magnetic resonance is similar to that presented here. However, due to its lighter mass, the value of 𝛾 e for an electron is larger than that for a proton and, as a consequence, the energy separation between the energy levels for the electron is approximately 2000 times greater than for the proton. For these reasons, one of the main difficulties of electron resonance spectroscopy is generation and detection of resonance frequencies above 35 000 MHz, which fall into the microwave range of the electromagnetic spectrum. Furthermore, electron resonance spectroscopy is only useful for the study of systems with unpaired electrons and its use is much more limited than that of nuclear magnetic techniques [31]. I=½ E

MI = –½

MI = +½ 0

Hz

Figure 1.3 Spin energy differences in an external magnetic field for a nucleus with I = 1/2.

13

14

1 Interaction of Radiation with Matter

Table 1.2 Some magnetic resonance parameters for selected nuclei with I = 1∕2. Nucleus 1H 13 C 19

F

31 P

𝝁m a)

𝜸 × 107 s−1 T−1

NMR frequency (MHz)b)

Relative sensitivity

2.79285 0.70241 2.62887 1.13160

23.751 6.726 25.167 10.830

42.5775 10.7084 40.0776 17.2515

1.00000 0.01591 0.83400 0.06652

a) Nuclear magnetic moments in units of the nuclear magneton 𝛽N . b) These values correspond to nuclei in a magnetic field H = 1.0 T.

1.7 Pulse Techniques in NMR Spectroscopy

According to the above discussion, continuous NMR spectra can be obtained by keeping constant the radiation frequency while varying the intensity of the external magnetic field until the resonance condition given in Equation 1.43 is achieved, or by keeping constant the value of the external magnetic field while the frequency of electromagnetic radiation is varied. However, these procedures are only suitable for sensitive nuclei with large magnetic moments and high natural abundance, and to obtain the NMR spectra of insensitive nuclei of low abundances, the use of pulse NMR techniques is mandatory. For a sample immersed in a magnetic field with nuclei with different resonant frequencies, all the nuclear magnetic moments precess around the applied field direction. As a consequence of the small energy difference between the nuclear spin levels, the number of nuclei in the lower energy state (n𝛼 ) is greater than that in the upper energy state (n𝛽 ) and the components of the nuclear magnetic moments along the field direction can be added to obtain a macroscopic magnetization, usually described by the vector M 0 (Figure 1.4). This magnetization vector M 0 is used to describe the interaction between the nuclear dipoles and the magnetic vector of the radiofrequency pulse. In NMR pulse methods, all the nuclei in a sample are excited simultaneously by a radiofrequency pulse. A radiofrequency generator can produce a pulse if it is switched on only for a short time, containing not a single frequency but a continuous band of frequencies around a given frequency center. Only a part of the frequency interval is effective in exciting transitions, and the choice of the pulse duration and the generator frequency depends on the magnetic field employed and on the nuclei to be studied. During the application of a pulse, the macroscopic magnetization vector M 0 is moved away from its equilibrium position through a pulse angle that depends on the angle between the direction of the static field and the direction in which the radiofrequency pulse is applied. Once the pulse is switched off, the magnetization vector M 0 reverts to its equilibrium state through a complicated motion, named relaxation. Bloch showed that the behavior of M 0 , both during the application of the pulse and the subsequent relaxation, can be

1.8

Line Widths

Hz M0 MI = –½ nα nβ MI = +½

Figure 1.4 Macroscopic magnetization M0 .

easily described in a rotating coordinate system by means of three magnetization components varying with time. Thus, the return of the Mz′ component to its equilibrium condition, named longitudinal relaxation and occurring at a rate determined by the spin-lattice relaxation time, T 1 , depends on the way the energy of the spin system is transferred to the surroundings. On the other hand, transverse relaxation determines how rapidly the Mx′ and My′ magnetization components decay, and the rate constant for this process depends on the spin–spin relaxation time, T 2 , which can be classically visualized as the energy transferred by the spin system during relaxation to the adjacent nuclei through fluctuating magnetic fields. In samples containing nuclei with different resonant frequencies, the decay curves of the transverse components of the magnetization superimpose and interfere producing a complex signal (Figure 1.5) that can be detected by a receiver coil. This free induction decay (FID) signal is obtained in the time domain and contains the resonance frequencies and intensities of the sample. However, the FID signal cannot be interpreted directly and must be transformed into a useful spectrum in the frequency domain by means of a mathematical operation named Fourier transformation. Additional details on the NMR pulse techniques will be given in subsequent chapters and can be found in more specialized literature [28–30]. 1.8 Line Widths

The transitions between energy levels should result in the absorption or emission of discrete frequencies of the electromagnetic spectrum, resulting in line spectra. However, in the experiments, spectral lines are always broadened, due to different effects: natural line width, Doppler shift, Lorentz broadening, and other physical or technical (depending on the experimental setup) phenomena. Natural line width does not depend on the experimental setup and is inherent to any studied system. It arises from the uncertainty principle, which states that

15

16

1 Interaction of Radiation with Matter

Sample: ethanol (CH3CH2OH) in trifluoracetic acid Acquisition parameters: 300 MHz, 8 pulses, spectral width 6000 Hz 16 K data points, acquisition time 2.7 s

0.5

1.0

1.5

2.0

2.5

s

(a)

0.02

0.04

0.06

0.08

0.10

s

(b)

(c)

Frequency (Hz)

Figure 1.5 Free induction decay (FID) and Fourier transformation. (a) 1 H NMR time domain spectrum of ethanol. (b) Zoomed area of the time domain spectrum between 0 and 0.1 s. (c) Frequency domain spectrum obtained by Fourier transform of the time domain spectrum.

1.9

Selection Rules

two conjugated variables cannot be exactly determined at the same time, so that, for example, ℏ (1.46) 2 In this case, Δt would represent the lifetime of the excited state and ΔE the uncertainty in the energy of this state, which will be reflected in an uncertainty in the frequency of the radiation associated with this transition. The Doppler effect is another source of bandwidth, due to the thermal motion of the atoms or molecules emitting radiation. The atoms or molecules that travel in the direction of the observer emit light at a higher frequency than those traveling away from him ) ( v ν = ν0 1 ± (1.47) c where ν0 is the frequency of the transition, v is the speed of the atom or molecule, and c is the speed of light. Pressure broadening is an umbrella term that includes the different effects that neighboring particles can have in the emission of an individual particle. Collision of other particles with the emitting particle can result in a decreased lifetime of the excited state, enhancing the uncertainty in its energy beyond that corresponding to the natural broadening, leading to what is called impact pressure broadening or Lorentz broadening. Other particles can also shift the energy levels of the target molecule through their electric fields (Stark broadening), through resonance (an energy exchange between particles of the same type), or other interactions (van der Waals broadening). Of the broadening mentioned above, natural line broadening is the smallest, while the others can be reduced changing the experimental conditions. Thus, pressure broadening can be removed working at low pressures, while Doppler broadening can be reduced using effusive or molecular beams where the velocity component of the sample in the direction of observation is small. ΔEΔt ≥

1.9 Selection Rules

As noted in Equation 1.26, the probability of the absorption or emission of a photon due to a transition between two states depends on the transition dipole moment integral. Application of symmetry considerations to the two states involved in the transitions can help identify when the integral is going to be zero without the need of explicitly solving it, resulting in what are called “selection rules.” Selection rules determine which transitions are allowed and are expected to appear in the spectrum, and which are forbidden and will not appear in the spectrum. Selection rules can be quite varied and depend on the type of spectrum considered and the properties of the system under study [17, 32]. The key requirement for a transition to be forbidden, that is, to have a zero probability of occurring, is that the dipolar transition moment 𝜇xnm =

∫

𝜓n∗ 𝜇x 𝜓m dv is

17

18

1 Interaction of Radiation with Matter

zero. For this, the product 𝜓n∗ 𝜇x 𝜓m needs to be antisymmetric, under the symmetry operations of the system. This condition can be easily checked by using the character table corresponding to the symmetry point group of the system and bearing in mind that the electric dipole operator transforms as x, y, z, the magnetic dipole as Rx , Ry , Rz and the electric polarizability (used, for instance, in Raman spectra) as x2 , y2 , z2 , xy, xz, yz. Using this, it is easy to explain, for instance, why the symmetric stretch in CO2 is inactive in IR spectroscopy while it is active in Raman spectroscopy [17, 19, 33–35]. Selection rules are expressed in terms of quantum numbers with physical significance derived from the system wave function, and some simple examples follow. Thus, selection rules governing atomic electronic spectra are Δn = 0, 1, 2, … with ΔL = ±1 for single electron transitions and ΔL = 0, ±1 for multielectron transitions, ΔS = 0 and ΔJ = 0, ±1 (except for the forbidden J = 0 → J = 0 transition), where n is the principal quantum number, L the orbital angular momentum, S, the spin angular momentum, and J, the total angular momentum. In molecular systems, the observation of pure rotational transitions requires the molecule to have a non-zero permanent electric dipole moment and the selection rules are ΔJ = 0, ±1 and ΔM = 0 or ±1, where J is the rotational angular momentum and M corresponds to the component of the rotational momentum along a given axis. For vibrational spectra, transitions are allowed within the harmonic oscillator model when the change in the vibrational quantum number is Δv = ±1 if, at the same time, the molecular dipole moment changes with the nuclear motion. When the Hamiltonian used for the system does not take spin into account, transitions between different spins are not allowed. It must be noted here that the distinction between allowed and forbidden transitions is strictly based on the assumptions made in the development of the model, but sometimes in experimental spectra allowed transitions are not appreciated due to very low intensities, while some forbidden transitions appear as low-intensity peaks. This happens usually if the transition takes place through a mechanism not involving the electrical dipole or due to the simplifications introduced in the quantum description of the system. Some examples are spin-orbit coupling, which allows the mixing of states of different multiplicity and explains phosphorescence, and vibronic coupling (the coupling between electronic and vibrational motions) or the mixture of ligand orbitals d of the metal, which explain the appearance of unexpected forbidden transitions in the electronic spectra in transition metal complexes [7, 8, 16, 17, 36].

1.10 Summary of Spectroscopic Techniques

The following summary and the associated classification of spectroscopic techniques are in no way comprehensive. Their purpose is just to provide a brief outlook of the wealth of methods available, highlighting the common principles behind very diverse experimental setups. The assignment of one

1.10

Summary of Spectroscopic Techniques

specific technique to one set or another is sometimes ambiguous, since two or more phenomena can be exploited at a time (scattering of emitted electrons, for example, or the side-by-side analysis of excitation and fluorescence spectra). 1.10.1 Absorption-Based Methods

A photon (sometimes two in two-photon spectroscopy) is destroyed while the absorbing medium (atom, molecule, or material) increases its energy by h𝜈. The most common experimental setup implies the measurement of the amount of radiation absorbed at different wavelengths, resulting in a spectrum where absorbance is plotted against frequency. Absorption of photons in different region of the electromagnetic spectrum leads to transitions between different levels of energy in atoms, molecules, or materials. As a result, radiation of different wavelengths can be used to obtain geometries, electronic structures, and so on, or as a probe for the presence of certain functional groups or atoms in a sample. Microwave spectroscopy uses microwave radiation to analyze transitions between molecular rotational energy levels, thus providing information on moments of inertia and, with the use of isotope substitutions, detailed and accurate molecular geometries [37–39]. Infrared radiation promotes transitions between vibrational energy levels, leading to spectra that allow for the identification of functional groups and which represent a very characteristic and sensitive fingerprint of a specific molecule [33–35, 40–43]. Irradiation of atoms and molecules with visible and near-UV light can lead to excitation of electronic states providing information on their electronic structure. Its most extended use is in quantitative analysis [32, 36]. The absorption of higher energy photons can result in the excitation of electrons to higher energy non-bound states in the continuum region and/or from deeper (core) orbitals. The study of the absorbance vs. frequency curves, and the dynamic behavior of the emitted electrons and their interactions with surrounding atoms (backscattering) provides information on the electronic energy levels of the substrate, its composition, and structure. This is the case of photoelectron spectroscopy, where an X-ray (XPS/electron spectroscopy for chemical analysis (ESCA)), far ultraviolet, or ultraviolet (UPS) photon excites a core or valence electron that is emitted (photoelectric effect) [44]. The kinetic energy of the emitted electron is then measured and used to infer information about the binding energy of electrons in the material. These techniques are very useful in the analysis of surfaces. X-ray absorption spectroscopy (XAS) is another example, which provides information on the energies of core electrons (it can be used to identify atoms) through analysis of the absorbance profile and on the environment of a certain atom through the features in the spectrum due to backscattering by neighboring atoms [25, 26].

19

20

1 Interaction of Radiation with Matter

Beyond the X-ray region, Mössbauer spectroscopy uses gamma rays to produce nuclear transitions. Changes in absorbance reflect with great accuracy information about the environment of the nuclei [45]. Finally, it must be recalled that some materials display different refractive indices for right and left circularly polarized light waves, resulting in a rotation of the plane of linearly polarized light when traversing a sample, a phenomenon called optical activity. In certain anisotropic media, the absorption coefficient can depend on the direction of polarization of the incoming radiation, resulting in preferential absorption of one polarization component. This phenomenon is named dichroism [46, 47]. More information on these two phenomena will be given in subsequent chapters of this book. 1.10.2 Emission-Based Methods

A photon is generated while the energy in the medium decreases by hν. For this to happen, the atom, molecule, or material needs to be in an excited state, emitting radiation in the decay to the ground state (or a less energetic state). The initial excitation can be achieved with irradiation, thermally, by collision with a beam of particles, and so on. As with the absorption spectroscopies, photons of different wavelengths can be involved in this process, depending on the kind of transitions being studied. One of the most common techniques in this family, used for both quantitative and qualitative analysis, is atomic emission spectroscopy, where electronic states of atoms are thermally excited and the wavelength and intensity of the UV–visible radiation emitted during relaxation to the ground state is used to identify and quantify them [11, 13, 48]. Fluorescence spectroscopies fall in this classification as well. In them, excitation of the material is produced by incoming electromagnetic radiation, and the radiation emitted has a very small delay and a lower frequency than the irradiating light. The most commonly used technique involves using the UV–visible frequency range to excite a molecule to a higher electronic state in an excited vibrational state. After excitation, the molecule undergoes vibrational relaxation and then emits a photon with an energy corresponding to that of the transition between the lowest vibrational level of the excited electronic state and the ground state. Phosphorescence is a similar phenomenon, where instead of just undergoing vibrational relaxation between the absorption and emission of a photon, the electron exerts intersystem crossing that traps it in an electronic state from which the radiation-emitting transitions to the ground state are forbidden and thus very slow [49–52]. Fluorescence spectroscopy is not restricted, however, to UV–visible light, and X-ray fluorescence spectroscopy is used for elemental analysis in materials. In this technique, atoms in a sample are bombarded by X-rays or gamma radiation, energetic enough to remove an electron from the core. The resulting ion is unstable

1.10

State 2

State 2

State 1

State 1

Absorption Absorbed photon

Emission Emitted photon

Photoelectron spectroscopy

State 3 =0

Phosphorescence

Fluorescence Radiationless transition

v

Summary of Spectroscopic Techniques

Electron v

v

Auger photoelectron spectroscopy

Figure 1.6 Schematic examples of the phenomena involved in some absorption and emission spectroscopies.

and the atom rearranges through a light-emitting transition that fills the hole with an electron from a higher orbital. Again, radiation does not need to be the only measurable output of a relaxation process. Auger electron spectroscopy (mainly used for surfaces and materials) excites a sample with radiation or an electron beam, ejecting an electron from a core orbital. Upon relaxation, an outer shell electron fills this hole and the energy liberated in this process is used to emit a second electron whose kinetic energy is measured by a detector [4, 8, 44] (Figure 1.6). 1.10.3 Scattering and Diffraction Methods

It has been established above that when electromagnetic radiation passes through an atomic or molecular sample it may be absorbed if the energy of the radiation corresponds to the energy separation of two stationary states of the atoms or molecules in the sample. If this is not the case, most of the radiation passes through the sample unaffected, but a small percentage of the light is scattered in all directions by the particles in the sample. Radiation scattering can be elastic or inelastic. If the wavelength of the scattered radiation is the same as the wavelength of the incoming beam, radiation is scattered elastically. This process, in a classical way, can be explained because the

21

22

1 Interaction of Radiation with Matter

oscillating electromagnetic field of the incoming radiation provokes that the electron cloud of the atoms or molecules in a sample vibrates at the same frequency of the incident radiation, and the system formed by the positive nuclei and the vibrating electron cloud constitutes an oscillating dipole that immediately radiates at the same frequency in random directions [27]. From a molecular point of view, scattering can be interpreted as a two-step process in which the incident photon collides with a molecule and excites it to a virtual state, which then relaxes back to its original state emitting a photon of the same energy as that of the incoming photon. It must be remarked that the two steps are simultaneous, and no stationary state exists in the interval between them. Therefore, scattering is a non-resonant process that should not be confused with fluorescence or phosphorescence, in which atoms or molecules absorb one photon and form an excited state (that lasts long enough to be characterized as a stationary state) and then decay by emitting a second photon [13, 16, 17]. Elastic scattering depends on the size of the particles that scatter radiation. Thus, if the incoming radiation wavelength is larger than the particle size of the matter with which it interacts, Rayleigh scattering is observed, and the intensity of the scattered light, I s , is proportional to the wavelength of the radiation according to I s ∝ 1/𝜆4 . This expression indicates that light of shorter wavelengths (blue) is more scattered by the particles in the atmosphere than light of longer wavelengths (red), so that Rayleigh scattering is one of the reasons for the blue color of the sky. When the wavelength of the incoming radiation is similar to the size of the particles, Mie scattering is observed. The intensity of Mie scattering depends only weakly on wavelength and becomes independent of it when the size of the particle exceeds that of the incoming wavelength radiation. For this reason, clouds in the sky, containing large droplets of water, scatter white light and do not present appreciable colors [13, 27]. If radiation scattering is inelastic, the frequency of the scattered radiation is different than that of the incoming beam. In this case, the incident radiation excites the atoms or molecules in the sample to a virtual state that takes part of the energy of the incoming light, and relaxation from this virtual excited state to a second state, higher or lower in energy than the initial state, results in a shift in frequency of the scattered light. Among the techniques based in inelastic scattering, Raman spectroscopy is one of the most popular. There are different applications of the Raman effect, but the most widely used makes visible or near-infrared light from a high intensity laser source pass through a sample, exciting molecular vibrational or rotational states. Most of the incoming radiation is scattered without a change in frequency (Rayleigh scattering) when the molecules relax to their initial state, but when some of the excited molecules relax to vibrational states higher or lower in energy than the initial state, Stokes or anti-Stokes Raman scattering is observed, respectively. Raman spectroscopy is widely used in the study of molecular vibrations, and provides complementary results to IR absorption spectroscopy, since some forbidden transitions in one case are allowed in the other and vice versa [33, 34, 40, 53–56].

References

Another extensively used group of techniques are those based on diffraction. The term diffraction refers to those phenomena that occur when a wave encounters an obstacle. According to Huygens, each point on a wave front can be considered as a source of secondary waves and the secondary waves that propagate beyond an obstacle may interfere and produce different diffraction patterns. Furthermore, since matter also has wavelike properties, small particles can also diffract [57–60]. For these reasons, X-rays and electrons or neutrons are especially suitable for the study of molecular structures, because their wavelengths roughly match the spacing between atoms in condensed phases, resulting in diffraction patterns that can be used to build a model of the electronic density of the studied material. X-ray diffraction is an essential tool in the structural elucidation of crystals, and can be also used to detect periodicity in complex materials. It is the structural characterization tool of choice for small molecules that can be crystallized, since it provides detailed information about the atomic positions, and is widely used in biochemistry to resolve the structure of proteins, DNA and RNA chains, or other biological structures such as viruses [61, 62]. Complementary tools can be electron diffraction (usually carried out in a transmission electron microscope), which provides information about both long-range and short-range order in solids, and neutron diffraction. The latter particles, in contrast with electrons or X-rays, scatter from nuclei, instead of interacting with the electron density, resulting in higher precision in the resolution of atomic positions and sensitivity to isotopes [63–65]. In the following chapters, the reader will acquire a deeper understanding of recent developments in spectroscopic techniques and their application to the structural elucidation of systems of chemical interest. For a more detailed discussion of the interaction of radiation with matter, the quantum mechanics needed for the calculation of the different energy levels and wave functions describing the states involved in the spectroscopic transitions, or specifics on any of the mentioned methods, the reader is referred to the texts cited in the references section.

References 1. Herzberg, G. (1945) Molecular Spec-

5. Struve, W.S. (1989) Fundamentals

tra and Molecular Structure, D. Van Nostrand, New York. 2. Barrow, G.M. (1962) Introduction to Molecular Spectroscopy, McGraw-Hill, New York. 3. Levine, I.N. (1975) Molecular Spectroscopy, John Wiley & Sons, Inc., New York. 4. Walker, S. and Straughan, B.P. (eds) (1976) Spectroscopy, Chapman & Hall, New York.

of Molecular Spectroscopy, WileyInterscience, New York. 6. Banwell, C.N. (1994) Fundamentals of Molecular Spectroscopy, 4th edn, McGraw-Hill, London. 7. Graybeal, J.D. (1998) Molecular Spectroscopy, 1st edn, McGraw-Hill, New York. 8. Hollas, J.M. (1998) High Resolution Spectroscopy, 2nd edn, John Wiley & Sons, Ltd, Chichester.

23

24

1 Interaction of Radiation with Matter 9. McHale, J.L. (1999) Molecular Spec-

10.

11.

12.

13.

14.

15.

16.

17.

18.

19. 20.

21.

22.

23.

24.

25.

troscopy, 1st edn, Prentice Hall, Upper Saddle River, NJ. Brown, J.M. (2003) Molecular Spectroscopy, Oxford University Press, Oxford. Bernath, P.F. (2005) Spectra of Atoms and Molecules, 2nd edn, Oxford University Press, New York. Chandra, S. (2009) Molecular Spectroscopy, Alpha Science International, Oxford. Svanberg, S. (2004) Atomic and Molecular Spectroscopy: Basic Aspects and Practical Applications, 4th edn, Springer, Berlin. Pavia, D.L., Lampman, G.M., Kriz, G.S., and Vyvyan, J.A. (2009) Introduction to Spectroscopy, 4th edn, Brooks-Cole, Belmont, CA. Hollas, J.M. (2010) Modern Spectroscopy, 4th edn, John Wiley & Sons, Ltd, Chichester. Berry, R.S., Rice, S.A., and Ross, J. (2000) Physical Chemistry, 2nd edn, Oxford University Press, Oxford. Atkins, P.W. (2011) Molecular Quantum Mechanics, 5th edn, Oxford University Press, Oxford. Engel, T. (2013) Quantum Chemistry and Spectroscopy, 3rd edn, Pearson, Boston, MA. Levine, I.N. (2013) Quantum Chemistry, 7th edn, Pearson, Boston, MA. Jensen, P. and Bunker, P.R. (eds) (2000) Computational Molecular Spectroscopy, John Wiley & Sons, Ltd, Chichester. Grunenberg, J. (ed.) (2010) Computational Spectroscopy: Methods, Experiments and Applications, WileyVCH Verlag GmbH, Weinheim. Hammes, G.G. (2005) Spectroscopy for the Biological Sciences, John Wiley & Sons, Ltd, Chichester. Laane, J. (ed.) (2009) Frontiers of Molecular Spectroscopy, 1st edn, Amsterdam, Elsevier. Domenicano, A. and Hargittai, I. (eds) (1992) Accurate Molecular Structures: Their Determination and Importance, Oxford University Press, New York. Leng, Y. (2008) Materials Characterization: Introduction to Microscopic and

26.

27. 28.

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

Spectroscopic Methods, John Wiley & Sons, Ltd, Chichester. Kuzmany, H. (2010) Solid-State Spectroscopy: An Introduction, 2nd edn, Springer, New York. Hecht, E. (2002) Optics, 4th edn, Addison-Wesley, San Francisco, CA. Harris, R.K. (1994) Nuclear Magnetic Resonance Spectroscopy: A Physicochemical View, Longman Scientific & Technical, Harlow Essex. Günther, H. (1995) NMR Spectroscopy: Basic Principles, Conceps and Applications in Chemistry, 2nd edn, John Wiley & Sons, Ltd, Chichester. Friebolin, H. (2011) Basic One- and Two-Dimensional NMR Spectroscopy, 5th edn, Wiley-VCH Verlag GmbH, Weinheim. Lund, A.S., Shiotani, M., and Shimada, S. (2011) Principles and Applications of Esr Spectroscopy, Springer, New York. Harris, D.C. and Bertolucci, M.C. (1989) Symmetry and Spectroscopy: An Introduction to Vibrational and Electronic Spectroscopy, Dover Publications, New York. Wilson, E.B. Jr., Decius, J.C., and Cross, P.C. (1980) Molecular Vibrations: The Theory of Infrared and Raman Vibrational Spectra, Dover Publications, New York. Schrader, B. (ed.) (1995) Infrared and Raman Spectroscopy: Methods and Applications, Wiley-VCH Verlag GmbH, Weinheim. Stuart, B.H. (2004) Infrared Spectroscopy: Fundamentals and Applications, John Wiley & Sons, Ltd, Chichester. Thomas, M.J.K. (1996) Ultraviolet and Visible Spectroscopy, 2nd edn, John Wiley & Sons, Ltd, Chichester. Carrington, A. (1974) Microwave Spectroscopy of Free Radicals, Academic Press, London. Townes, C.H. and Schawlow, A.L. (1975) Microwave Spectroscopy, 1st edn, Dover Publications, New York. Brown, J.M. and Carrington, A. (2003) Rotational Spectroscopy of Diatomic Molecules, Cambridge University Press, Cambridge. Colthup, N.B., Daly, L.H., and Wiberley, S.E. (1990) Introduction to Infrared an

References

41.

42.

43.

44.

45.

46.

47.

48.

49.

50.

51.

52.

53. 54.

Raman Spectroscopy, 3rd edn, Academic Press, Boston, MA. Diem, M. (1993) Introduction to Modern Vibrational Spectroscopy, John Wiley & Sons, Inc., New York. Duxbury, G. (2000) Infrared VibrationRotation Spectroscopy: From Free Radicals to the Infrared Sky, John Wiley & Sons, Ltd, Chichester. Günzler, H. and Gremlich, H.-U. (2002) IR Spectroscopy: An Introduction, WileyVCH Verlag GmbH, Weinheim. Hüfner, S. (1995) Photoelectron Spectroscopy: Principles and Applications, Springer-Verlag, Berlin. Herber, R.H. (ed.) (1984) Chemical Mössbauer Spectroscopy, Plenum Press, New York. Berova, N., Polavarapu, P.L., Nakanishi, K., and Woody, R.W. (eds) (2012) Comprehensive Chiroptical Spectroscopy, John Wiley & Sons, Inc., Hoboken, NJ. Kobayashi, N., Muranaka, A., and Mack, J. (2012) Circular Dichroism and Magnetic Circular Dichroism Spectroscopy for Organic Chemists, RSC Publishing, Cambridge. Robinson, J.W. (1990) Atomic Spectroscopy, Marcel Dekker, Inc., New York. Rendell, D. (1987) Fluorescence and Phosphorescence Spectroscopy, John Wiley & Sons, Ltd, Chichester. Sharma, A. and Schulman, S.G. (1999) Introduction to Fluorescence Spectroscopy, John Wiley & Sons, Inc, New York. Lakowicz, J.R. (2006) Principles of Fluorescence Spectroscopy, 3rd edn, Springer, New York. Albani, J.R. (2007) Principles and Applications of Fluorescence Spectroscopy, Blackwell Science, Oxford. Long, D.A. (1977) Raman Spectroscopy, McGraw-Hill, New York. Ferraro, J.R. and Nakamoto, K. (2003) Introductory Raman Spectroscopy, 2nd edn, Academic Press, Amsterdam.

55. Le Ru, E.C. and Etchegoin, P.G.

56.

57.

58. 59.

60.

61.

62.

63.

64.

65.

(2009) Principles of Surface-Enhanced Raman Spectroscopy and Related Plasmonic Effects, 1st edn, Elsevier, Amsterdam. Schlucker, S. (ed.) (2011) Surface Enhanced Raman Spectroscopy: Analytical, Biophysical and Life Science Applications, Wiley-VCH Verlag GmbH, Weinheim. Cullity, B.D. (1978) Elements of X-Ray Diffraction, 2nd edn, Addison-Wesley, Reading, MA. Warren, B.E. (1990) X-Ray Diffraction, Dover Publications, New York. De Graef, M. and McHenry, M.E. (2007) Structure of Materials: An Introduction to Crystallography, Diffraction and Symmetry, Cambridge University Press, Cambridge. Hammond, C. (2009) The Basics of Crystallography and Diffraction, 3rd edn, Oxford University Press, Oxford. David, W.I.F., Shankland, K., McCusker, L.B., and Baerlocher, C. (eds) (2002) Structure Determination from Powder Diffraction Data, Oxford University Press, Oxford. Pecharsky, V.K. and Zavalij, P.Y. (2009) Fundamentals of Powder Diffraction and Structural Characterization of Materials, 2nd edn, Springer, New York. Eberhart, J.-P. (1991) Structural and Chemical Analysis of Materials: X-Ray, Electron and Neutron Diffraction, X-Ray, Electron and Ion Spectrometry, Electron Microscopy, John Wiley & Sons, Ltd, Chichester. Cowley, J.M. (ed.) (1992) Electron Diffraction Techniques, Oxford University Press, Oxford. Champness, P.E. (2001) Electron Diffraction in the Transmission Electron Microscope, Bios Scientific Publishers Ltd, Oxford.

25

27

2 Computational Spectroscopy Tools for Molecular Structure Analysis Cristina Puzzarini and Malgorzata Biczysko

2.1 Introduction

Proper determination of the molecular structure of synthetic or natural compounds has been a very challenging task over the years, and in many cases several hypothesis existed for a long time, till unequivocal answers have been given with the aid of spectroscopic methods [1]. Nowadays, computational methodologies greatly facilitate prediction of molecular structures along with their spectroscopic signatures, which in turn can be compared to the available experimental data (see, e.g., Refs [2–4]). The standard computational outcomes are molecular structures, relative energetics of isomers and/or conformers, description of reaction paths, harmonic frequencies and infrared (IR) intensities, as well as vertical excitation energies, and so on. These features along with the available range of computational methodologies and techniques, from molecular mechanics (MM) to semi-empirical approaches toward fully quantum mechanical (QM) models, in the gas phase and more complex environments, are well described in several volumes; to give some examples, we mention Refs [5–9]. In this chapter, we focus on the recent advances in computational spectroscopy, whose predictive and interpretative capabilities have largely extended in the last decade (see, e.g., Refs [3, 4, 10–12]). The detection, recording, and interpretation of experimental spectra can nowadays be significantly facilitated by theoretical predictions. The high accuracy that can be reached has been clearly demonstrated, for example, in Refs [3, 4, 12–14] and, whenever the most advanced theoretical models are involved, any disagreement between computational and experimental findings casts serious doubts on the reliability of the latter (see, for instance, Refs [4, 15, 16] and references therein). For large systems, computational chemistry has not yet reached the accuracy available for small- to medium-sized molecules, the difficulties being mostly related to the system size, that is, to the dimensionality of the potential energy surface (PES) (which depends on the number of atoms) and to the computational cost of single-point energy calculations (which depends on the number of electrons in the system). Further complications arise from the fact that in real life, molecules are constantly under movement; thus, molecular Structure Elucidation in Organic Chemistry: The Search for the Right Tools, First Edition. Edited by María-Magdalena Cid and Jorge Bravo. © 2015 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2015 by Wiley-VCH Verlag GmbH & Co. KGaA.

28

2 Computational Spectroscopy Tools for Molecular Structure Analysis

dynamics (MD) needs to be accounted for as well. Since all systems are usually exposed to sunlight, photochemistry might also play a crucial role in many physicochemical processes. Even more involved is the case of weakly bounded systems, as they show high flexibility and their structures and dynamics depend on a delicate balance between inter- and intramolecular interactions (hydrogen bond, stacking or long range dispersion/van der Waals forces), which play a relevant role in many processes such as folding of biomolecules, supramolecular assembly, and molecular recognition. Despite these difficulties, large systems and complex spectroscopic features are nowadays successfully studied by means of accurate computational spectroscopic methods thanks to increased computational power and advances in theoretical models. In this chapter, we draw attention to approaches aiming at the direct comparison of experimental and theoretical spectroscopic data. It can be foreseen that the development and validation of versatile and user-friendly computational approaches will allow routine and reliable simulations of the spectroscopic signals [17] for relatively large and complex molecular systems under realistic conditions, thus greatly facilitating the understanding of experimental results. Among structural determinations, those of large and flexible systems turn out to be the most challenging and interesting at the same time. Conformational/tautomeric properties of isolated large molecules, such as biomolecules or weakly bonded molecular adducts, can be obtained by means of different spectroscopic techniques. To cite recent developments and applications, we can mention (i) double resonance (IR-UV, UV-UV) spectroscopies in the gas phase [18, 19], (ii) resonance enhanced multiphoton ionization (REMPI) spectroscopy combined with high-resolution laser-induced fluorescence (HR-LIF) of systems isolated in molecular beams [20, 21], (iii) IR laser helium nanodroplet isolation (HENDI) spectroscopies [22, 23], (iv) chiroptical spectroscopies ranging from the most widely used circular dichroism (CD) methods (electronic and vibrational) to frontier areas such as nonlinear spectroscopy and photoelectron CD [24, 25], and (v) laser ablation technique combined with chirped Fourier transform microwave spectroscopy (see, e.g., Ref. [26] and references therein). The latter was particularly successful in unraveling the conformational/tautomeric equilibria of amino acids, nucleobases, neurotrasmitters, sugars, and drugs (for significant examples, see Refs [27, 28] and references therein). To give another example of relevance in the present context, helium nanodroplet spectroscopies combine advances of molecular beam and matrix isolation spectroscopy into a method that allows mimicking the gas-phase conditions also for unstable molecular systems, and it may be seen as a nanocryostat for growing novel species, including biomolecules, free radicals, ions, and weakly bounded complexes [22, 23]. Such spectroscopic investigations that rely on indirect interpretation need quantum-chemical computations for supporting the analysis, verifying the results, and/or providing the final answer among different hypotheses. The interplay of experimental and computational techniques is becoming more and more a reliable route to retrieve structural information from spectral analysis.

2.2

Potential Energy Surface and Molecular Structure

The aim of the present chapter is to provide an overview of computational spectroscopic tools that allow for retrieving information on molecular structure from experimental outcomes. Different spectroscopic techniques, spanning from rotational to vibrational and electronic toward magnetic resonance spectroscopies, are considered. By means of some case studies, the capabilities of computational spectroscopy in this field will be demonstrated. 2.2 Potential Energy Surface and Molecular Structure

Under typical physical conditions, the electrons adjust quickly to any movement of the nuclei, and we can thus consider that electronic relaxation with respect to nuclear motion is instantaneous. This leads to the so-called Born–Oppenheimer approximation: these two motions can be decoupled, and the Schrödinger equation splits into two equations, the electronic and nuclear ones. Solution of the electronic Schrödinger equation provides the electronic energy at the geometry considered. The electronic energy as a function of the nuclear coordinates defines the so-called PES: in the Born–Oppenheimer picture, the nuclei move on a PES. The definition of the PES is thus an important implication of the Born–Oppenheimer approximation. The latter has another profound consequence: without the Born–Oppenheimer approximation the concepts of equilibrium and transition state geometries, of stationary points in general, would no longer exist, since these are defined as critical points on the PES. The PES is a hypersurface defined by the electronic energy of the system under consideration over all possible atomic arrangements: if N is the number of atoms, the PES has 3N – 6 internal coordinate dimensions. The complete PES for a polyatomic molecule cannot be visualized, since it involves too many dimensions. Typically, slices of the PES, with the energy as a function of only a single coordinate (e.g., a bond length) or two coordinates, are considered. An example is provided by Figure 2.1, which shows a slice of the full-dimensional PES for dihydrazine [29]. This depicts the three minima (the global one: trans-N2 H2 and two local ones cis-, and iso-N2 H2 ) along with the transition states between them. 2.2.1 Minima and Conformational Analysis

“Geometry optimization” is the general term for denoting the search of stationary points on the PES, that is, of those points for which the first derivative of electronic energy with respect to nuclear coordinates1) is zero. Usually, the desired stationary points are minima, that is, those points for which the Hessian (the matrix of the second derivatives of electronic energy) contains only positive terms. In most cases, of interest is the lowest in energy minimum, that is, the global minimum; in 1) For brevity, in the following, the derivatives of electronic energy with respect to nuclear coordinates are shortly referred to as derivatives of electronic energy.

29

2 Computational Spectroscopy Tools for Molecular Structure Analysis

6 Energy/Eh

cis

0 −0.05 −0.1 −0.15 −0.2 −0.25 −0.3 −0.35 −0.4 −0.45 −0.5

4 MIN 2 Y/a.u.

30

0 TS

−2

iso

MIN TS

−4

−6

MIN

trans −6

−4

−2

0 X/a.u.

2

4

6

Figure 2.1 PES of N2 H2 . Contour plot for a hydrogen atom moving coplanarly around a partially relaxed N2 H fragment, along with the structures of trans-, cis-, iso-N2 H2 local minima and transition states between them.

other cases, it is important to sample a large, representative set of local minima. The former is the case of a rigid or semi-rigid molecule, while the latter is the case of a flexible molecule, having large amplitude motions. Among possible conformational changes, that associated with rotation about a single bond is the simplest. In some cases (e.g., in the case that a reaction path is under investigation), one might also be interested in locating first-order saddle points, that is, those stationary points for which the second derivative of electronic energy is negative in one direction and positive in all others. More rarely, high-order saddle points are of interest. In the literature, implemented in various quantum-chemical packages, different optimization algorithms are available. Most of them are efficient only for local minima search, that is, for locating the nearest minima. More complicated is the location and characterization of all minima on the PES. In particular, it is clear that if the degrees of freedom exceed 15–20, a systematic search becomes impossible. Even if energy arguments can be used to restrict the number of possible conformations to be considered, finding “reasonable” minima for large biomolecular systems is still a challenging task. One way of attempting this is by “building up” the structure, that is, smaller fragments of the whole structure are subjected to minima search and, by combining such pre-optimized fragments, the sampling of the PES is carried out. For even larger systems, there are methods that can be used for perturbing a geometry from one local minimum to another. Examples of methods commonly used for conformational sampling are stochastic and Monte

2.2

Potential Energy Surface and Molecular Structure

Carlo methods, MD, genetic algorithms, diffusion methods, and molecular docking. As in the present chapter we restrict our discussion to systems ranging from medium-sized molecules to small biomolecules, we do not go further in detail and refer interested readers to specialistic literature (a basic overview can be, for instance, found in Refs [7, 8] while, examples of recent advances can be found in Refs [30–33]). One important implication of conformational analysis is related to thermochemistry. Theoretical methods and computational technology available have produced several approaches that can reliably predict thermochemical properties to an accuracy that exceeds the so-called “chemical accuracy,” 1 kcal mol−1 (see, e.g., Refs [34, 35] and references therein). 2.2.2 Spectroscopic Tools for Structure Determination

Each electronic state of a molecule has a separate PES, and transitions between these surfaces yield the electronic spectrum. Properties of molecules such as dipole moment, polarizability, NMR (nuclear magnetic resonance) shielding, and so on, depend on the response of the energy to applied electric and magnetic fields, and their values as a function of the nuclear coordinates define the so-called property surfaces (PS). Both PES and PS are strongly correlated to spectroscopic properties, the latter thus representing a powerful tool for the characterization of molecular systems [12, 36–38]. However, in most cases the interpretation of experimental spectra is difficult due to the inherent complexity caused by thermal or environmental effects and/or to intrinsic properties of the system itself. In this context, computational spectroscopy turns out to be a valuable tool to help unravel the various contributions to spectroscopic features, thus allowing a better understanding of the underlying phenomena [3, 10–12, 36, 39, 40]. In addition to problems related to a reliable description of the molecular system, a direct comparison with experimental outcomes requires computational tools able to explicitly simulate spectroscopic features [3, 17, 41–44]. One of the biggest advantages of molecular spectroscopy (within the plethora of types and techniques available) is that it is able to probe the static and dynamic properties in a noninvasive manner. As a consequence, spectroscopic techniques have found practical applications essentially in all scientific fields, ranging from astrophysics to drug design and biomedical studies, from cultural heritage to characterization of materials and technological processes. The focus here is on their capability to gain information on molecular structure, which is related to the fact that for all spectroscopies there is a strong relationship between the experimental outcome and the electronic structure of the system. Unfortunately, from such knowledge it is seldom straightforward to derive molecular structure information, and it is in this frame that computational techniques play a key role [2, 3]. Moreover, since computational approaches allow for predicting the spectroscopic properties for a large set of molecular structures, they can help in making a selection among similar candidates to be synthesized, thus leading to in silico design of molecules with the desired/optimal spectral features [45].

31

32

2 Computational Spectroscopy Tools for Molecular Structure Analysis

2.3 Computational Aspects for Spectroscopic Techniques

In the following, a short overview of the spectroscopic techniques and of the corresponding computational aspects is given. Before proceeding with such an overview, we briefly introduce the density functional theory (DFT) and hybrid approaches as they are the methods of choice for investigating medium-to-large molecular systems at the required accuracy. 2.3.1 DFT and Hybrid Approaches for Spectroscopic Applications

Models rooted in DFT can be successfully applied to fairly large molecular systems, well beyond the capabilities of more sophisticated ab initio methods. DFT and its time-dependent density functional theory (TD-DFT) extension [46, 47] have proved to be very successful for the prediction of ground and excited-state equilibrium structures, of a broad range of linear and nonlinear spectral responses, and of magnetic (NMR and EPR) parameters (see the recent review provided in Ref. [3] and references therein). However, the quality of the results strongly depends on a careful choice of the DFT functional and on sufficiently flexible basis sets [48–50]. Nevertheless, as extension to even larger systems requires the use of relatively small sets, purposely tailored basis sets have been set up in order to adequately describe, for instance, spectroscopic properties. These permit to reach an accuracy similar to that obtainable with much larger basis sets (e.g., aug-cc-pVTZ) even for difficult properties such as Raman intensities [51] or rotatory strengths [52] (an example is provided by the recently introduced “spectroscopic” aug-N07D (SNSD) basis set [17, 53, 54]). This refers not only to the electric and/or magnetic properties but also to a description of nuclear motion. An accurate prediction of vibrational frequencies is a mandatory prerequisite for quantitative comparisons with experiment not only in the field of vibrational spectroscopy but also in all cases where vibrational properties are used for deriving vibrational corrections, as, for example, in the evaluation of thermodynamic properties. To give an example, when discriminating among different possible conformers, energy differences play an important role and the correct energy order might be obtained only when zero-point vibrational energy (ZPVE) corrections are included. The recent investigation of the proteinogenic glutamic acid [55] provides an illustrative case, clearly showing that large energy differences can be reduced significantly by accounting for ZPVE corrections and that the stability order might even change if free energy is considered. In this respect, standard hybrid-DFT functionals provide satisfactory results when coupled to basis sets of at least polarized double-zeta quality, supplemented by diffuse functions. The performances of several DFT models for computation of spectroscopic properties have been investigated and compared in Refs [17, 56–58]. In the quest for a computational approach capable of reproducing different spectroscopic properties with consistent accuracy, the DFT/N07D(SNSD)

2.3

Computational Aspects for Spectroscopic Techniques

model [54] has recently been introduced and, when density functionals such as B3LYP [59], CAM-B3LYP [60], and PBE0 [61] are considered, it provides results of remarkable quality for a broad range of spectroscopic parameters (ESR (electronic spin resonance), IR, UV–vis, ECD (electronic circular dichroism)) [16, 52, 62] at a relatively low computational cost. Further improvements can be obtained by means of the double-hybrid B2PLYP [57, 63] functional (see Refs [57, 64–66] for detailed accounts on different properties), but at a significantly increased computational cost due to the inclusion of second-order perturbation treatment of electron correlation [57]. Another route to obtain accurate results, even for relatively large molecular systems (few dozens of atoms), is provided by hybrid QM models [67], which combine cheap electronic structure approaches (especially DFT models) with a posteriori refinement of selected properties at higher level of theory (for a set of representative examples, the reader is referred to Refs [17, 68–71]). The effectiveness of these approaches has already been demonstrated for anharmonic frequencies [72–74], electronic spectra [69, 75], and magnetic resonance properties [16, 62]. Recently, highly accurate computations have become accessible for significantly larger systems including important biological “building blocks,” such as DNA bases and their precursors [69, 76, 77], thus allowing subsequent detailed analyses of several perturbing effects (e.g., hydrogen bonding, environmental effects, etc.). For larger systems (hundreds of atoms) a feasible route to compute spectroscopic properties is provided by integrated QM/MM [40, 78–82] schemes or tailored/effective QM approaches [83–85]. 2.3.2 Rotational Spectroscopy

The information required for predicting and/or analyzing rotational spectra are accurate estimates of the following: 1) Rotational parameters. They include rotational as well as centrifugal distortion constants. The former are inversely proportional to the moments of inertia, which in turn are related to the molecular structure. The corresponding rotational constants are thus those at the equilibrium. The vibrational ground-state rotational constants can be subsequently obtained by adding the corresponding vibrational corrections, which require anharmonic force field calculations. With regard to centrifugal distortion, this effect arises from the fact that bond distances and angles vary because of the centrifugal force produced by rotation. The corresponding constants require force field calculations [86]. 2) Dipole moment. The dipole moment components (along the inertial axes) can be determined by computing first derivatives of the energy with respect to an applied external electric field. This information is required for predicting the intensity and the type of spectra.

33

34

2 Computational Spectroscopy Tools for Molecular Structure Analysis

3) Hyperfine parameters. Among the various hyperfine parameters, we mention the coupling between the quadrupole moment of a nucleus and the electricfield gradient at the nucleus itself. The corresponding parameters are denoted as nuclear quadrupole-coupling constants (NQCC) and require electric-field gradient computations. As the determination of centrifugal-distortion constants as well as of hyperfine parameters other than NQCCs are of limited interest to the topic of this chapter, we refer interested readers to Ref. [4], while in the following we address rotational and quadrupole-coupling constants in more detail in view of their relation to molecular structure. Nuclear quadrupole-coupling constants will also be addressed in view of their use in elucidating conformational analysis. As rotational spectroscopy is by definition a high-resolution spectroscopy, quantum-chemical calculations of the corresponding parameters need to be very accurate. To fulfil such requirement, the key point is the employment of coupled-cluster (CC) techniques. As is well known, the CC singles and doubles approximation augmented by a perturbative treatment of triple excitations (CCSD(T)) [87] provides a very good compromise between accuracy and computational cost. Since accurate equilibrium rotational constants imply accurate equilibrium structures, in the electronic structure calculations it is necessary to account simultaneously for the principal error sources, that is, basis-set truncation effects as well as higher excitations, and for core-correlation effects. In this respect, the equilibrium geometry can be obtained by making use of composite schemes, where the various contributions are evaluated separately at the highest possible level and then combined in order to derive the best theoretical estimate [88–92]. Ground-state rotational constants, which are the quantity experimentally determinable, are then estimated by adding to the equilibrium rotational constants (straightforwardly obtained from the equilibrium structure [4, 93]) the corresponding vibrational corrections (the reader is referred to Refs [4, 93] for the computational and theoretical background). The most effective way to obtain these quantities is provided by second-order vibrational perturbation theory (VPT2) [94, 95] applied to cubic force field [95–97]. The computational determination of nuclear quadrupole couplings necessitates the evaluation of the electric-field gradient tensors at the corresponding nuclei. These are first-order properties and, thus, can be easily computed either as expectation value of the corresponding (one-electron) operator or as first derivative of the energy with respect to the nuclear quadrupole moment. 2.3.3 Vibrational Spectroscopy: Infrared (IR), Vibrational Circular Dichroism (VCD), Raman

The information required for predicting and/or analyzing spectra in the field of vibrational spectroscopy are vibrational frequencies and the corresponding intensities. While the former are univocally defined, the definition of the latter depends on the technique considered (IR, vibrational circular dichroism (VCD),

2.3

Computational Aspects for Spectroscopic Techniques

and Raman). As a deep analysis of the theoretical background of the various spectroscopies is outside the scope of the present chapter, we refer interested readers to well-established textbooks [98, 99] or recent reviews [12, 43, 44, 56]. We restrict ourselves to mentioning that from a computational point of view, in order to fulfil the accuracy (for frequencies) and interpretability (for intensities) requirements, it is mandatory to go beyond the so-called double-harmonic approximation and thus to account for both mechanical and electrical anharmonic effects. Anharmonic vibrational frequencies can be computed within perturbative or variational models (see Refs [13, 56, 100, 101] for recent reviews). A particularly effective approach is obtained when VPT2 [94], based on a normal mode representation, is combined with a polynomial approximation (to the fourth order) of the PES. The latter representation leads to the definition of force field, where the coefficients are the so-called force constants [5, 7]. These can be obtained in an automatic (black-box) manner for several computational methods thanks to the implementations available in various commercial quantum-chemistry packages [95, 97, 102–104]. Concerning the transition intensities, we note that anharmonic effects are mandatory in order to simulate spectra that can be directly compared with experiment, as the harmonic approximation yields null intensity for overtones and combination bands. In this respect, within the VPT2 approach, several expressions to compute IR intensities have been proposed [105–107]. Moreover, a fully automated implementation that allows for simulating several types of vibrational spectra, from IR to Raman and VCD (see Refs [17, 108] for detailed discussion), has recently been included into a generalized second-order vibrational perturbation (GVPT2) approach [95] available within the Gaussian [109] package. As mentioned above, proper inclusion of vibrational effects, via ZPVE corrections, is important whenever relative energies of conformers are investigated, as these are required to predict the spectra of complex molecular mixtures. In principle, there are several possibilities to evaluate the conformers’ distribution from spectroscopic data and simulate the spectra under experimental conditions (e.g., temperature effects). A first option is to simulate fully ab initio spectra, with the contribution of each conformer estimated from the Boltzmann population, which in turn is based on free energy computations (see, e.g., Ref. [74] for definition and application of elaborated theoretical models). Alternatively, the abundances can be estimated from the analysis of some relevant features of the experimental spectra and then used to simulate the overall band shapes [110]. It is also possible to estimate the relative abundance by fitting the theoretical spectrum to the experimental counterpart, with the contributions of each conformer as variables. Since the computational burden for simulating anharmonic spectra is mostly related to the underlying electronic structure calculations required for describing the PES and PS, cost-effective approaches rely on anharmonic force fields computed at the DFT level. In particular, the standard B3LYP functional [59] combined with the N07D basis set [53, 54] or its modified version aug-N07D (SNSD) [17, 53] provides an excellent compromise between reliability and computational effort [17, 57, 72], even for large systems (over 100 atoms) through reduced-dimensionality VPT2 schemes [111, 112]. To further improve the

35

36

2 Computational Spectroscopy Tools for Molecular Structure Analysis

accuracy, hybrid CCSD(T)/DFT approaches (shortly denoted CC/DFT) can be used, assuming that the differences between anharmonic frequencies calculated at the CCSD(T) and DFT levels are limited to the harmonic terms. In this respect, the hybrid CC/DFT scheme has already been validated for several closed- and open-shell systems [71, 73, 113] and provides a viable route to extend predictions of accurate anharmonic frequencies to relatively large systems [77, 114]. The CC/B3LYP approach can be actually applied to molecules with up to 10–15 atoms, while for larger systems an alternative model is provided by double-hybrid (especially B2PLYP [57, 64]) functionals in conjunction with medium-sized basis sets. In particular, it has been demonstrated that the B2PLYP/B3LYP approach allows the extension of hybrid models to systems of biological and/or technological interest [57]. 2.3.4 Electronic Spectroscopy: One-Photon Absorption (OPA) and Electronic Circular Dichroism (ECD)

Electronic spectra involve transitions between vibrational energy levels of two different electronic states, the upper state being neutral or ionic, and deriving from valence or core electron excitation. Therefore, even the apparently structureless band-shape of broad electronic transitions observed in UV–vis absorption or emission spectra hides a complex set of vibronic transitions, which can be unraveled by coupling the electronic excitation with vibrational effects. However, the most popular approaches to simulate electronic spectra (UV–vis, CD, photoelectron, X-ray, etc.) still rely on computation of vertical excitation energies, which are further convoluted to simulate the broad band observed in the experimental lineshape. Such a treatment completely neglects the influence of nuclear motions, despite the well-recognized fact that a proper account of vibrational effects is often mandatory in order to interpret correctly the experimental findings [3]. Electronic spectral lineshapes, based on the underlying vibrational pattern, can be simulated by assuming that the electronic transition takes place in such a short time that the position of the nuclei remains almost unchanged. This leads to the so-called Franck–Condon (FC) approximation [115, 116], which assumes that the transition dipole moment can be considered to be invariant during the transition. Then, the vibrational pattern of electronic spectra can be obtained from the computation of the overlap integrals, also known as FC integrals, between the vibrational wavefunctions of the electronic states involved in the transition (see Ref. [117] and references therein). Here, we mainly refer to the integrated procedure within the Born–Oppenheimer and harmonic approximations (along with Eckart conditions), which is described in detail in Refs [52, 118]. This approach can be applied to both absorption and emission spectra, and to transitions between any initial and final states. However, in the following we focus on the transitions between the ground (initial) and excited (final) electronic states. In this frame, the theoretical models are defined according to the description of the PES for the electronic states involved and the approximation used for the

2.3

Computational Aspects for Spectroscopic Techniques

evaluation of the transition dipole moment. The choice for the description of the PESs involved leads to the definition of vertical and adiabatic models. Within vertical models (like the vertical gradient (VG) model), the focus is on the knowledge of the final state PES at the equilibrium geometry of the initial state, that is, on the region corresponding to the most intense transitions, while the PES around equilibrium of the final state is extrapolated. Within adiabatic models (like the adiabatic Hessian (AH) model), the focus is on the equilibrium structure of the final state, and the spectral features close to the 0–0 transition, that is, the transition between the vibrational ground states of two electronic states. In practice, the methods also differ for the type and cost of electronic structure computations required to describe the PES of the final (excited) state, while the ground state PES is computed in the same way in all cases. In fact, for AH models the computation of the equilibrium structure and harmonic frequencies for both the ground and excited electronic states is needed, while for the VG models the computation of the excited state energy gradients at the ground state equilibrium structure (much less computationally demanding) is sufficient (see Refs [52, 117] for detailed discussion). It should be noted that for semi-rigid semi-harmonic systems both approaches provide similar results, while anharmonic effects lead to enhanced differences between them (see for instance Ref. [119] and references therein). As a general remark, we only mention that vertical approaches are more sensitive to the PES anharmonicity. However, in all cases when the harmonic approximation is reliable, vertical models allow relatively inexpensive computations of electronic spectra lineshape for medium-to-large systems. Furthermore, bulk and specific environmental effects as well as the consideration of a large energy region encompassing several electronic states can be rather easily accounted for [17, 52, 117]. A suitable example is represented by chlorophyll-a, for which FC|VG computations considering eight excited electronic states, polarizable continuum description of the methanol solution, and Mg-coordination by explicit CH3 OH molecules lead to an excellent agreement with the experimental electronic spectrum in the entire UV–vis range [17]. Two further issues that should be addressed in choosing the computational models and level of approximations are related to the description of normal modes and electronic transition dipole moments. As a general rule, normal modes in the two electronic states are different; to account for the mode mixing, a common procedure is to use a linear transformation proposed by Duschinsky [120]. Concerning the second issue, it is noted that there is no general analytic expression of the transition dipole moments in terms of nuclear coordinates. As already mentioned above, the FC approximation [115, 116] simply assumes invariant transition dipole moments. While this model is accurate enough in most cases, and in particular for fully allowed transitions, it is not suited for weakly allowed or dipole-forbidden transitions. In such cases, it can be corrected by inclusion of a linear variation of the electric dipole moment with respect to normal coordinates, as done by Herzberg and Teller (HT) [121]. The HT effects might become very important for ECD spectra (see the example given in Section 2.4.2.3) due to the fact that the transition intensity is related to the dot product of two different transition dipole moments (electric and magnetic). Therefore, their relative

37

38

2 Computational Spectroscopy Tools for Molecular Structure Analysis

orientation is an additional factor to be taken into account, which might lead to unexpected results. For example, even if the transition is strongly allowed, the overall intensity is almost negligible whenever the electric and magnetic moments are nearly orthogonal. The general procedure described above relies on the harmonic approximation; however, anharmonic effects on excited electronic state frequencies can be taken into account by applying mode-specific anharmonic corrections [75]. These are based on the Duschinsky matrix and anharmonic corrections for the ground electronic state, computed by suitable models as described in Section 2.3.3. Finally, it is noted that the issue of the infinite number of vibronic transitions has been overcome by the development of pre-screening black-box procedures [109, 122] and time-dependent path-integral models [123]. The latter are characterized by an automatic inclusion of all vibrational states, while the former procedures allow for identifying and assigning single vibronic transitions; both approaches can be effectively combined in order to take into account their respective advantages [17]. 2.3.5 Magnetic Resonance Spectroscopy: Electronic Spin Resonance (ESR)

Spin relaxation techniques, such as NMR and ESR spectroscopies, represent powerful and sensitive tools for studying structural and dynamic properties of macromolecular systems.2) In particular, ESR is extensively applied to investigate complex biological systems, either directly or with the help of site-directed labeling techniques. To give an example, nitroxides are among the most widely used spin probes to study different classes of organic free radicals because of their remarkable stability and of strong localization of the unpaired electron on the NO moiety [124]. However, the interpretation of ESR spectra is not a trivial task and QM computations of the magnetic parameters involved are needed to support the analysis of experimental results. In the following, we briefly summarize the theoretical aspects of ESR spectroscopy (a deeper discussion can be found, for instance, in Refs [125, 126]). The interaction of the electron spin (S) of a radical containing a nucleus of spin I with an external magnetic field (𝐁) can be approximated by the spin Hamiltonian Ĥ s : Ĥ s = 𝝁B S ⋅ 𝐠 ⋅ 𝐁 + S ⋅ 𝐀 ⋅ I + · · ·

(2.1)

where the first term is the Zeeman interaction between the electron spin and the external magnetic field in terms of the Bohr magneton, μB , and the electronic gtensor. The second term is the hyperfine interaction between S and I, described through the hyperfine coupling tensor 𝐀, which in turn can be split into two terms: (K) 𝐀 = aK 𝟏 + 𝐀𝑑𝑖𝑝

(2.2)

2) We limit our discussion to ESR spectroscopy, since the corresponding nuclear spin counterpart, NMR spectroscopy, is widely addressed in this book. On the contrary, only this chapter deals with ESR. For this reason, we also provide the reader with a more detailed overview of the theoretical background than that given for the other spectroscopies.

2.3

Computational Aspects for Spectroscopic Techniques

where the first contribution is the isotropic hyperfine coupling constant (HFCC), while the second term is the anisotropic hyperfine coupling tensor. The former is the so-called Fermi contact term, which is related to the spin density at the Kth nucleus under consideration, while the anisotropic contribution, also denoted as dipolar hyperfine coupling term, can be derived from the classical expression of interacting dipoles. The essential quantities to be calculated are therefore the spin density at the Kth nucleus and the dipole–dipole coupling terms, respectively, and the isotropic and anisotropic hyperfine contributions are then evaluated as expectation values of the corresponding one-electron operators. From a computational point of view, HFCCs are among the most challenging parameters to be accurately computed by quantum-chemical calculations. The main reasons are two: first, conventional Gaussian basis sets are not well suited for describing nuclear cusps; second, the overall parameters result from differences between large quantities of opposite sign [127]. However, for medium-to-large systems, remarkable results for both isotropic and dipolar terms can be obtained at the DFT level by coupling hybrid functionals with purposely tailored basis sets [62]. For example, the B3LYP [59] functional in conjunction with either the EPR-III [128] or N07D(SNSD) [53, 54] basis sets provide reliable results, as demonstrated in Refs [129, 130]. The choice of the basis set is a delicate issue in view of obtaining quantitative predictions of the isotropic HFCCs. In fact, to correctly describe the spin density at a nucleus, very tight s primitives on the nucleus of interest are needed, together with diffuse functions on surrounding atoms [131]. If the interest is in the ESR spectroscopic investigation of large biological systems, the strategy to be adopted relies on integrated QM/MM schemes, where the molecular region surrounding the radical center is described at a high level of theory in conjunction with a large basis set, while MM is employed to describe the remaining part of the system. These QM/MM schemes are, for instance, well suited for the study of ESR properties of radicals embedded in complex and non-standard media such as proteins, micelles, or cellular membranes. When aiming at high accuracy and the size of the molecule (or molecular fragment) allows, computation of the magnetic parameters should be performed at the CC level of theory. In this context, we refer interested readers to the benchmark study carried out in Ref. [132]. Another important issue is that in most cases it is crucial to take into account the effects of nuclear motion. In particular, the ESR parameters often show a strong dependence on the molecular geometry, and vibrational effects can change their values by even more than 25% [127]. This has been, for example, demonstrated in Refs [113, 133], where halogenated nitroxides have been investigated. For semi-rigid molecules, vibrational effects can be suitably treated by means of perturbation theory. Another option for accounting for nuclear motion effects, which is suitable for large systems, relies on MD simulations [40, 130].

39

40

2 Computational Spectroscopy Tools for Molecular Structure Analysis

2.4 Application and Case Studies

In this section, a few selected case studies are presented in order to demonstrate the capabilities of joint computational–experimental spectroscopic techniques in elucidating the molecular structure analysis. 2.4.1 Semi-Experimental Equilibrium Structure

While rotational spectroscopy is the method of choice for obtaining highly accurate structural information, it is still a formidable task to extract the desired information from the experimental data. The first problem is that as many rotational constants as the number of independent structural parameters are needed. To increase the number of rotational constants, the investigation of more than one isotopologue (of the molecule considered) is required. A second issue is that the derivation of an equilibrium structure requires explicit consideration of vibrational effects. As a consequence, a pure experimental approach would require knowledge of vibrational corrections to rotational constants for all isotopic species considered. A way out of this problem is the use of quantum chemical methods to compute them. Combining the experimentally determined ground-state rotational constants with these theoretical corrections then allows the determination of equilibrium rotational constants. The corresponding equilibrium structure, denoted as semi-experimental (SE), is obtained by a leastsquares fit of the molecular parameters to the mixed experimental–theoretical equilibrium moments of inertia, which are obtained in a straightforward manner from the corresponding equilibrium rotational constants (see Ref. [4] for all details). The uncertainties affecting the SE equilibrium geometries mainly arise from the errors in the calculated vibrational corrections. Since the latter are small contributions compared to the rotational constants, the accuracy of the determined equilibrium structure is high, the uncertainties of bond distances and angles being usually of the order of one thousandth of Å and a few hundredths of degrees, respectively [4, 96, 134]. In recent years, this combined experimental–theoretical approach has turned out to be a powerful tool (see, e.g., Refs [4, 134] and references therein). In particular, this type of structure determination has been successfully applied to biomolecules [76, 135–137]. In such cases, due to the lack of experimental data, not all geometrical parameters can be evaluated. It is therefore important to fix the undeterminable parameters to reliable, as much as possible accurate, values. In this respect, hardware and software developments have made the CCSD(T) method in conjunction with triple-zeta quality basis set accessible for larger and larger systems, with this level of theory already providing rather accurate results [138]. As mentioned in Section 2.3.2, the use of composite schemes allows to further improve the accuracy of the computed structural parameters. As an example, we briefly discuss the determination of the equilibrium structure of

2.4

8) 83 4 5. 68( 2 1 5.7 7) 12 8.8( 11

1.3433 1.34496(59) 1.379(4)

Application and Case Studies

1.3 1.3 974 9 1.3 793 8(2 (40 ) )

) .91 121 24(10 .9 121 3(6) . 122 5 53) 78 ( 1.3 8175 1.3 6(5) 8 1.3

Figure 2.2 Molecular structure of uracil (along with the atom labeling) and selected geometrical parameters (distances in Å, angles in degrees): theoretical best-estimated (bold), semi-experimental values (normal text), and rs (in italic).

uracil by means of the SE approach introduced above, also supported by the quantum-chemical evaluation of a best-estimated structure [76]. While we refer interested readers to Ref. [76] for a complete account, selected geometrical parameters from the SE and pure theoretical (obtained by means of a composite scheme) structures are compared in Figure 2.2. On one hand, the comparison shows a remarkably good agreement; on the other hand, we note the high accuracy that characterizes the SE distances and angles. In Figure 2.2, the corresponding values for the so-called substitution structure (rs ) are also given. The latter is a purely experimental geometry, based on a model that tries to account for vibrational effects in an empirical way (see Ref. [93] for a detailed description). As is well known (see, e.g., Ref. [4] and references therein), the rs structure is less accurate and might fail in correctly reproducing the right bond order. To further address the accuracy of the SE and best-estimated structures obtained in Ref. [76], in Table 2.1, in addition to a detailed comparison of all geometrical parameters, the corresponding rotational constants are compared to experimental values. The last comment concerns the importance of fixing the undeterminable parameters to accurate and reliable values and of correctly describing the anharmonic force field used for computing the vibrational corrections to rotational constants. In Ref. [114], improvement in the SE equilibrium structure obtained for the Ip conformer of glycine (with respect to Ref. [136]) is ascribed to the best description of the large amplitude motions provided by the B3LYP/SNSD [53] force field as well as to more accurate values for the fixed parameters (best-estimated equilibrium values). As accurate experimental structures for the basic building blocks of biomolecules are usually not available, Ref. [76] together with the investigations of amino acids reported in Refs [114, 135–137] provide a turning point in the field of molecular structure characterization of biomolecules, since an inconceivable accuracy can be now obtained.

41

42

2 Computational Spectroscopy Tools for Molecular Structure Analysis

Table 2.1 Equilibrium structure (Distances in Å, angles in degrees) and rotational constants (MHz) of uracil.a) Best estimateb)

A0 f ) B0 f ) C0 f ) Distances N1-C2 C2-N3 N3-C4 C4-C5 C5-C6 C6-N1 C2-O7 C4-O8 N1-H9 N3-H10 C5-H11 C6-H12 Angles C2-N1-C6 N1-C6-C5 C6-C5-C4 C5-C4-N3 C4-N3-C2 N3-C2-N1 N1-C2-O7 C5-C4-O8 C2-N1-H9 C2-N3-H10 C6-C5-H11 N1-C6-H12

3885.475 2027.763 1332.761

Semi-experimentalc)

3883.848 2023.967 1330.929

1.3785 1.3756 1.3974 1.4539 1.3433 1.3723 1.2112 1.2138 1.0046 1.0090 1.0766 1.0793 123.38 121.91 119.49 113.97 127.75 113.51 123.62 125.83 115.22 115.70 122.11 115.34

1.38175(53) 1.3763 1.39793(40) 1.45500(57) 1.34496(59) 1.37196(55) 1.21025(21) 1.21278(24) 1.0046fix 1.0090fix 1.0766fix 1.0793fix 123.374(19) 121.924(10) 119.516(16) 113.860(22) 127.942 113.383 123.883(44) 125.768(48) 115.22fix 115.70fix 122.11fix 115.34fix

rs d)

Experimente)

— — —

3883.86951(14) 2023.73119(19) 1330.926922(56)

1.386(5) — 1.38(2) 1.451(4) 1.379(4) 1.352(14) 1.219(4) 1.22(2) — — — —

— — — — — — — — — — — —

123.0(11) 122.3(6) 118.8(12) 115.4(16) — — 122.3(8) 118.8(7) — — — —

— — — — — — — — — — — —

a) Atom labeling given in Figure 2.2. Standard error is given in parentheses (parameters without error bar are either fixed or derived a posteriori). b) Best-estimated ab initio equilibrium structure: for details see Ref. [76]. c) Semi-experimental equilibrium structure: for details see Ref. [76]. d) Substitution structure: for details see Ref. [76]. e) Ref. [139]. f ) For SE and theoretical structures, the ground-state rotational constants have been obtained by adding vibrational corrections at the B3LYP/N07D level to the corresponding equilibrium values. For details see Ref. [76].

2.4.2 Identification of Conformers/Tautomers

In the following, the issue of the identification and characterization of different conformers or tautomers is addressed by making use of a few selected case studies.

2.4

Application and Case Studies

These have been chosen in order to give an overview on how different spectroscopic techniques can deal with the conformational/tautomeric analysis. 2.4.2.1 Rotational Spectrum of Proteinogenic Glutamic Acid

In view of the relationship between molecular structure and rotational constants, the latter can be used for the identification of the conformers of a given molecule present in a gas-phase mixture. Actually, three are the tools that can be employed in the field of rotational spectroscopy for conformers assignment: rotational constants, nuclear quadrupole-coupling constants, and dipole moment components. While rotational constants provide information on the mass distribution, quadrupole-coupling constants yield information on the electronic environment of the quadrupolar nuclei and can be decisive to identify conformers with similar mass distributions but different intramolecular interactions. In this respect, it should be pointed out that nitrogen is usually present in biomolecules and its main isotopologue, 14 N, is a quadrupolar nucleus. Finally, since the rotational line intensities depend on the dipole moment components, the prediction of the latter can be used for estimating the relative abundances of the conformers observed. A significant example in this context is provided by the investigation of the rotational spectrum of proteinogenic glutamic acid [55]. First of all, a computational investigation was carried out, predicting 37 conformers to lie within 900 cm−1 . The assignment of the experimental rotational spectra led to the assignment of only five conformers, initially denoted as A, B, C, D, and E. By comparing the experimental rotational and nitrogen quadrupole-coupling constants to the computed counterparts, the authors were able to identify the observed conformers. While we refer interested readers to the original paper for a full account, here we focus our attention on the identification of the rotamer B. While the values of the rotational constants permitted to indicate the family of conformers to which it belongs (the families of glutamic acid are classified according to the dihedral angles, see Ref. [55] for details), discrimination among the members of the same family could be possible only on the basis of the values of the quadrupole coupling constants. Furthermore, it should be noted that energetic arguments could not help the identification as the two possible candidates turned out to have very similar energy once ZPVE corrections are considered, with the stability order reversing if free energy (instead of electronic energy) is considered. 2.4.2.2 IR Spectrum of Glycine

Glycine is the simplest natural amino acid, but it provides an illustrative case of conformational flexibility due to the presence of three internal rotational degrees of freedom, which leads to a rather complex PES with several possible local minima separated by low energy barriers (Figure 2.3). Very recently, several new experiments focused on the investigation of less stable conformers, and new computational studies, based on advanced methodologies, have been performed (for a complete account, see Ref. [114] and references therein). Nowadays, there is a general agreement on the structure and energetics of the two most stable conformers, that is, the Ip/ttt and IIn/ccc rotamers, which have even been

43

44

2 Computational Spectroscopy Tools for Molecular Structure Analysis

IR intensity (arbitrary units)

Ip/ttt

IIIp/tct

IIIp/tct IIn/ccc IIn/ccc

Ip/ttt

SUM

Exp. 1820 1800 1780 1760 1740 Wavenumber (cm−1)

2000

1800

1600

1400

1200

1000

800

600

400

Wavenumber (cm−1)

Figure 2.3 Theoretical IR spectra (from the top to the bottom) of the IIIp, IIn, and Ip glycine conformers along with their sum weighted according to their relative abundances (see text for details) compared to the experimental spectrum [142]. In the main

panel, the most intense bands of the Ip conformer are highlighted, while the less intense features observed in the C=O stretching region assigned to IIn and IIIp are highlighted in the inset.

detected by means of rotational spectroscopy [140, 141], with the corresponding semi-experimental equilibrium structures [114, 136] determined by the procedure described in Section 2.4.1. Another slightly less stable conformer, the IIIp/tct one, has also been experimentally observed by means of vibrational spectroscopy, employing different techniques [142–146]. Processes of interconversion between different conformers have also been studied experimentally [142, 145–147]. From an experimental point of view, because the sublimation of the molecule is often accompanied by its degradation, the detection of glycine in the gas phase is rather complicated. Alternatively, low-temperature vibrational spectra of neutral glycine trapped in inert gas matrices or nanodroplets represent valuable sources for experimental data [142–146]. These well-resolved experiments are also best suited for an integrated analysis assisted by theoretical studies. Indeed, a mixture of at least three conformers, each of them showing different chemical and electronic features, was obtained at temperatures below 13 K.

2.4

Application and Case Studies

In such a case, the identification of each conformer is based on the analysis of those intense vibrational transitions that remarkably differ in frequency from one conformer to another (e.g., C=O stretch, O–H stretch, CH2 bending). For example, Adamowicz et al. measured the IR spectrum of glycine trapped in Ar matrix at low temperature and interpreted the results with the support of harmonic frequencies and intensities computed at the MP2/TZP level [142]. Their analysis of the IR intensities, which included several glycine isotopologues and annealing studies, allowed them to determine the relative abundances of the Ip, IIn, and IIIp conformers to be about 70, 15, and 15%, respectively. A more reliable strategy is based on the computation of the fully anharmonic vibrational spectra (IR, Raman, VCD), by means of perturbation theory (as described in Section 2.3.3), for all the species possibly present in the experimental mixture and on subsequent comparison with the experimental outcomes. To give an example, the simulated IR spectra of Ip, IIn, and IIIp in the 400–2000 cm−1 energy range, computed at the B3LYP/aug-N07D level of theory within the DVPT2/GVPT2 approach, are shown in Figure 2.3. The overall simulated spectrum obtained by weighting the contribution of each conformer according to its abundance, as obtained from theoretical Boltzman population at 410 K (i.e., Ip=77, IIn=18, IIIp=6%, see Ref. [114] for the details), is also depicted in Figure 2.3 and compared to its experimental counterpart [142, 143]. It is demonstrated that the most intense transitions are indeed related to the most stable conformer, Ip/ttt, but the fingermarks of IIn and IIIp are also clearly present. It should be pointed out that, in variance to simple methodologies based on double-harmonic approximation, anharmonic spectra take also into account intensities of overtones and combination bands. This allows dissecting between low-intensity features related to non-fundamental transitions of the most abundant conformer and the fundamental transitions of the less abundant ones. The same computational procedure can be easily applied also to a set of isotopologues in view of obtaining an unequivocal identification of several concomitantly present conformers when the situation is not so clear for the main isotopic species. This strategy can be even extended to combine complementary vibrational spectroscopies, for example, IR and Raman, and can be useful also for the identification of molecular species, such as free radicals concomitantly present in experimental mixture. Proper assignment is performed with the aid of computations that allow first of all removing from the experimental spectra those transitions belonging to other species. The IR and Raman spectra of the phenyl radical [148], depicted in Figure 2.4, clearly show that the combination of anharmonic spectra provides more accurate (band positions) and more detailed (number of transitions) information than simple harmonic simulations, thus enabling correct analysis of the experimental findings. In conclusion, vibrational spectroscopies (IR, Raman) supported by quantumchemical calculations can provide qualitative as well as quantitative information on the conformational species that characterize a flexible molecule or any set of species possibly present in the experimental mixture.

45

2 Computational Spectroscopy Tools for Molecular Structure Analysis

IR

Intensity (arbitrary units)

anh

Harm

2000 1900 1800 1700 1600 1500 1400 1300 1200 1100 1000 900 Frequency (cm−1)

800

Raman

Intensity (arbitrary units)

46

anh

Harm

2000 1900 1800 1700 1600 1500 1400 1300 1200 1100 1000 900 Frequency (cm−1)

800

Figure 2.4 Harmonic and anharmonic IR (a) and Raman (b) spectra of the phenyl radical in the 800–2000 cm−1 frequency range.

2.4

Application and Case Studies

2.4.2.3 Vibrational (IR/VCD) and Electronic (OPA/ECD) Spectra of (Z)-8-Methoxy-4-Cyclooctenone

For chiral molecules, different enantiomers can be identified by means of chiroptical spectroscopies, and in general, conformational studies can be performed by making use of both chiroptical and linear spectroscopies in the vibrational and electronic part of the spectrum. An illustrative example is provided by the experimental observation of the IR, VCD, OPA (one-photon absorption), and ECD spectra of (Z)-8-Methoxy-4-Cyclooctenone (MCO), carried out by Inoue and coworkers [149], further supported by a standard computational analysis (harmonic approach and vertical transitions). In detail, the simulated IR and VCD spectra (scaled B3LYP/6-311+G(2d,p) harmonic frequencies, see Ref. [149] for the details) were compared to the corresponding experimental counterparts with the conclusion that both IR and VCD patterns were satisfactorily reproduced by considering the two most stable conformers, MCO1A and MCO1B (Figure 2.5), which differ in energy in a negligible manner, that is, by 3 > 1 > 5 > 4. Thus, one of the rare tautomers, and not the canonical form, was initially predicted as the most stable in solution. But a thorough comparison of the experimental isotropic HFCCs of N and H with the corresponding computed values (Table 2.2) pointed out that only for the tautomer (1) the HFCCs are compatible with the experimental data, whereas very significant deviations are observed for all the other cases. In conclusion, the comparison of computational and experimental ESR parameters provided a very consistent and clear solution: the canonical form (1) is the anionic tautomer of the uracil radical observed in aqueous solution. This case study further confirms that the interplay of experiment and theory is a powerful tool for gaining structural information from spectroscopic investigations. 2.4.3 3D Structure: Molecular Complexes and Flexible Macromolecules 2.4.3.1 Molecular Structure of Anisole Complexes

Recent experimental studies characterized several molecular complexes of anisole in terms of structure as well as electronic and vibrational properties starting from the determination of rotational constants, the measurement of the vibrational spectrum, and the detailed study of the first excited singlet electronic state at a full rotational resolution [21, 161–164]. Among aromatic molecules, anisole is particularly interesting because of the coexistence of prototypical functional groups: the aromatic ring, H-bond donor and acceptor moieties, and the methyl group. Thus, different intermolecular interaction schemes are possible: hydrogen bond, van der Waals, and dipole–dipole interactions, but none of them is dominant [21, 161–164]. Recent studies of the anisole–water [21] and anisole–ammonia [161] 1 : 1 adducts pointed out the complexity of the corresponding PESs and a different behavior for the two complexes. In fact, anisole–water is a planar complex stabilized by hydrogen bonding, with water acting as an acid [21], while anisole–ammonia is nonplanar since ammonia is located above anisole (hydrogen bond of one N–H with the oxygen’s lone pair, improper hydrogen bond of another N–H with the aromatic electron density and of the anisole methyl group anisoles with the nitrogen lone pair) [161]. In both cases, it was possible to determine the relative position of the “solvent molecule” (i.e., either water or ammonia) from the analysis of the experimental rotational constants, determined in the ground and excited electronic states. The relative position of the two moieties can be calculated by a perturbative approach starting from the inertia tensor of anisole, assuming anisole did not change upon complexation. In particular, the distance between the centers of mass of anisole and ammonia/water (rc.m. ) can be calculated from the experimental data using Kraitchmann equations [93], assuming the “solvent molecule” as a rigid sphere. In the case of ammonia, from the structural parameters defined in Figure 2.6 and reported in Table 2.3, it is clear that the complex is nonplanar in both the ground

2.4

Application and Case Studies

X,a

r γ Y,b

α Z,c

Figure 2.6 Structure of the anisole–ammonia/water 1 : 1 complexes: definition of the geometrical parameters. Table 2.3 Structural parameters of the anisole–ammonia complex in the S0 and S1 electronic states [161], as defined in Figure 2.6.

rc.m. (Å) R𝑋𝑌 (Å) α (deg) γ (deg)

S0

S1

3.512 1.340 80.6 77.6

3.392 1.156 71.0 70.1

R𝑋𝑌 is the rc.m. projection on XY plane. γ is the elevation angle with respect to the aromatic ring plane.

and excited electronic states. Alternatively, the structures of complexes can be characterized by means of quantum-chemical computations that allow locating all possible local minima, and the corresponding rotational constants can then be compared to the experimental data. For the anisole–ammonia 1 : 1 complex, a total of five different structures were localized on the PES, as shown in Figure 2.7. There is only one nonplanar structure, with ammonia hydrogens involved in a H–π interaction, while the other four structures are planar. In agreement with experiment, computations predict the nonplanar complex as the most stable one (by more than 6 kJ mol−1 in the ground electronic state). Furthermore, the ground and excited state rotational constants and geometrical parameters deduced from experimental data are in very good agreement with those from QM calculations, thus allowing an unambiguous determination of the molecular structure of the anisole–ammonia complex.

51

52

2 Computational Spectroscopy Tools for Molecular Structure Analysis

H..π

NH...O

H..N..H

N..H–C3

N..H–C5

Figure 2.7 The five local minimum structures for anisole–ammonia 1 : 1 complexes.

I (O–H...O)

II (O–H..π)

III (stacking)

Figure 2.8 Structures of the three local minima of the anisole–phenol complex in the ground state, optimized at the M052X/aug-N07D level. For the experimentally observed structure, I (O–H … O), the plot of the electron density difference (ELD) between the S1 and S0 electronic states,

at the TD-M05-2X/aug-N07 level, is also depicted. The regions where the electron density decreases upon electronic transition are in light grey, whereas the regions where the electron density increases are in dark grey. An isovalue threshold of 0.0004 has been used to evaluate ELD.

The simplified procedure to derive structural information from experimental data mentioned above cannot be applied to larger systems such as the anisole dimer or the anisole–phenol complex. In such cases, the determination of the 3D structure fully relies on the comparison of the computational results with the corresponding experimental counterpart. In Ref. [162], this approach was exploited to determine the structure of the anisole dimer in the gas phase, which turned out to have the two units placed in a parallel configuration at a 3.4 Å distance and stabilized by a π-stacking interaction [162, 163]. For the anisole–phenol complex, three different local minima were located on its ground electronic state PES (Figure 2.8). Namely, two different H-bonded structures, with phenol acting as a proton-donor and anisole as a proton-acceptor, via its methoxy group in the first case (structure I) or via the electronic density of the aromatic ring in the second

2.4

Application and Case Studies

Table 2.4 Comparison of the experimental rotational constants (in cm−1 ) of the ground and first singlet electronic excited states with those computed at the M05-2X/augN07D//TD-M05-2X/aug-N07D level for the three different equilibrium structures of the anisole–phenol complex (for notation, see Figure 2.8) [164]. Experimental

A B C MAE

0.0352912(27) 0.0101269(7) 0.0091991(5)

A B C MAE

0.0349400(27) 0.0100983(7) 0.0091132(6)

I (O–H· · ·O)

S0 0.0367542 0.0102426 0.0094080 2.5 S1 0.0347829 0.0105963 0.0095210 3.2

II (O–H· · · 𝛑)

III (stacking)

0.0339721 0.0142783 0.0129196 28.4

0.0321614 0.0147848 0.0125471 30.4

0.0349740 0.0146453 0.0131481 29.7

0.0314809 0.0206862 0.0177403 69.7

MAE stands for the mean absolute error in percentage.

case (structure II); the third structure is the result of stacking interactions (structure III). The structure of the complex observed in the REMPI experiment was elucidated by means of an integrated computational–experimental study [164]; in fact, the remarkable agreement for the rotational constants (Table 2.4) allowed resolving the structure of the complex and identifying the main stabilizing interactions occurring between the two partners. In detail, the anisole–phenol complex is stabilized by a hydrogen bond between the phenol, acting as a proton donor, and the anisole molecule, acting as an acceptor via the lone pairs of the oxygen atom. A secondary interaction involving the hydrogen atoms of the anisole methyl group and the electron system of the phenol molecule stabilizes the complex in a nonplanar configuration. Finally, the computation of electronic properties in the excited state provided information about the character of the transition, which turned out to be localized on the phenol moiety. 2.4.3.2 ESR Spectrum of Peptides

As mentioned above, ESR spectroscopy is widely used to characterize the properties of macromolecular systems of biological interest giving access to important information on structural and dynamical properties. As already said, the interpretation of ESR spectra for such complex systems needs to be supported by quantum-chemical computations of the magnetic parameters involved. Furthermore, since the ESR parameters often show a strong dependence on the molecular geometry, a direct comparison with experiment requires that dynamic effects are properly taken into account. In some cases, it is sufficient to compute vibrationally averaged parameters using a perturbative approach, but large amplitude motions and solvent librations require direct dynamic simulations. For the latter, in most cases the classical MD treatment combined

53

54

2 Computational Spectroscopy Tools for Molecular Structure Analysis

Methanol

Toluene 350 K

7.7 Å

6.9 Å

320 K 340 K 330 K 310 K

320 K 310 K

300 K

300 K 290 K

α-helix structure

280 K

280 K

310 helix structure

270 K 3300

3320

3340

3360

3380 3285

B / Gauss

3305

3325

3345

3365

B / Gauss

Experiment Simulated Figure 2.9 Experimental (solid lines) and theoretical (dashed lines) CW-ESR spectra of heptapeptide in methanol and toluene solutions at different temperatures [166].

with a posteriori quantum-chemical computations is sufficient. In the case of fast motion of the labeled molecules, the structural information can be derived from a time-independent perturbative model [40, 130]. On the other hand, in the slow-motion regime more sophisticated theoretical approaches are required, due to the profound effects that molecular motions exert on the spin relaxation processes. In such cases, the dynamical parameters are evaluated by applying the stochastic Liouville equation (SLE) [42, 126], while quantum mechanics is used for computing magnetic parameters. The simulation of EPR/ESR spectra can be performed by means of dedicated computational tools integrated in a user-friendly virtual spectrometer aimed at being used by experimentalists as a sort of extension of their laboratory equipment [165]. To give an example, this approach was applied to unravel the solvent-driven equilibria between 𝛼- and 310 -helices for a double labeled heptapeptide by direct comparison of the simulated spectrum with its experimental counterpart [166]. A combined computational and experimental study pointed out that Aib-rich peptides change their conformation from 310 - to α-helix as a function of increasing polarity and hydrogen-bond donor capability of the solvent: α-helix in protic solvents and at low temperature, 310 -helix in aprotic ones. The spectra simulated in different solvents and at various temperatures, depicted in Figure 2.9, clearly show a good agreement with experiment for α-helix in methanol (aqueous solution) and 310 conformation in toluene (non-aqueous solution), thus confirming the conclusions drawn above. Analogous computations can also be extended to larger systems paving the route for systematic studies of spin labeled peptides and proteins.

References

Acknowledgments

The authors acknowledge the fruitful collaboration as well as illuminating discussions with Professor Vincenzo Barone. Both authors are strongly indebted to him for his continuous, enthusiastic suggestions of new research lines and topics as well as his scientific guidance in all challenging aspects. The work described herein was possible thanks to the efforts of several people along the years, and in particular thanks to Dr. Julien Bloino, Dr. Giuseppe Brancato, Dr. Ivan Carnimeo, Dr. Paola Cimino, Prof. Orlando Crescenzi, Dr. Michele Pavone, Prof. Nadia Rega and Dr. Fabrizio Santoro. MB also acknowledges a fruitful collaboration with the experimental group of Dr. Maurizio Becucci on the structure and properties of anisole complexes. CP also acknowledges Prof. J. Gauss for fruitful discussions and collaboration. This work was supported by Italian MIUR (in the frame of the PRIN funding scheme). The high performance computer facilities of the DREAMS center (http://dreamshpc.sns.it) are acknowledged for providing computer resources. The support of COST CMTS-Action CM1002 “COnvergent Distributed Environment for Computational Spectroscopy (CODECS)” is also acknowledged.

References 1. Nicolaou, K.C. and Snyder, S.A. (2005)

2.

3.

4.

5.

6.

Chasing molecules that were never there: misassigned natural products and the role of chemical synthesis in modern structure elucidation. Angew. Chem. Int. Ed., 44 (7), 1012–1044. Mazzanti, A. and Casarini, D. (2012) Recent trends in conformational analysis. WIREs Comput. Mol. Sci., 2 (4), 613–641. Barone, V. (ed.) (2011) Computational Strategies for Spectroscopy, from Small Molecules to Nano Systems, John Wiley & Sons, Inc., Hoboken, NJ. Puzzarini, C., Stanton, J.S., and Gauss, J. (2010) Quantum-chemical calculation of spectroscopic parameters for rotational spectroscopy. Int. Rev. Phys. Chem., 29, 273–367. Cramer, C.J. (2005) Essentials of Computational Chemistry: Theories and Models, John Wiley & Sons, Ltd, Chichester. Young, D. (2004) Computational Chemistry: A Practical Guide for Applying Techniques to Real World Problems, John Wiley & Sons, Inc., New York.

7. Jensen, F. (2006) Introduction to Com-

8.

9.

10.

11.

12.

13.

14.

putational Chemistry, John Wiley & Sons, Ltd, Chichester. Leach, A.R. (2009) Molecular Modelling: Principles and Applications, 2nd edn, Pearson Education, Harlow. Hinchliffe, A. (2011) Molecular Modelling for Beginners, John Wiley & Sons, Ltd, Chichester. Jensen, P. and Bunker, P.R. (2000) Computational Molecular Spectroscopy, John Wiley & Sons, Ltd, Chichester. Grunenberg, J. (ed.) (2010) Computational Spectroscopy, Wiley-VCH Verlag GmbH & Co. KGaA. Quack, M. and Merkt, F. (eds) (2011) Handbook of High-Resolution Spectroscopy, John Wiley & Sons, Inc. Csaszar, A.G., Fabri, C., Szidarovszky, T., Matyus, E., Furtenbacher, T., and Czako, G. (2012) The fourth age of quantum chemistry: molecules in motion. Phys. Chem. Chem. Phys., 14, 1085–1106. Tennyson, J. (2012) Accurate variational calculations for line lists to model the

55

56

2 Computational Spectroscopy Tools for Molecular Structure Analysis

15.

16.

17.

18.

19.

20.

21.

22.

23.

vibration-rotation spectra of hot astrophysical atmospheres. WIREs Comput. Mol. Sci., 2, 698–715. Puzzarini, C., Coriani, S., Rizzo, A., and Gauss, J. (2005) Critical analysis of the spin-rotation constants of CF2 and CCl2: a theoretical investigation. Chem. Phys. Lett., 409, 118–123. Barone, V., Bloino, J., and Biczysko, M. (2010) Validation of the DFT/N07D computational model on the magnetic, vibrational and electronic properties of vinyl radical. Phys. Chem. Chem. Phys., 12, 1092–1101. Barone, V., Baiardi, A., Biczysko, M., Bloino, J., Cappelli, C., and Lipparini, F. (2012) Implementation and validation of a multi-purpose virtual spectrometer for large systems in complex environments. Phys. Chem. Chem. Phys., 14, 12404–12422. Zwier, T.S. (2006) Laser probes of conformational isomerization in flexible molecules and complexes. J. Phys. Chem. A, 110 (12), 4133–4150. de Vries, M.S. and Hobza, P. (2007) Gas-phase spectroscopy of biomolecular building blocks. Annu. Rev. Phys. Chem., 58, 585–612. Roscioli, J.R. and Pratt, D.W. (2003) Base pair analogs in the gas phase. Proc. Natl. Acad. Sci. U.S.A., 100, 13752. Becucci, M. and Pietraperzia, G. (2011) Quest for accurate models: some challenges from gas-phase experiments on medium-size molecules and clusters, Computational Strategies for Spectroscopy, from Small Molecules to Nano Systems, John Wiley & Sons, Inc., pp. 25–35. Callegari, C., Lehmann, K.K., Schmied, R., and Scoles, G. (2001) Helium nanodroplet isolation rovibrational spectroscopy: methods and recent results. J. Chem. Phys., 115 (22), 10090–10110. Choi, M.Y., Douberly, G.E., Falconer, T.M., Lewis, W.K., Lindsay, C.M., Merritt, J.M., Stiles, P.L., and Miller, R.E. (2006) Infrared spectroscopy of helium nanodroplets: novel methods for physics and chemistry. Int. Rev. Phys. Chem., 25 (1-2), 15–75.

24. Berova, N., Polavarapu, P.L., Nakanishi,

25.

26.

27.

28.

29.

30.

31.

32.

33.

K., and Woody, R.W. (2012) Comprehensive Chiroptical Spectroscopy: Applications in Stereochemical Analysis of Synthetic Compounds, Natural Products, and Biomolecules, vol. 2, John Wiley & Sons, Inc., Hoboken, NJ. Polavarapu, P.L. (2012) Molecular structure determination using chiroptical spectroscopy: where we may go wrong? Chirality, 24, 909–920. Lesarri, A., Mata, S., López, J.C., and Alonso, J.L. (2003) A laser-ablation molecular-beam Fourier transform microwave spectrometer: the rotational spectrum of organic solids. Rev. Sci. Instrum., 74, 4799–4804. Steber, A.L., Neill, J.L., Zaleski, D.P., Pate, B.H., Lesarri, A., Bird, R.G., Vaquero-Vara, V., Jahn, M.K., and Pratt, D.W. (2011) Structural studies of biomolecules in the gas phase by chirppulse Fourier-transform microwave spectroscopy. Faraday Discuss., 150, 227–242. Cabezas, C., Peña, M.I., López, J.C., and Alonso, J.L. (2012) Seven conformers of neutral dopamine revealed in the gas phase. J. Phys. Chem. Lett., 4, 486–490. Poveda, L.A., Biczysko, M., and Varandas, A.J.C. (2009) Accurate ab initio based dmbe potential energy surface for the ground electronic state of N2 H2 . J. Chem. Phys., 131 (4), 044309. Acevedo, O. and Jorgensen, W.L. (2010) Advances in quantum and molecular mechanical (QM/MM) simulations for organic and enzymatic reactions. Acc. Chem. Res., 43 (1), 142–151. PMID: 19728702. Leone, V., Marinelli, F., Carloni, P., and Parrinello, M. (2010) Targeting biomolecular flexibility with metadynamics. Curr. Opin. Struct. Biol., 20 (2), 148–154. Zuckerman, D.M. (2011) Equilibrium sampling in biomolecular simulations, in Annual Review of Biophysics, vol. 40 (eds D.C. Rees, K.A. Dill, and J.R. Williamson), Annual Reviews, Palo Alto, CA, pp. 41–62. Jain, A. and Stock, G. (2012) Identifying metastable states of folding

References

34.

35.

36. 37.

38.

39.

40.

41.

42.

43.

proteins. J. Chem. Theory Comput., 8 (10), 3810–3819. Peterson, K.A., Feller, D., and Dixon, D.A. (2012) Chemical accuracy in ab initio thermochemistry and spectroscopy: current strategies and future challenges. Theor. Chem. Acc., 131, 1079. Harding, M.E., Vázquez, J., Gauss, J., Stanton, J.F., and Kállay, M. (2011) Towards highly accurate ab initio thermochemistry of larger systems: benzene. J. Chem. Phys., 135, 044513. Laane, J. (ed.) (2009) Frontiers of Molecular Spectroscopy, Elsevier, Amsterdam. Siebert, F. and Hildebrandt, P. (2008) Vibrational Spectroscopy in Life Science, Wiley-VCH Verlag GmbH and Co, KGaA. Astrid, G., Rudolf, R., and Jerker, W. (2010) Single Molecule Spectroscopy in Chemistry, Physics and Biology: Nobel Symposium, Springer-Verlag, Berlin Heilderberg. Pedone, A., Biczysko, M., and Barone, V. (2010) Environmental effects in computational spectroscopy: accuracy and interpretation. Comput. Phys. Commun., 11, 1812–1832. Barone, V., Biczysko, M., and Brancato, G. Extending the range of computational spectroscopy by QM/MM approaches: time-dependent and time-independent routes. (2010) Adv. Quantum Chem., 59, 17. Zhuang, W., Hayashi, T., and Mukamel, S. (2009) Coherent multidimensional vibrational spectroscopy of biomolecules: concepts, simulations, and challenges. Angew. Chem. Int. Ed., 48 (21), 3750–3781. Barone, V. and Polimeno, A. (2006) Toward an integrated computational approach to CW-ESR spectra of free radicals. Phys. Chem. Chem. Phys., 8, 4609–4629. Berova, N., Polavarapu, P.L., Nakanishi, K., and Woody, R.W. (2012) Comprehensive Chiroptical Spectroscopy: Instrumentation, Methodologies, and Theoretical Simulations, vol. 1, John Wiley & Sons, Inc., Hoboken, NJ.

44. Nafie, L.A. (2011) Vibrational Optical

45.

46.

47.

48.

49.

50.

51.

52.

53.

Activity: Principles and Applications, John Wiley & Sons, Ltd, Chichester. Prampolini, G., Bellina, F., Biczysko, M., Cappelli, C., Carta, L., Lessi, M., Pucci, A., Rugger, G., and Barone, V. (2013) Computational design, synthesis, and mechanochromic properties of new thiophene-based π-conjugated chromophores. Chem.-Eur. J., 19, 1996–2004. Scalmani, G., Frisch, M.J., Menucci, B., Tomasi, J., Cammi, R., and Barone, V. (2006) Geometries and properties of excited states in the gas phase and in solution: theory and application of a time-dependent density functional theory polarizable continuum model. J. Chem. Phys., 124, 094107. Stratmann, R.E., Scuseria, G.E., and Frisch, M.J. (1998) An efficient implementation of time-dependent density-functional theory for the calculation of excitation energies of large molecules.. J. Chem. Phys., 109, 8218. Jacquemin, D., Wathelet, V., Perpete, E.A., and Adamo, C. (2009) Extensive TD-DFT benchmark: singlet-excited states of organic molecules. J. Chem. Theory Comput., 5 (9), 2420–2435. Pecul, M., Ruud, K., and Helgaker, T. (2004) Density functional theory calculation of electronic circular dichroism using London orbitals. Chem. Phys. Lett., 388 (1-3), 110–119. Stephens, P.J., Devlin, F.J., and Pan, J.-J. (2008) The determination of the absolute configurations of chiral molecules using vibrational circular dichroism (VCD) spectroscopy. Chirality, 20, 643. Halls, M.D. and Schlegel, H.B. (1999) Comparison of the prediction of Raman intensities using electronic structure methods. J. Chem. Phys., 111, 8819. Bloino, J., Biczysko, M., Santoro, F., and Barone, V. (2010) General approach to compute vibrationally resolved onephoton electronic spectra. J. Chem. Theory Comput., 6 (4), 1256–1274. Dreamslab (2012) Double and triple-ζ basis sets of SNS and N07 families, are available for download, visit http://compchem.sns.it/downloads (accessed 1 February 2013).

57

58

2 Computational Spectroscopy Tools for Molecular Structure Analysis 54. Barone, V., Cimino, P., and Stendardo,

55.

56.

57.

58.

59.

60.

61.

62.

63.

E. (2008) Development and validation of the B3LYP/N07D computational model for structural parameter and magnetic tensors of large free radicals. J. Chem. Theory Comput., 4, 751. Peña, M.I., Sanz, M.E., López, J.C., and Alonso, J.L. (2012) Preferred conformers of proteinogenic glutamic acid. J. Am. Chem. Soc., 134, 2305–2312. Cappelli, C. and Biczysko, M. (2011) Time-independent approach to vibrational spectroscopies, Computational Strategies for Spectroscopy, from Small Molecules to Nano Systems, John Wiley & Sons, Inc., pp. 309–360. Biczysko, M., Panek, P., Scalmani, G., Bloino, J., and Barone, V. (2010) Harmonic and anharmonic vibrational frequency calculations with the doublehybrid B2PLYP method: analytic second derivatives and benchmark studies. J. Chem. Theory Comput., 6, 2115–2125. Biczysko, M., Panek, P., and Barone, V. (2009) Toward spectroscopic studies of biologically relevant systems: vibrational spectrum of adenine as a test case for performances of long-range/dispersion corrected density functionals. Chem. Phys. Lett., 475, 105–110. Becke, D. (1993) Density-functional thermochemistry. III. The role of exact exchange. J. Chem. Phys., 98, 5648–5652. Yanai, T., Tew, D.P., and Handy, N.C. (2004) A new hybrid exchangecorrelation functional using the Coulomb-Attenuating Method (CAMB3LYP). Chem. Phys. Lett., 393, 51–57. Adamo, C. and Barone, V. (1999) Toward reliable density functional methods without adjustable parameters: the PBE0 method. J. Chem. Phys., 110, 6158–6170. Barone, V., Biczysko, M., and Cimino, P. (2010) Interplay of stereo electronic vibrational and environmental effects in tuning physico-chemical properties of carbon centered radicals, CarbonCentered Free Radicals and Radical Cations, John Wiley & Sons, Inc., pp. 103–137. Grimme, S. (2006) Semiempirical hybrid density functional with perturbative

64.

65.

66.

67.

68.

69.

70.

71.

second-order correlation. J. Chem. Phys., 124, 034108. Kozuch, S., Gruzman, D., and Martin, J.M.L. (2010) DSD-BLYP: a general purpose double hybrid density functional including spin component scaling and dispersion correction. J. Phys. Colloid Chem., 114, 20801–20808. Grimme, S. and Neese, F. (2007) Double-hybrid density functional theory for excited electronic states of molecules. J. Chem. Phys., 127, 154116/1–18. Grimme, S. and Goerigk, L. (2009) Calculation of electronic circular dichroism spectra with time-dependent doublehybrid density functional theory. J. Phys. Chem. A, 113, 767–776. Riley, K.E., Pitoniak, M., Jurecka, P., and Hobza, P. (2010) Stabilization and structure calculations for noncovalent interactions in extended molecular systems based on wave function and density functional theories. Chem. Rev., 110, 5023–5063. Gordon, M.S., Fedorov, D.G., Pruitt, S.R., and Slipchenko, L.V. (2012) Fragmentation methods: a route to accurate calculations on large systems. Chem. Rev., 112, 632–672. Biczysko, M., Bloino, J., Brancato, G., Cacelli, I., Cappelli, C., Ferretti, A., Lami, A., Monti, S., Pedone, A., Prampolini, G., Puzzarini, C., Santoro, F., Trani, F., and Villani, G. (2012) Integrated computational approaches for spectroscopic studies of molecular systems in the gas phase and in solution: pyrimidine as a test case. Theor. Chem. Acc., 131, 1201/1–19. Neugebauer, J. and Hess, B.A. (2004) Resonance Raman spectra of uracil based on kramers–kronig relations using time-dependent density functional calculations and multireference perturbation theory. J. Chem. Phys., 120 (24), 11564–11577. Begue, D., Carbonniere, P., and Pouchan, C. (2005) Calculations of vibrational energy levels by using a hybrid ab initio and DFT quartic force field: application to acetonitrile. J. Phys. Chem. A, 109 (20), 4611–4616.

References 72. Puzzarini, C., Biczysko, M., and

73.

74.

75.

76.

77.

78.

79.

Barone, V. (2010) Accurate harmonic/anharmonic vibrational frequencies for open-shell systems: performances of the B3LYP/N07D model for semirigid free radicals benchmarked by CCSD(T) computations. J. Chem. Theory Comput., 6, 828–838. Carbonniere, P., Lucca, T., Pouchan, C., Rega, N., and Barone, V. (2005) Vibrational computations beyond the harmonic approximation: performances of the B3LYP functional for semirigid molecules. J. Comput. Chem., 26, 384–388. Bloino, J., Biczysko, M., and Barone, V. (2012) General perturbative approach for spectroscopy, thermodynamics and kinetics: methodological background and benchmark studies. J. Chem. Theory Comput., 8, 1015–1036. Bloino, J., Biczysko, M., Crescenzi, O., and Barone, V. (2008) Integrated computational approach to vibrationally resolved electronic spectra: anisole as a test case. J. Chem. Phys., 128 (24), 244105. Puzzarini, C. and Barone, V. (2011) Extending the molecular size in accurate quantum-chemical calculations: the equilibrium structure and spectroscopic properties of uracil. Phys. Chem. Chem. Phys., 13, 7189–7197. Puzzarini, C., Biczysko, M., and Barone, V. (2011) Accurate anharmonic vibrational frequencies for uracil: the performance of composite schemes and hybrid CC/DFT model. J. Chem. Theory Comput., 7, 3702–3710. Gao, J. (1996) Hybrid quantum and molecular mechanical simulations: an alternative avenue to solvent effects in organic chemistry. Acc. Chem. Res., 29, 298–305. (a) Vreven, T. and Morokuma, K. (2003) Investigation of the S-0 -> S-1 excitation in bacteriorhodopsin with the ONIOM(MO : MM) hybrid method. Theor. Chim. Acta, 109 (3), 125–132; (b) Vreven, T. and Morokuma, K. (2001) Symposium on Methods and Applications of Combined Quantum Mechanical and Molecular Mechanical Potentials held at the 222nd American Chemical

80.

81.

82.

83.

84.

85.

86.

87.

88.

89.

Society National Meeeting, Chicago, IL, August 26–30, 2001. Senn, H.M. and Thiel, W. (2009) QM/MM methods for biomolecular systems. Angew. Chem. Int. Ed., 48, 1198–1229. Arul Murugan, N., Kongsted, J., Rinkevicius, Z., Aidas, K., and Ågren, H. (2010) Modeling the structure and absorption spectra of stilbazolium merocyanine in polar and nonpolar solvents using hybrid QM/MM techniques. J. Phys. Chem. B, 114, 13349–13357. Lipparini, F., Cappelli, C., Scalmani, G., De Mitri, N., and Barone, V. (2012) Analytical first and second derivatives for a fully polarizable QM/classical hamiltonian. J. Chem. Theory Comput., 8 (11), 4270–4278. Bulheller, B.M., Rodger, A., and Hirst, J.D. (2007) Circular and linear dichroism of proteins. Phys. Chem. Chem. Phys., 9, 2020–2035. Neugebauer, J. (2010) Chromophorespecific theoretical spectroscopy: from subsystem density functional theory to mode-specific vibrational spectroscopy. Phys. Rep., 489, 1–87. Barone, V., Carnimeo, I. and Scalmani, G. (2013) Computational spectroscopy of large systems in solution: the DFTB/PCM and TD-DFTB/PCM approach. J. Chem. Theory Comput., 9, 2052–2071. Aliev, M.R. and Watson, J.K.G. (1985) Molecular Spectroscopy: Modern Research, vol. III, Academic Press, New York. Raghavachari, K., Trucks, G.W., Pople, J.A., and Head-Gordon, M. (1989) A fifth-order perturbation comparison of electron correlation theories. Chem. Phys. Lett., 157, 479–483. Heckert, M., Kállay, M., Tew, D.P., Klopper, W., and Gauss, J. (2006) Basis-set extrapolation techniques for the accurate calculation of molecular equilibrium geometries using coupledcluster theory. J. Chem. Phys., 125, 044108. Heckert, M., Kállay, M., and Gauss, J. (2005) Molecular equilibrium geometries based on coupled-cluster

59

60

2 Computational Spectroscopy Tools for Molecular Structure Analysis

90.

91.

92.

93.

94.

95.

96.

97.

calculations including quadruple excitations. Mol. Phys., 103, 2109–2115. Stanton, J.F., Gauss, J., Harding, M.E., and Szalay, P.G. (2011) CFOUR a quantum chemical program package. with contributions from Auer, A.A., Bartlett, R.J., Benedikt, U., Berger, C., Bernholdt, D.E., Bomble, Y.J., Christiansen, O., Heckert, M., Heun, O., Huber, C., Jagau, T.-C., Jonsson, D., Jusélius, J., Klein, K., Lauderdale, W.J., Matthews, D., Metzroth, T., Mück, L.A., O’Neill, D.P., Price, D.R., Prochnow, E., Puzzarini, C., Ruud, K., Schiffmann, F., Schwalbach, W., Stopkowicz, S., Tajti, A., Vázquez, J., Wang, F., Watts, J.D. and the integral packages MOLECULE (Almløf, J. and Taylor, P.R.), PROPS (Taylor, P.R.), ABACUS (Helgaker, T., Jensen, H.J.Aa., Jørgensen, P., and Olsen, J.), and ECP routines by Mitin, A.V. and van Wüllen, C. For the current version, see http://www.cfour.de (accessed 13 September 2012). Puzzarini, C. (2009) Extrapolation to the complete basis set limit of structural parameters: comparison of different approaches. J. Phys. Chem. A, 113, 14530–14535. Puzzarini, C. and Barone, V. (2009) On the stability of X2 NO radicals (X = F, Cl, Br, I). Phys. Chem. Chem. Phys., 11, 11463–11470. Gordy, W. and Cook, R.L. (1984) Microwave Molecular Spectra, 3rd edn, John Wiley & Sons, Inc., New York. Mills, I.M. (1972) Molecular Spectroscopy: Modern Research, Academic Press, New York. Barone, V. (2005) Anharmonic vibrational properties by a fully automated second-order perturbative approach. J. Chem. Phys., 122, 014108/1–10. Pawlowski, F., Jørgensen, P., Olsen, J., Hegelund, F., Helgaker, T., Gauss, J., Bak, K.L., and Stanton, J.F. (2002) Molecular equilibrium structures from experimental rotational constants and calculated vibration–rotation interaction constants. J. Chem. Phys., 116, 6482–6496. Stanton, J.F., Lopreore, C.L., and Gauss, J. (1998) The equilibrium structure

98.

99. 100.

101.

102.

103.

104.

105.

106.

107.

and fundamental vibrational frequencies of dioxirane. J. Chem. Phys., 108, 7190–7196. Wilson, E.B., Decius, J.C., and Cross, P.C. (1955) Molecular Vibrations: The Theory of Infrared and Raman Vibrational Spectra, McGraw-Hill, New York. Califano, S. (1976) Vibrational States, John Wiley & Sons, Inc.. Christiansen, O. (2007) Vibrational structure theory: new vibrational wave function methods for calculation of anharmonic vibrational energies and vibrational contributions to molecular properties. Phys. Chem. Chem. Phys., 9 (23), 2942–2953. Roy, T.K. and Gerber, R.B. (2013) Vibrational self-consistent field calculations for spectroscopy of biological molecules: new algorithmic developments and applications. Phys. Chem. Chem. Phys., 115, 9468–9492. Barone, V. (2004) Vibrational zero-point energies and thermodynamic functions beyond the harmonic approximation. J. Chem. Phys., 120 (7), 3059–3065. Stanton, J.F. and Gauss, J. (2000) Analytic second derivatives in highorder many-body perturbation and coupled-cluster theories: computational considerations and applications. Int. Rev. Phys. Chem., 19, 61–95. Ruud, K., Åstrand, P.O., and Taylor, P.R. (2000) An efficient approach for calculating vibrational wave functions and zero-point vibrational corrections to molecular properties of polyatomic molecules. J. Chem. Phys., 112, 2668–2683. Gaw, F.J., Willetts, A., Handy, N.C., and Green, W.H. (1991) SPECTRO - A Program for Derivation of Spectroscopic Constants from Provided Quartic Force Fields and Cubic Dipole Fields, vol. 1B, JAI Press, pp. 169–185. Vázquez, J. and Stanton, J.F. (2006) Simple(r) algebraic equation for transition moments of fundamental transitions in vibrational second-order perturbation theory. Mol. Phys., 104, 377–388. Bloino, J., Guido, C., Lipparini, F., and Barone, V. (2010) A fully automated

References

108.

109.

110.

111.

112.

113.

114.

115.

implementation of VPT2 infrared intensities. Chem. Phys. Lett., 496, 157–161. Bloino, J. and Barone, V. (2012) A second-order perturbation theory route to vibrational averages and transition properties of molecules: general formulation and application to infrared and vibrational circular dichroism spectroscopies. J. Chem. Phys., 136 (12), 124108. Frisch, M.J., Trucks, G.W., Schlegel, H.B., Scuseria, G.E., Robb, M.A., Cheeseman, J.R., Scalmani, G., Barone, V., Mennucci, B., Petersson, G.A. et al. (2013) Gaussian 09 Revision D.01, Gaussian Inc. Wallingford, CT 2009. Biczysko, M., Julien, B., Carnimeo, I., Panek, P.Å., and Barone, V. (2012) Fully ab initio IR spectra for complex molecular systems from perturbative vibrational approaches: glycine as a test case. J. Mol. Spectrosc., 1009, 74–82. Barone, V., Biczysko, M., Bloino, J., Borkowska-Panek, M., Carnimeo, I., and Panek, P. (2012) Toward anharmonic computations of vibrational spectra for large molecular systems. Int. J. Quantum Chem., 112, 2185–2200. Carnimeo, I., Biczysko, M., Bloino, J., and Barone, V. (2011) Reliable structural, thermodynamic, and spectroscopic properties of organic molecules adsorbed on silicon surfaces from computational modeling: the case of glycine@Si(100). Phys. Chem. Chem. Phys., 13, 16713–16727. Puzzarini, C. and Barone, V. (2008) Toward spectroscopic accuracy for organic free radicals: molecular structure, vibrational spectrum, and magnetic properties of F2 NO. J. Chem. Phys., 129, 084306/1–7. Barone, V., Biczysko, M., Bloino, J., and Puzzarini, C. (2013) The performance of composite schemes and hybrid CC/DFT model in predicting structure, thermodynamic and spectroscopic parameters: the challenge of the conformational equilibrium in glycine. Phys. Chem. Chem. Phys., 15, 10094–10111. Franck, J. (1926) Elementary processes of photochemical reactions. Trans. Faraday Soc., 21, 536–542.

116. Condon, E.U. (1928) Nuclear motions

117.

118.

119.

120.

121.

122.

123.

124.

125.

associated with electron transitions in diatomic molecules. Phys. Rev., 32 (6), 858–872. Biczysko, M., Bloino, J., Santoro, F., and Barone, V. (2011) Time independent approaches to simulate electronic spectra lineshapes: from small molecules to macrosystems, Computational Strategies for Spectroscopy, from Small Molecules to Nano Systems, John Wiley & Sons, Ltd, Chichester, pp. 361–443. Barone, V., Bloino, J., Biczysko, M., and Santoro, F. (2009) Fully integrated approach to compute vibrationally resolved optical spectra: from small molecules to macrosystems. J. Chem. Theory Comput., 5 (3), 540–554. Avila Ferrer, F.J. and Santoro, F. (2012) Comparison of vertical and adiabatic harmonic approaches for the calculation of the vibrational structure of electronic spectra. Phys. Chem. Chem. Phys., 14, 13549–13563. Duschinsky, F. (1937) On the interpretation of electronic spectra of polyatomic molecules. Acta Physicochim. U.R.S.S., 7, 551. Herzberg, G. and Teller, E. (1933) Schwingungsstruktur der elektronenübergänge bei mehratomigen molekülen. Z. Phys. Chem. Abt. B, 21, 410–446. Santoro, F. (2008) ℱ 𝒞 𝑐𝑙𝑎𝑠𝑠𝑒𝑠, a fortran 77 code, visit http://www.pi.iccom.cnr.it/fcclasses. Lami, A. and Santoro, F. (2011) Time independent approaches to calculation of steady-state vibronic spectra: from fully-quantum to classical approaches, Computational Strategies for Spectroscopy, from Small Molecules to Nano Systems, John Wiley & Sons, Ltd, Chichester, pp. 475–516. Berliner, L.J., Eaton, S.S., and Eaton, G.R. (eds) (2000) Biological Magnetic Resonance, vol. 19, Chapter 12, Kluwer, Dordrecht/Plenum, New York. Cimino, P., Neese, F., and Barone, V. (2010) Calculation of Magnetic Tensors and EPR Spectra for Free Radicals in Different Environments, Wiley-VCH Verlag GmbH & Co. KGaA, pp. 63–104.

61

62

2 Computational Spectroscopy Tools for Molecular Structure Analysis 126. Polimeno, A., Barone, V., and Freed,

127.

128.

129.

130.

131.

132.

133.

134.

J.H. (2011) Stochastic methods for magnetic resonance spectroscopies, Computational Strategies for Spectroscopy, from Small Molecules to Nano Systems, John Wiley & Sons, Inc., pp. 549–582. Improta, R. and Barone, V. (2004) Interplay of electronic, environmental, and vibrational effects in determining the hyperfine coupling constants of organic free radicals. Chem. Rev., 104 (3), 1231–1254. PMID: 15008622. Rega, N., Cossi, M., and Barone, V. (1996) Development and validation of reliable quantum mechanical approaches for the study of free radicals in solution. J. Chem. Phys., 105, 11060. Brancato, G., Rega, N., and Barone, V. (2007) Unraveling the role of stereo-electronic, dynamical, and environmental effects in tuning the structure and magnetic properties of glycine radical in aqueous solution at different pH values. J. Am. Chem. Soc., 129 (49), 15380–15390. PMID: 18004849. Pavone, M., Biczysko, M., Rega, N., and Barone, V. (2010) Magnetic properties of nitroxide spin probes: reliable account of molecular motions and nonspecific solvent effects by timedependent and time-independent approaches. J. Phys. Chem. B, 114 (35), 11509–11514. Fau, S. and Bartlett, R.J. (2003) Gaussian basis sets for highly accurate calculations of isotropic hyperfine coupling constants at hydrogen. J. Phys. Chem. A, 107, 6648. Puzzarini, C. and Barone, V. (2010) Toward spectroscopic accuracy for open-shell systems: molecular structure and hyperfine coupling constants of H2 CN, H2 CP, NH2 , and PH2 as test cases. J. Chem. Phys., 133, 184301/1–11. Puzzarini, C. and Barone, V. (2009) Theoretical study of the X2NO systems (X = F, Cl, Br, I): effects of halogen substitution on structural and spectroscopic properties. J. Chem. Theory Comput., 5, 2378–2387. Demaison, J. (2007) Experimental, semiexperimental and ab initio equilibrium

135.

136.

137.

138.

139.

140.

141.

142.

143.

144.

145.

structures. Mol. Phys., 105 (23-24), 3109–3138. Allen, W.D., Czinki, E., and Császár, A.G. (2004) Molecular structure of proline. Chem.-Eur. J, 10, 4512. Kasalova, V., Allen, W.D., Schaefer, H.F. III, Czinki, E., and Csaszar, A.G. (2007) Molecular structures of the two most stable conformers of free glycine. J. Comput. Chem., 28, 1373. Jaeger, H.M., Schaefer, H.F. III, Demaison, J., Császár, A.G., and Allen, W.D. (2010) Lowest-lying conformers of alanine: pushing theory to ascertain precise energetics and semiexperimental Re structures. J. Chem. Theory Comput., 6, 3066. Helgaker, T., Jørgensen, P., and Olsen, J. (2000) Electronic-Structure Theory, John Wiley & Sons, Ltd, Chichester. Vaquero, V., Sanz, M.E., López, J.C., and Alonso, J.L. (2007) The structure of uracil: a laser ablation rotational study. J. Phys. Chem. A, 111, 3443. Godfrey, P.D. and Brown, R.D. (1995) Shape of glycine. J. Am. Chem. Soc., 117, 2019–2023. McGlone, S.J., Elmes, P.S., Brown, R.D., and Godfrey, P.D. (1999) Molecular structure of a conformer of glycine by microwave spectroscopy. J. Mol. Spectrosc., 485–486, 225–238. Stepanian, S.G., Reva, I.D., Radchenko, E.D., Rosado, M.T.S., Duarte, M.L.T.S., Fausto, R., and Adamowicz, L. (1998) Matrix-isolation infrared and theoretical studies of the glycine conformers. J. Phys. Chem. A, 102 (6), 1041–1054. Huisken, F., Werhahn, O., Ivanov, A.Y., and Krasnokutski, S.A. (1999) The O-H stretching vibrations of glycine trapped in rare gas matrices and helium clusters. J. Chem. Phys., 111, 2978. Espinoza, C., Szczepanski, J., Vala, M., and Polfer, N.C. (2010) Glycine and its hydrated complexes: a matrix isolation infrared study. J. Phys. Chem. A, 114 (18), 5919–5927. Bazso, G., Magyarfalvi, G., and Tarczay, G. (2012) Near-infrared laser induced conformational change and uv laser photolysis of glycine in low-temperature matrices: observation of a short-lived conformer. J. Mol. Struct., 1025, 33–42.

References 146. Bazso, G., Magyarfalvi, G., and Tarczay,

147.

148.

149.

150.

151.

152.

153.

154.

G. (2012) Tunneling lifetime of the ttc/VIp conformer of glycine in lowtemperature matrices. J. Phys. Chem. A, 116 (43), 10539–10547. Balabin, R.M. (2012) Experimental thermodynamics of free glycine conformations: the first Raman experiment after twenty years of calculations. Phys. Chem. Chem. Phys., 14, 99–103. Barone, V., Biczysko, M., Bloino, J., Egidi, F., and Puzzarini, C. (2013) Accurate structure, thermodynamics, and spectroscopy of medium-sized radicals by hybrid coupled cluster/density functional theory approaches: the case of phenyl radical. J. Chem. Phys., 138, 234303/1-14. Tanaka, T., Oelgemöller, M., Fukui, K., Aoki, F., Mori, T., Ohno, T., and Inoue, Y. (2007) Unusual CD couplet pattern observed for the pi∗ 90∘ . The rotatory strength has the same magnitude but opposite sign for a particular transition in a pair of enantiomers and, as a consequence, their CD spectra are mirror images of each other. A chiroptical property, which is also related to the rotatory strength, is ORD, a rotation of LPL when interacting with a chiral molecule at different wavelengths (𝜆). Quantum mechanics (ab initio) is able to predict the energy as well as the D and R of electronic transitions and, therefore, the UV/Vis and CD spectra of any chiral molecule can be simulated (Figure 3.5). Programs such as Gaussian 09 give the optical rotation for the required 𝜆. Similarly, the IR and VCD spectra can also be theoretically predicted.

Figure 3.5 ETDM (black bar) and MTDM (light gray bar) representation for the lowest electronic transition of (P,P,P,P)-(−)alleno-acetylenic macrocycle simulated with ZINDO [4]. The angle between ETDM

and MTDM of the presented transition is about 180∘ for the (P,P,P,P)-(−) enantiomer while it is about 0∘ for the (M,M,M,M)-(−) enantiomer.

69

70

3 Absolute Configuration and Conformational Analysis of Chiral Compounds

Conformers spectra simulation

Potential energy surface

Boltzmann averaged spectra

Absolute configuration assignment

Figure 3.6 General procedure to determine the AC of a molecule with a combination of experimental and theoretically predicted chiroptical responses.

For the construction of the final chiroptical spectra, dipole and rotational strengths for each of the normal modes need to be converted to molar extinction coefficients. The simulation of the UV/Vis spectra can be easily carried out using the equation: 𝜀(𝜈) =

[ ( ] 𝜈 − 𝜈i )2 exp − √ 𝜎 4 ⋅ 2.296 × 10−39 π𝜎 Di 𝜈i

where 𝜎 is the bandwidth in electronvolt, taken as the mid-height width (typically 𝜎 ≈ 0.2–0.4 eV), while frequencies 𝜈 are in cm−1 [5]. Similarly, the ECD spectra can be obtained using the following equation: Δ𝜀(𝜈) =

Ri 𝜈i 2.296 × 10

√ −39

[ ( ] 𝜈 − 𝜈i )2 exp − . 𝜎 π𝜎

Chiroptical spectroscopies are dependent not only on the configuration but also on the conformation of the molecules and therefore the comparison of theoretically predicted and experimental ECD, ORD, and VCD is often used for the overall structural characterization of chiral molecules. Because of the chiroptical response dependence on the overall geometry of the system, establishment of the potential energy surface (PES) is necessary before spectral simulation. Generally, four steps should be followed to determine the AC of a molecule (Figure 3.6). After the PES has been surveyed, the spectra for all stable conformers significantly present in solution (typically with energy not higher than 3 kcal mol−1 above the global minimum) should be simulated. Subsequently, one needs to generate average spectra considering the relative population of the conformers as determined by the Boltzmann equation. Finally, a comparison of the averaged spectrum and the experimental one may yield the AC assignment. Within a domain of VCD spectroscopy there is an increasing compliance to a quantitative level of comparison, while within domains of ECD and ORD spectroscopies, the comparison is mostly qualitative. It is also important to note that when a molecule exhibits N chiral centers, it is sufficient to perform theoretical predictions on half of all possible (2N ) diastereomers, as chiroptical responses for the first half of diastereomers provide mirror image spectra of the other half of diastereomers. To optimize the number of calculations to be performed, one can create a theoretical model, explore PES, and perform chiroptical predictions on 2N−1 diastereomers and then obtain the full set of chiroptical data by multiplying chiroptical intensities by (−1).

3.4

Quantum Mechanical (Ab Initio) Methods for Predicting Chiroptical Properties

3.4 Quantum Mechanical (Ab Initio) Methods for Predicting Chiroptical Properties

The theoretical prediction of chiroptical properties has become one of the streamline applications of quantum chemistry in the last two decades. The most renowned program package that provides an ab initio tool box for predicting the chiroptical responses is Gaussian [6], with the lastly implemented G09 version. Even though computer programs such as Gaussian are available nowadays for nearly automated use as “black-box” applications, in order to avoid inaccurate chiroptical predictions and wrong conformational interpretations along with stereochemical assignments, users have to become aware of the scope of the computational methods under consideration. Reliable determination of the AC requires optimal choice of the computational method, also referred to as the level of theory: that is, HF, MP2, and DFT along with the selection of functionals and basis sets. For predicting electronic chiroptical properties, ORD and ECD, the most conferred quantum mechanical approaches are DFT and coupled-cluster (CC) theory [7]. The highly correlated wave function-based methods such as CC and complete active space self-consistent field (CASSCF) methods have been reported to be more accurate than any DFT functional. However, the challenge with such predictions is that they are substantially time consuming and are restricted to smaller molecules. The more cost-effective method of choice has hence been DFT. Even though the initial DFT-based calculations of ORD were not accurate near the resonance frequencies (region were electronic transitions occur), the improved implementation of the DFT method has overcome this limitation [8]. Furthermore, as emphasized in Section 3.6, when predicting optical rotation, it is essential to calculate this property at several wavelengths, especially when the theoretically predicted and/or experimentally obtained response at a given wavelength is less than ±100∘ . This rule holds true regardless of the choice of ab initio method for optical rotation prediction. Similarly to the discussion associated with ECD and ORD, higher electroncorrelation methods such as MP2 are computationally too demanding and hence are currently not suggested for predicting VCD. By now, it is generally accepted that DFT theory applied for VCD consideration yields more accurate results than the electron-correlation deprived HF approach. Wide adoption of DFT since the 1990s had brought its dominance in predicting chiroptical properties as it provides reasonably accurate results at moderate computational cost. The DFT theory mandates the selection of density functionals and basis sets. Hybrid functionals B3LYP and B3PW91 are most frequently used as they give the best agreement with experimental observations while simpler functionals yield less accurate results even when combined with relatively large basis sets [9]. Furthermore, it is worth noting that the new hybrid exchange–correlation functional, the so-called Coulomb attenuated approximation B3LYP (CAM-B3LYP) functional, has been shown to provide a more optimal reproduction of both the position and the intensity of the experimental ECD peaks in comparison

71

72

3 Absolute Configuration and Conformational Analysis of Chiral Compounds

to the generally more popular hybrid B3LYP functional [10–13]. It is worth noting additionally that recent chirality studies have alluded to the use of a newer generation DFT functional, the so-called M06-2X, which has been reported [14] to provide good accuracy in reproducing relative stabilities of conformers in solution. In terms of the basis sets, the current consensus is that the smallest level basis set recommended for chiroptical predictions is 6-31G* (also referred to as 6-31G(d)). In some cases, dramatic quantitative improvements have been noted by increasing the size of the basis set to TZ2P and cc-pVTZ [15]. Both polarization and diffuse basis sets such as 6-311++G**, cc-pVDZ, and cc-pVTZ are necessary to predict the important experimental VCD features for molecules with propensity for intra- or intermolecular interactions. Also, in particular cases, reliable ECD and ORD predictions require the use of moderate to large basis sets (i.e., 6-311++G**, cc-pVDZ, cc-pVTZ) [16]. The intensity and occasionally even the sign of chiroptical responses are sensitive to the molecular environment. The chiroptical response perturbations induced by solute–solvent interactions translate into the need for ab initio solvent consideration in cases where such interactions are anticipated. If a specific directional solute–solvent interaction is known, then spectral effect should be considered with an explicit solvent model [17]. As an example, in VCD spectroscopy, the shift of experimental vibrational absorption (VA) bands can provide insight into intermolecular interactions (i.e., H-bonding typically results in lower frequency stretching modes due to borrowed electron density). When employing an explicit solvent model, prior to subjecting the chiral solute–solvent system to geometry optimization, one should apply either Monte Carlo or molecular dynamics algorithms to determine the optimal initial orientation(s) of the explicit solvent relative to the chiral solute. A less rigorous prediction, which also accounts for solvent effect implicitly, involves the use of polarizable continuum solvent models (IEF-PCMs being the most popular) or conductor-like screening solvent models (CPCM, COSMO) [15]. It is worth noting that recently there have been suggestions that in order to achieve a more efficient geometry optimization of the system that includes an explicit solvent model, one should simultaneously apply the corresponding implicit solvent model. The sole implementation of the implicit solvent model is suitable for case studies where Van der Waals intermolecular interactions are dominant, as the exact directionality of those interactions is more ambiguous. With respect to the calculated vibrational frequencies, in VCD spectroscopy these are usually overestimated and hence should be downscaled by a constant that is dependent on the specific basis set used. The effect that causes nonuniform shifts in predicted VA and VCD band positions relative to the observed ones is attributed to vibrational anharmonicity. Similarly, scaling and/or shifting of the predicted ORD or ECD are generally accepted to provide a better resemblance with the experimental data. Future improvements of the application of ab initio methods will need to account for these effects. Nevertheless, rapid improvements within quantum theory models as well as computational power capacities are

3.5

Electronic Circular Dichroism (ECD)

paving the way for elucidating the structure of increasingly more complex chiral systems.

3.5 Electronic Circular Dichroism (ECD)

ECD is the most used chiroptical method to date. Firstly, it has been used with empirical correlation rules such as the octant rule. However, the application of this method is limited by the need for particular prerequisites in the structure of the studied chiral system. For example, the exciton chirality method, successfully applied in a large number of cases, needs the presence of two appropriate chromophores in a molecule. Thanks to the fast development of ab initio methods, nowadays ECD combined with theoretical simulations can be used in the stereochemical elucidation of a broader variety of compounds. It is worth mentioning that even though majority of ab initio-based ECD studies are complemented by solution-state experimental measurements, in more recent years there have been reports on successful ECD studies on solid state [18]. The key reported advantage of solid-state ECD applications is that by knowing the solid-state geometry (X-ray structure), one may use it as the input structure for ab initio ECD calculations and hence bypass the challenges associated with the conformational flexibility in a solution state. Nonetheless, great care should be taken in avoiding artifacts due to linear birefringence effects and intermolecular interactions in solid state. 3.5.1 Advantages of ECD

• Very small amount of compound is needed due to its high sensitivity (of about 10−5 M solutions are required).

• Very easy to measure. The same sample can be used for UV/Vis measurement. • Availability of ECD spectrometers. • When suitable chromophores are present the AC can be easily assigned by exciton chirality. 3.5.2 Limitations of ECD

• The molecule should contain chromophores, with UV/Vis absorption(s) in order to enable the appearance of Cotton effects in the ECD spectrum.

• Only few different bands are present in the spectra because of moderate to low signal resolution.

• The theoretical prediction of the spectra needs the prediction of electronic excited states.

• The presence of significant vibronic coupling may hamper the analysis.

73

3 Absolute Configuration and Conformational Analysis of Chiral Compounds

3.5.3 Applications of ECD

The text below describes several ECD spectroscopic methods that have been developed over the years for the purpose of establishing the AC assignment of chiral molecules. 3.5.3.1 Empirical Methods

The presence of positive and negative bands in the ECD spectrum, known as Cotton effects, is an empirical evidence for the existence of chiral systems in an isotropic medium. In this way, just the presence of ECD bands has been proved to be very efficient in the relative configurational assignment. As an example, the synthesis of allenophanes was carried out starting from racemic allenes providing a diastereoisomeric mixture. Even though nuclear magnetic resonance (NMR) techniques helped in the assignment of some of the diastereoisomers, they could not discriminate between a few isomers with very similar symmetry. The ECD analysis of different fractions resolved via HPLC using a chiral stationary phase (CSP) was crucial to discriminate between chiral and achiral stereoisomers (Figure 3.7). The enantiomeric isomers present mirror image spectra while the achiral isomers do not show any signal in the ECD [19]. A semi-empirical method, the so-called “octant rule,” has been used for the characterization of saturated ketones and aldehydes [20]. These intrinsically achiral chromophores show a n → π∗ transition in the UV region (∼300 nm). According to this rule, the carbonyl group is placed in the center of three nodal planes dividing eight sectors. Any atom or group of atoms located at a particular sector will contribute to the CD signal with a positive or negative term defined by the particular sector. The summation of all contributions will give the estimated CD band (Figure 3.8). Originally formulated on the basis of empirical observations, the octant rule has later received a significant theoretical support [21]. 10 8 6 4 2 0 −2 −4 −6 −8 −10 230

Δε (mdeg)

74

255

280

305 λ (nm)

330

355

Figure 3.7 ECD spectra in CH2 Cl2 of the HPLC fractions of a resolved allenophane racemate [19].

3.5

Front octants

O

C

Electronic Circular Dichroism (ECD)

Rear octants

–

+

+

–

+

–

–

+

Figure 3.8 The nodal planes of the chromophore define eight octants; the signs of the contributions to the CD of the band around 300 nm are shown [22].

However, when more than one group is located in oppositely signed octants, it may not be clear which has the larger contribution. Additional challenge associated with this empirical rule is that the presence of more than one conformer may decrease the reliability of configurational assignments [22]. Very recently, in a case study where application of the octant rule was taken into consideration, yet concluded as not suitable, derivatization of a diketone was undertaken in order to determine its AC using the exciton chirality method (see below) [23]. 3.5.3.2 Exciton Coupling

Interchromophoric interaction in chiral molecules may induce a bisignated CD response referred as exciton coupling. The measurements of UV/Vis or ECD spectra in a solution are typically performed at concentrations around 10−3 to 10−4 M or below. Under these conditions, the average intermolecular distance is longer than 10 nm, and consequently for compounds having 𝜀 < 104 M cm−1 the interaction between two molecules can be neglected. In a molecule bearing two identical chromophores with no conjugation between them, both chromophores have the same probability to undergo an electronic excitation and therefore split into two degenerated transitions, namely, one of lower and the other of higher energy than the monomer excited state. This phenomenon is referred to as Davydov splitting and is responsible for the exciton coupling in the CD spectrum [24]. As mentioned above, the ETDM 𝝁 is the vector that indicates the orientation in which the electron density is displaced upon excitation. However, when a chromophore is excited, both orientations along 𝝁 are equally probable for the electron displacement. Consequently, when two chromophores are very close to each other, in-phase and out-of-phase simultaneous transitions must be considered. In this case, three situations are possible considering the angle 𝜃 between them (Figure 3.9) [25]: • When 𝜃 = 90∘ , in-phase and out-of-phase excitations are equivalent and therefore the observed 𝜆max coincides with the energy absorption of the single chromophore 𝜆o .

75

76

3 Absolute Configuration and Conformational Analysis of Chiral Compounds

In-phase

Out-of-phase

μ1 = μ2 = μ1 + μ2 = Amax ∝(μ1 + μ2)2

θ = 90°

λo

θ < 90° More stable

λo

λ

θ > 90° More stable

λ

Figure 3.9 Representation of the possible situations considering the angle 𝜃 between 𝝁 of two chromophores present in a molecule.

• When 𝜃 < 90∘ , in-phase excitation is energetically less favorable than for the single chromophore since partial charges of the same sign are close to each other, while the opposite is true for the out-of-phase excitation. The in-phase 𝝁 is larger than the out-of-phase 𝝁 and therefore, 𝜆max < 𝜆o . • When 𝜃 > 90∘ , out-of-phase excitation is energetically less favorable than for the single chromophore since partial charges of the same sign are close to each other, while the opposite is true for the in-phase excitation. The in-phase 𝝁 is larger than the out-of-phase 𝝁 and therefore, 𝜆max > 𝜆o . The experimentally observed bisignated CD band can be used for the AC determination. When the less energetic band is negative followed by a more energetic positive one, it is referred to as a negative CD couplet and vice versa. According to a non-empirical rule, when looking through the center of both chromophores, if the shortest way from the front to the rear chromophore is counterclockwise, it is assigned a negative sign and it always presents a negative CD couplet (Figure 3.10). The opposite is true for a positive CD couplet. As an example, one could assign the AC of allene (M)-1 (Figure 3.10) [26]. As mentioned above, the presence of more than one carbonyl group may hamper the applicability of the octant rule; as a clear example, the dihydroxyl precursor of diketone (+)-2 was derivatized as the dibenzoate (+)-3 to apply the exciton chirality method (Scheme 3.1). A strong electronic transition along the long axis in benzoates makes them very suitable to generate exciton coupling. The negative exciton couplet presented by (+)-3 (Figure 3.11) along with a conformational analysis uncovers its AC to be (1S, 2S, 5S, 6S) [23]. The AC of diketone (+)-2 was assigned accordingly. In addition,

3.5

Electronic Circular Dichroism (ECD)

77 1000

80

800

200 0

0 –20

–200

–40

–400 –600

–60 N N

(M)-1

(a)

–800

–80 250

275

300

(b)

Figure 3.10 (a) Representation of (M)-1 and (b) ECD spectrum of (M)-1 (e.g. ≥ 91 : 9) recorded in hexane (black line), calculated ECD curve for (M)-1 at the TDDFT

325 350 λ (nm)

375

B3LYP/6-31G(d) level of theory (s = 0.08, scaled to 0.5, black dashed line), and rotational strengths for the different transitions (bars) [27].

BzO O

BzO

N

R

PhCOCI, DMAP TEA, DCM

N

Boc

O (+)−3

(+)−2

Scheme 3.1 Transformation of dibenzoate (+)-3 on the diketone (+)-2 [23].

the AC was confirmed by comparison of TDDFT simulated and experimental ECD spectra, similarly to the examples discussed below. Exciton chirality has been extensively used for the relative and absolute configuration determination of very complex molecules derivatized with benzoates or porphyrins [28–30], functioning as the interacting chromophores [31]. The dihedral angle of biaryls has been demonstrated to have a strong effect on the exciton coupling response [32]. More recently, exciton coupling theory in combination with theoretical calculations has served for the AC determination of several compounds. 3.5.3.3 ECD Simulation via Ab Initio Methods: Conformational Analysis and Determination of AC

As mentioned above, the interpretation of an ECD spectrum can be trivial occasionally. However, for most of the cases, this interpretation needs the assistance of ab initio calculations. Since chiroptical properties can be predicted theoretically, comparison of experimental and theoretical responses is a very powerful tool for conformational analysis and determination of AC.

–1000 400

–40

400

20

Rotational strength / –1 erg-esu-cm Gauss

600

40

10

Δε (M–1cm–1)

60

3 Absolute Configuration and Conformational Analysis of Chiral Compounds

10 8 6 4 Δε (M–1cm–1)

78

2 0 −2 −4 −6 −8

−10 200

225

250

275

300

λ (nm) Figure 3.11 ECD spectra of dibenzoate (+)-3 presenting a negative exciton coupling [23].

Chiroptical responses, in general, are very sensitive to the geometry of the molecules. Therefore, it is crucial to establish the pool of possible conformers prior to chiroptical response simulation. The simplest situation is when only one conformer is possible. As an example, the ECD of the allenic compound (M)-1 presented above showing exciton coupling has also been predicted at the TDDFT B3LYP/6-31G(d) level of theory. As shown in Figure 3.10, the exciton coupling centered at ∼315 nm is very well resembled by the theoretical simulations, thereby further confirming the AC determined by the exciton chirality method [27]. Expectedly, the ECD-based analysis is more complex when the molecule is more flexible and consequently exhibits multiple stable conformers. An example of such case study is the investigation of thiazolopyrimidine (±)-2, which was synthesized as a racemic mixture and the two enantiomers were resolved using HPLC on a CSP [33]. In order to determine the AC of both enantiomers, ECD was measured showing two clear Cotton effects at 380 and 280 nm (Figure 3.12). Exploration of the PES by manual rotation of torsion angles followed by optimization and frequency calculations at the B3LYP/6-31G(d) afforded five conformers (R)-4a–4e in an energy range of 0.2 kcal mol−1 (Figure 3.13). Since all conformers are very close in energy, upon applying Boltzmann equation, it was found that they are all significantly present in solution. Accordingly, the ECD spectra for conformers (R)-4a–4e were predicted at (TD)-B3LYP/6-31G(d), and the Boltzmann-weighted theoretical spectrum was compared with the experimental one. As depicted in Figure 3.12, the predicted

3.5

Electronic Circular Dichroism (ECD)

20 15 10

Δε (M–1cm–1)

5 0 –5 –10 –15 –20 230

280

330

380

430

480

λ (nm) Figure 3.12 ECD spectra. Experimental spectra in CHCl3 of (R)-4 (gray line) and (S)-4 (gray dashed line) and Boltzmann-weighted ECD simulation for (R)-4 (black line) at the TD-B3LYP/6-31G(d) level of theory [33].

(R)-4a O O

O

O

(R)-4b

N N

S Br

Br

OH

(R)-4c

(R)-4e

(R)-4d

Figure 3.13 Conformers (R)-4a–4e at the TD-B3LYP/6-31G(d) level of theory [33].

79

80

3 Absolute Configuration and Conformational Analysis of Chiral Compounds

N N N N

N N

N N (M)-5

N

N

Figure 3.14 Structure of bis-TCBD (M)-5 [27].

ECD spectra (R)-4a–4e resemble very well the experimental ECD for one of the resolved enantiomers, and therefore the AC could be assigned unambiguously. As chiroptical responses are very sensitive to the conformation, this phenomenon is often used to determine the conformation of chiral molecules in solution. The reaction of tetracyanoethene with electron-rich acetylenes is a very efficient reaction leading to tetracyanobutadienes (TCBDs). In this respect, reaction of the above-mentioned (M)-1 with TCNE yielded bis-TCBD (M)-5 (Figure 3.14) [27]. The experimental ECD spectrum exhibits a remarkable Cotton effect at 530 nm. Since electronic transitions around this energy are assigned to charge transfer from the aniline moieties into the TCBDs, this chiroptical response suggests a chiral induction from the allene to the neighboring TCBDs [27]. In order to verify this assumption, simulation of the ECD spectra was performed. Manual scanning was undertaken to characterize the PES of (M)-5 with systematic torsion angle modifications every 60∘ for the TCBD moieties. A total of 18 initial geometries were optimized at the B3LYP/6-31G(d) level of theory leading to 15 different conformers, (M)-5a–5o, characterized as true minima by the frequency calculations at the same level of theory. However, the global minimum (M)-5b is 3.9 kcal mol−1 more stable than the second less stable conformer, and, therefore, it is expected that (M)-5b is the only conformer significantly present in solution. In this conformation the bulky tert-butyl groups of the (M) allene induce an opposite twist into both neighboring TCBDs (Figure 3.15). The simulated ECD spectra for this conformer at the (TD)-B3LYP/6-31G(d) level of theory are in good agreement with the experimental ones, enabling the conformational assignment of (M)-5 in solution. This geometry is very close to the one found in solid state by X-ray [27]. In order to verify the reliability of ECD for the conformational assignment of (M)-5, the ECD of conformers (M)-5i and (M)-5n, which have an opposite twist for one and two TCBD moieties respectively compared to the global minimum, were simulated and compared with the experimental ECD for (M)-5 in CH2 Cl2 and predicted ECD for (M)-5b. As shown in Figure 3.16, in this case study, CD was very sensitive to small conformational changes, underlining the reliability of this method for conformational assignment.

3.5 40

Electronic Circular Dichroism (ECD)

81

300 +69

+69

250

30

200 20

150

–1

Δε (M cm )

50 0

–1

0

−50

–10

−100 −150

–20

Rotational strength / 10–40 erg-esu-cm Gauss–1

100

10

(M)-5b

(b)

−200

–30

−250

–40 300

350

400

450

(a)

500

550

600

650

−300 700

λ (nm)

(c) obtained via B3LYP/6-31G(d) geometry optimization; arrows show positive conformational helicity across both TCBDs. (c) Overlay of the geometry for the global minimum (M)-5b (B3LYP 6-31G(d)) and the geometry obtained from X-ray crystallographic analysis (CCDC-691333) [27].

Figure 3.15 (a) CD spectrum of (M)-5 (recorded in CH2 Cl2 (black line)), calculated CD curve for (M)-5b at the TDDFT B3LYP/631G(d) level of theory (s = 0.10, scaled to 1.0, gray line), and rotational strengths for the different transitions (gray bars). (b) Global minimum-energy conformer (M)-5b

(–)

NC

CN NC

CN

NC NC

(+)

CN CN

NC

CN NC

CN

NC NC

Δε (cm–1cm–1)

(+) 80 50 40 30 20 10 0 –10 –20 –30 –40

300

350

400

(–) CN CN

NC

CN NC

CN

NC NC

250

(–)

450 500 λ (nm)

(+)

(M)-5n

(M)-5i

(M)-5b

CN CN

550

600

650

700

Figure 3.16 From top to bottom: calculated CD curves for (M)-5n, (M)-5i, and (M)-5b (s = 0.10, scaled to 1.0) at the TDDFT B3LYP/6-31G(d) level of theory, and CD spectrum of (M)-5 recorded in CH2 Cl2 [27].

82

3 Absolute Configuration and Conformational Analysis of Chiral Compounds

3.5.4 Challenge due to Vibronic Coupling

Vibronic coupling originates from the interaction between vibrational and electronic transitions. Often, this phenomenon hampers the correct prediction of UV/Vis and ECD spectra by simply considering electronic transitions. Particularly, molecules bearing acetylene groups typically present fine structures in the UV/Vis spectra with spacing between the bands of about 2200 cm−1 , corresponding to the vibrational frequency of the acetylene bond stretch. As an example, the shape persistent alleno–acetylenic (P,P,P,P)-(−)-6 [4] presents a strong vibronic coupling in the ECD spectrum (Figure 3.17). Both the system size and the presence of high density of states around the transition originating the vibronic coupling disable the prediction of the fine structure present in the UV/Vis and ECD. However, when comparing the theoretical ECD spectra at different levels of theory without considering the vibronic coupling with the experimental one, the overall agreement allows the AC elucidation of this complex system [34]. On the other hand, the calculation of the Franck–Condon integrals on the simpler system presented in Figure 3.18 could successfully reproduce the experimentally observed vibrational progression bands. This phenomenon splits the electronic transition at 330 nm into several vibronic bands. The good agreement between experimental and theoretically predicted spectra of (P,P)-7 was used for the conformational preference of acyclic chiral oligomers in solution (Figure 3.18) [35].

3.6 Vibrational Circular Dichroism (VCD)

The VCD method, with the first reported measurement dating to 1974 [36], represents the youngest analog of CD-based spectroscopy. It originates from vibrational transitions within the ground electronic state of a molecule, triggered by the IR domain of circular polarization. The appreciation of VCD spectroscopy as a method for reliable AC assignment has increased exponentially in the past four decades, as evidenced by the corresponding increase in the number of successful reported cases. The basic considerations needed for carrying out a VCD measurement are as follows: the criterion that dictates the combination of the sample concentration and path length used in an experiment is the need for the VA band to be in the range 0.2–1 (absorbance units). Typical sample concentrations required are 1–50 mg ml−1 , with volumes ranging from 30 to 100 μl needed to fill up the 25–100 μm path length cell. Typical solvents used are CCl4 , CS2 , CH3 OH, CHCl3 , CH2 Cl2 , CH3 CN, DMSO, H2 O and often, their deuterated analogs. The listed pool of solvents is considered to be relatively IR “silent.” The solvent choice is dictated by the need for minimal interference of the solvent’s absorption in

3.6 Vibrational Circular Dichroism (VCD)

83

1000

800

Δε (M–1cm–1)

500 S2 and S3

1000

0

–500

600 –1000

400 –1 –1

250

300 λ (nm)

350

0

0

10 –1000

–400 –600

–2000

S1 –800 –1000 200

–3000 220

240

260

280

300

320

340

Rotational strength / –1 erg-esu-cm Gauss

–200

–40

Δε (M cm )

200 200

(P,P,P,P)-6

360

λ (nm)

Figure 3.17 Experimental (black line) and simulated CD spectrum of (P,P,P,P)-(−)-6 (gray line, scaled by 0.6, not shifted, rotational strength in gray bars) at the CAM-B3LYP/6-31G(d) level of theory. The inset shows experimental (black line) and simulated CD spectrum of (P,P,P,P)-(−)-6 at the HF/6-31G(d) (dashed black line scaled by 0.2, not shifted), ZINDO (dashed gray line scaled by 0.4, not shifted), and CAM-B3LYP/6-31G(d) (gray line scaled by 0.6, not shifted) levels of theory [34].

3 Absolute Configuration and Conformational Analysis of Chiral Compounds

100 000 90 000 80 000 70 000 θ 60 000 ε (M–1cm–1)

84

(P,P)-7

50 000 40 000 30 000 20 000 10 000 0 200

220

240

260

280

300

320

340

360

λ (nm) Figure 3.18 Black line: calculated electronic UV/Vis at the HF/6-31G(d) level of theory (20 transitions, blue-shifted 1 eV, 𝜎 = 0.2, scaled by 3.0). Black dashed line: Franck–Condon prediction for transition 2 at the HF/6-31G(d) level of theory (blue-shifted 0.05 eV, 𝜎 = 0.07,

scaled by 2.0) of (P,P)-(+)-7. Gray line: summation of the FC trace and the electronic UV/Vis trace excluding the transition 2. These calculations were performed on (P,P)-(+)-7 with 𝜃 = +45∘ with tert-butyl groups substituted by protons [35].

the frequency region of anticipated vibrational normal modes of the sample. Deuterated samples are beneficial for shifting away the solvent band that could be potentially interfering with sample bands (i.e., strong hydroxyl group bending modes of H2 O at ∼1500 cm−1 are shifted to 1250 cm−1 in the case of D2 O). The IR region of electromagnetic radiation spans three subregions: near-IR, mid-IR, and far-IR. Upon absorbing mid-IR radiation (800–4000 cm−1 ), functional groups within a molecule engage in normal modes (stretching and bending motions). Since mid-IR region arises from fundamental vibrational normal modes that can be reliably predicted via ab initio calculations, this region is the best choice for determining molecular stereochemistry. Despite the fact that VCD activity can be experimentally detected in the near and far-IR regions, theoretical predictions, measurements, and interpretations are not routinely feasible at this point in time. For example, the presence of overtones and combination bands in the near-IR region represent a challenge for the VCD interpretation. Similarly to UV and ECD intensities, the theoretical quantities appropriate for VA and VCD intensities of normal modes are dipole strength (D) and rotational strength (R), respectively. The Lorentzian band shape is used for simulating the VCD trace with a bandwidth of ∼6–10 cm−1 . Typically, global scale factors

3.6

Vibrational Circular Dichroism (VCD)

(i.e., 0.9613 for 6-31G* basis set) are applied to compensate for the harmonic overestimation of the simulated frequencies. In the qualitative interpretation of VCD spectra, the correct signs of the R parameter are crucial when assigning AC, while the accuracy of the magnitude of the R is less important. For the purpose of determining the AC, it is sufficient to compare predicted and experimental mid-IR VCD signs on a qualitative level. However, if an additional goal is to determine the populations of individual conformers, then quantitative comparison is desirable. In the past few years, several VCD studies have emphasized the importance of establishing an intrinsic measure for the identification of overly sensitive, and, hence, unreliable theoretical VCD bands. Two such recently developed methodologies include the robustness concept and 𝜻-factor analysis, with 𝜻 = R/D [37–40]. According to the definition of robustness, if the angle between ETDMs and MTDMs is close to 90∘ (±30∘ ), then a given band is not to be considered robust, which means that it is not reliable. Furthermore, in a recent report, Góbi et al. [9] have suggested that if the magnitude of the so-called 𝜻-factor is below 10 ppm, the associated band can be disregarded from the correlation. Even though both analyses have been recently applied in investigations of a few chiral systems, these reliability gauges have not yet been widely tested and verified in terms of suitability for broad application [41]. Most recently, a new robustness criterion has been suggested [42] to be applied not only to calculated VCD and VA spectra, but also to the experimental analogs. This newest method, based on the so-called dissymmetry factor as imposition of robustness, seems to have the potential to be the most practical as it considers robustness of regions of the VCD spectra rather than of individual transitions. Certainly, future publications will show which method serves as the most practical quantitative measure of the simulated–experimental correlations within the VCD spectroscopy in order to increase the confidence level of the AC assignment. 3.6.1 Advantages of VCD

• The investigated chiral molecules do not need to have any chromophoric groups, as every vibrational normal mode is a potential chirality probe. For nonlinear molecules with N atoms there are 3N –5 normal modes, each of which could be structurally diagnostic. As a consequence, VCD spectra typically have a richer structural content and hence AC assignment involves correlation of multiple bands. • In contrast to NMR, which yields weighted averages for fast molecular movements, VCD detects each species present as a linear combination of all contributing conformers. Therefore, in the case of more flexible molecules, the higher spectral resolution of VCD allows simultaneous elucidation of configuration and conformation. • Reliable theoretical support is another advantage of the VCD methodology. Namely, ab initio predictions of VCD are typically reliable as they are within

85

86

3 Absolute Configuration and Conformational Analysis of Chiral Compounds

the ground electronic state with a much lower probability for incorrect interpretations. 3.6.2 Limitations of VCD

• VCD probes chirality less efficiently compared to ECD, since the signals are ∼three–four orders of magnitude smaller. This limitation is the outcome of the fact that (i) mid-IR light probes chirality less efficiently than the UV/Vis light and (ii) mid-IR detectors are intrinsically less sensitive at this stage of instrumental development. • In the case of VCD, the chiral susceptibilities for nuclear vibrations are considerably smaller than the corresponding signals in the UV/Vis range. Competition of such weak effect with largely fluctuating incident IR beams is the reason why it typically takes 1–3 h data accumulation time to acquire statistically meaningful VCD spectra. • Detectors are inherently less sensitive than the ones used in ECD methodology. As a result the acceptable signal-to-noise ratio mandates not only longer accumulation time but also higher concentration (1–50 mg ml−1 ). Nevertheless, the advantages have outweighed the disadvantages and VCD has acquired the status of a reliable and convenient tool for determining molecular stereochemistry. 3.6.3 Application of VCD

Four levels of complexity can be encountered during the AC assignment of chiral molecules as tackled by VCD spectroscopy:

• AC assignment of moderately flexible molecules with one chiral center • AC assignment of flexible molecules with more than one chiral center • Establishing solute–solvent and solute–solute intermolecular interactions of chiral molecules

• AC assignment via VCD exciton coupling methodology, the future perspective. It should be noted that the utility of VCD provided in the examples that follow is frequently, yet not universally, applicable. 3.6.3.1 AC Assignment of Moderately Flexible Molecules with One Chiral Center

An example of a molecule with moderate conformational flexibility and with a single chiral center is an isolated chromane (+)-8 presented in Figure 3.19 [43]. The survey of the PES has been initially simplified by performing molecular mechanics conformational search on the fragment molecule 9. Conformers within the 6 kcal mol−1 energy window have been subjected to geometry optimization at the B3LYP/6-31G(d) level of theory. Among the 54 conformers calculated, 11 (each with Boltzmann population >2%) were selected to build up the whole molecular

3.6

Vibrational Circular Dichroism (VCD)

OH

87

OH

R1

R1 c-2

c-2 O (R)

O

8a R1 = H 8b R1 = COOH

9a R1 = H 9b R1 = COOH

(a)

(b)

Figure 3.19 (a, b) Structure of chromane 8 isolated from leaves of Peperomia obtusifolia and its fragment analog 9 used for more efficient conformational search [43].

0 −50 50

15 10 5 0 −5 −10 −15

Observed VCD 96

Conformer 3 96

94

77 83 87

82 80

95

73

79

74

86

66

65 64

71

Molar absorptivity (ε)

77

Conformer 2

−50 Conformer 1

200 100 0

77

74

105 82 101 98/96 89 88 80 94/93 86 83 79 92

68 64 77

Calculated IR

(R)-8a

300

89/88 74

0 98/96 94 93 101 92

−50

40 20 0 −20 −40 −60

(+)-8a

Observed IR

105

(a)

(R)-8a

89

0

−100

74 71

79

88

92

66 65 64

73

80

86

89

105

−100 50

83 82 87

Calculated VCD

−50

−100 50

(+)-8a

88

92

95

105

0 Δε X 103

94

200

83 82 86

80 79

68 64

100 0

1400

1300

1200

1100

1000

Wavenumber (cm−1)

Figure 3.20 (a) Displays calculated VCD spectra for four stable, low-energy conformers of (R)-8a. (b) Provides comparison of VA and VCD spectra measured for (+)-8a

1400

(b)

Δε X 103

Δε X 103

Conformer 4

1300

1200

1100

Wavenumber (cm−1)

with the analogous calculated spectra of the Boltzmann average of the four lowest energy conformers of the (R)-8a [43].

model of (R)-8. After full geometry optimization of (R)-8, four lowest energy conformers with an overall 80% Boltzmann population were considered for the VCD calculations. The predicted VCD spectra for the individual conformers of (R)-8a are presented in Figure 3.20a, while the correlation between experimental and Boltzmann averaged theoretical spectra are presented in Figure 3.20b. It is worth noting that differences in the VCD spectral traces among the four most stable conformers exemplify the capacity to distinguish and hence identify the different conformers

1000

Molar absorptivity (ε)

50

88

4′′′

3 Absolute Configuration and Conformational Analysis of Chiral Compounds

O

OH

2′′′ 1′′′ O

+ O C-2 (+)-10 Figure 3.21 Structure of monoterpene chromane ester (+)-10 isolated from leaves of Peperomia obtusifolia along with VCD spectral traces as localized responses of monoterpene versus chromane segments of the molecule [47].

present in solution based on the VCD spectra. While VCD of the three most stable conformers (conformers 1–3) are more qualitatively similar, the spectral signature is notably different for conformer 4, especially in the region ∼1000–1200 cm−1 . The key difference among conformers 1–3 and conformer 4 is the axial versus equatorial position of the bulky isoprenoid chain at C-2 (Figure 3.19). The satisfactory agreement between experimental and Boltzmann-weighted theoretical VCD spectra validates conformational dominance of the axial orientation of the isoprenoid chain. Furthermore, the confidence level for the assignment of (+)-8 to (R)-8 with (P)-helicity of the chromane ring is reflected in the highly satisfactory correlation between multiple experimental and theoretical VCD bands. In the present case study, VCD serves as a reliable probe of both the AC and predominant conformers in solution. It should be noted, however, that in less prominent cases, VCD can suffer from the existence of too many conformers [44, 45]. Few studies, such as VCD-based investigation of 1,2 and 1,3-diols, have engaged in chemical “rigidification” of the mobile groups to amplify the VCD signals and hence provide an unambiguous AC analysis [46]. 3.6.3.2 AC Assignment of Flexible Molecules with More Than One Chiral Center

VCD displays a capacity to reliably distinguish between diastereomers. Compound 10 is also chromane based similarly to 8, yet a closer inspection of its structure (Figure 3.21) promptly suggests two reasons for a higher level of complexity in assigning the AC than in the previous case study: first, the presented monoterpene chromane ester [47] is endowed with more than one chiral center; second, it exhibits considerable conformational flexibility, implying that each of the diastereomers could possibly have several conformations. The lack of UV/Vis chromophores within the monoterpene moieties makes VCD the best choice for structural characterization. Once the relative stereochemistry has been assessed for the monoterpene segment (1′′′ , 2′′′ , 4′′′ ) via NMR, the VCD-based challenge was to establish the relative stereochemistry at C-2 and subsequently determine the AC at each of the four chiral centers. Figure 3.22 presents a very good agreement between the spectra of one of the (+)-diastereomers and those calculated for (2R, 1′′′ S, 2′′′ R, 4′′′ S) using two levels of theory. A thorough spectral analysis unveils the presence of

3.6 B3PW91/TZVP

132

149

194

35

142 139

180/167 192

300

189

196

Molar absorptivity (ε)

127 122

160

0

B3LYP/6-31G* 600

194

192

166 167 174 160 155 189

196

194

193

127 122

103 116 108

142 139

166

124 116

149

193

101 124 114 111 116 103

142

155 139 136

194 167

Observed VCD

122

(+)-10

124

193

122 116

0

103 108

194

−35

189

Wavenumber (cm−1)

Figure 3.22 (a) Displays experimental VA for two of the stereoisomers compared to the calculated VA of 10. (b) Displays experimental VCD for two stereoisomers, which are

167 155

101

130

162 149

127

103

122

130

0

35

111 101

136

(2R, 1′′′S, 2′′′R, 4′′′S)-10

162

−35

111 114 116 103

136 139 122

0 1800 1700 1600 1500 1400 1300 1200 1100 1000

(a)

139

167

35

130

180/167 155 160

192 196

−35

149

Observed IR

142

155 194

132

0

300

162 149

B3LYP/6-31G*

139

193

300

108103 116

132 130 142 132

149

193

0

166

89

130

B3PW91/TZVP

130

193

Δε X 103

600

Vibrational Circular Dichroism (VCD)

1800 1700 1600 1500 1400 1300 1200 1100 1000

(b)

Wavenumber (cm−1)

mutual enantiomers, compared to the calculated VCD, respectively for (+)-10 and (2R, 1′′′ S, 2′′′ R, 4′′′ S); calculated data are presented for two levels of theory [47].

localized VCD features that can be assigned to the monoterpene and chromane motifs separately, while other bands predominantly result from vibrations involving the rest of the molecular frame. For example, VCD bands labeled 101, 103, 111, and 116 (Figure 3.22) are due to vibrations localized within the monoterpenes and permit the identification of AC within this segment of the molecule. On the other hand, the VCD bands designated as 122 and 130 serve as diagnostic markers for the configuration at C-2. Specifically, as it pertains to the AC at C-2 chiral center, it has been noted that a negative and positive combination of 122 and 130 bands respectively accounts for the (R) configuration, whereas the opposite corresponds to (S). Finally, if the relative configuration of the molecule under study is unknown, one should simulate the VCD spectra for all possible diastereomers. As mentioned in Section 3.2, in cases where a molecule exhibits multiple chiral elements, only half of all possible diastereomers require VCD or, in general, chiroptical simulations. Therefore, in the present case study, 8 out of 16 possible diastereomers have been subjected to VCD simulations. The spectra of all diastereomers has been obtained by multiplying the VCD response by (−1) factor. The precaution of considering the VCD of all diastereomers ensures that satisfactory spectral resemblance with experimental spectra is displayed by only one theoretical model of a given AC.

90

3 Absolute Configuration and Conformational Analysis of Chiral Compounds

3.6.3.3 Establishing Solute–Solvent and Solute–Solute Intermolecular Interactions of Chiral Molecules

In recent years, VCD has opened up new horizons for identifying and monitoring intermolecular interactions, primarily of the H-bonding and van der Waals variety. Such investigations can be grouped into two categories: (i) studies of chiral induction of solvent due to solute–solvent interaction and (ii) studies that enable monitoring dimer, trimer, or high-order complex formation due to solute–solute interaction. For each category, representative studies have been selected to illustrate the relevance of VCD in providing the spectral fingerprint of intermolecular interactions. Solute–Solvent Interactions The newest findings demonstrate that the VCD modes of the non-chiral solvent molecule acquire significant rotational strengths upon forming H-bonding with a chiral solute. It was additionally found that the VCD spectra of different solute–solvent conformers often exhibit not only different shapes but also different signs reflecting the geometry of the complex. These generic changes in spectral features allow VCD spectroscopy to serve as a conclusive interpretation tool of the specific types of solute–solvent interactions. VCD investigation of interaction between D-lactic acid and water demonstrates the above-stated utility [41]. It was found that the lactic acid monomer is not the dominant form in the solution and that the clusters of lactic acid and water best reproduce the experimental VCD spectra [48, 49]. The calculated VCD spectra (Figure 3.23) of two different solute–solvent complexes demonstrate the ability to discern the characteristic spectral patterns associated with specific configuration of intermolecular H-bonding in the lactic acid–water complexes: (i) upon complexation, a non-chiral water molecule can acquire a VCD signal with significant rotational strength, specifically notable for bending modes at ∼1600 cm−1 , as seen in the spectrum of both 11-Ia and 11-IIa; (ii) the sign in rotational strengths of one of the stretching modes of water at ∼3600 cm−1 is opposite for both conformers (positive for 11-Ia and negative for 11-IIa), which demonstrates that VCD can be used as a discerning marker of the two H-bonding conformations; and (iii) besides the opposing sign of the stretching band, the intensity maximum of this band also exhibits a 30 cm−1 difference in frequency. This theoretically predicted frequency-based distinction is observable through VCD but hardly observable through IR intensities. Finally, theoretical VCD studies on even more complex models of lactic acid and water have been attempted. As can be seen from Figure 3.24, the stretching OH mode from COOH at 3315 and 3292 cm−1 has a different VCD sign and hence represents a diagnostic band between the two solute–solvent complexes [49]. In conclusion, since solute–solvent intermolecular interactions can even change the sign of some VCD transitions, the spectral interpretation has to be done with care. The strategy could be twofold: either intermolecular interaction effects have to be accounted for in the quantum mechanical treatment of VCD spectra or the intermolecular interactions during the VCD measurements have to be eliminated or at least minimized. From an experimental perspective, one

3.6

Vibrational Circular Dichroism (VCD)

150

11-ΙΙa

100

50

Strength

3635 0

−50

O −100

1607

−150

HO

−200 0

500

1000

1500

2000

(a)

OH

2500

Frequency 150

ΙΙa 11-ΙΙ

100

Strength

50

0

3603 −50

−100

1610 −150 0

(b)

500

1000

1500

2000

2500

3000

3500

4000

Frequency

Figure 3.23 (a,b) Calculated VCD spectra of the two stable solute–solvent conformations 11-Ia and 11-IIa displaying H-bonding interaction between D-lactic acid and water [49].

could select weakly interacting solvents to stabilize the monomeric form of a chiral solute. If the solubility allows, the formation of solute–solvent interactions can be avoided by resorting to CCl4 or other apolar solvents. In some cases, satisfactory estimation of the solvation effects on VCD spectra can be determined using implicit solvent models, such as the previously mentioned polarizable continuum (PCM, IEF-PCM) models. One way to rule out necessity for accounting for solute–solvent interactions is to make measurements in polar (CHCl3 ) and apolar (CCl4 ) media. This is conditioned by the ability to

91

3 Absolute Configuration and Conformational Analysis of Chiral Compounds 200

11-ΙΙaΙb VCD intensity 10−44esu2cm2

150

3315

1730

100

50

0

561

−50 −100 −150

1603

−200 0

500

1000

1500

2000

2500

3000

3500

4000

Wavenumbers (cm−1)

(a) 150

11-ΙaΙc 100

VCD intensity 10−44esu2cm2

92

1745 50

0

3292 −50

−100

0

(b)

1604

576

−150

500

1000

1500

2000

2500

3000

3500

4000

Wavenumbers (cm−1)

Figure 3.24 (a,b) Calculated VCD spectra of the two trimer conformations left 11-IaIb and right 11-IaIc of lactic acid–(water)2 [49].

dissolve the sample of interest in both solvent media. The implicit solvation model is sufficient if the spectra display no significant differences between solvents such as CCl4 and CHCl3. It is worth noting that one of the more recent investigations [50, 51] indicate that the inclusion of both explicit solvation and implicit solvation with the PCM is crucial to capture all the observed VCD features in addition to the observed VA bands and thus provide accurate information about conformational distributions. Accurate prediction of conformational distribution is ultimately imperative

3.6

Vibrational Circular Dichroism (VCD) 450

250

200

PENC 375 300

solv. PENC

150

PENC dimer

150 75

100

calc. Δε

NC

Δε [10−4]

225

CH3

solv. dimer

(S)-12

0 50 −75

exp 0

−150

1600

1500

1400

1300

1200

1100

1000

Wavenumber (cm−1) Figure 3.25 Comparison of the experimental VCD for (S)-12 (PENC) with VCD calculated for the isolated monomer, solvated monomer, dimer, and solvated dimer. Solvated monomer and dimer are in chloroform [52].

for reliable AC assignment of molecules with moderate to high conformational degrees of freedom. Solute–Solute Interactions The notion that VCD spectra can potentially be used to

better characterize the intermolecular solute–solute interactions (dimer, trimer, or even higher complex formation) comes naturally for this technique due to a need for higher sample concentrations [16]. If bulky groups do not inhibit the intermolecular solute–solute or solute–solvent interactions, comparison of the predicted spectra of the complexes with the experimental spectra recorded in relatively concentrated solutions is mandatory. A recent case study in which the solvated dimer had to be accounted for is that of (S)-α-phenylethyl isocyanide (PENC, (S)-12) in chloroform [52]. As can be seen from Figure 3.25, PENC is a small chiral molecule with only one relevant conformational degree of freedom associated with the phenyl moiety. According to the conformational search and geometry optimization analysis, there is only one conformation significantly present in solution. The results of spectral calculations for the energetically favored conformer are compared to the experimental spectra. Considering the fairly rigid nature of the small molecule in this case study, the experimental VCD spectra show only partially good agreement with calculated VCD for the monomeric form of (S)-12. There are two VCD segments that are not correlated with the calculations of the monomer. In particular, these are the negative peaks around 1100 cm−1 and the pattern between 1400 and 1300 cm−1 . In search for better spectral correlation, the authors have taken into account the implicit solvent model, explicit solvent model, dimer, and explicitly solvated dimer (Figure 3.26). VCD patterns arising from VA bands located at ∼1330 cm−1 change dramatically when going from the monomer

93

94

3 Absolute Configuration and Conformational Analysis of Chiral Compounds

(a) Isolated PENC

(c) PENC dimer

(b) Solvated PENC

–5∙10−2

5∙10−2 (d) Solvated PENC dimer

Figure 3.26 Molecular electrostatic potential mapped on the total electron density distribution for (a) (S)-12 monomer, (b) solvated monomer, (c) dimer, and (d) solvated dimer [52].

to the dimer. Thus, the introduction of the dimer and especially explicitly solvated dimer definitely serves as an improvement. The VCD spectrum of 𝛼-PENC in chloroform is one of the few examples for which both solute–solute and solute–solvent interactions have to be taken into account in order to obtain a good theoretical description of its structure in solution [17]. 3.6.3.4 AC Assignment via VCD Exciton Coupling Methodology – The Future Perspective

The most recent advance in applying VCD to establish AC has been to employ the exciton coupling method in the IR regime, which is an intriguing idea proposed by Taniguchi [53]. Similarly to the ECD-based exciton coupling methodology, bisignate VCD couplet originates from two chiral moieties (the most notably reported acetate and carbonyl chromophores qualify for VCD exciton coupling method, Figure 3.27; as a specific example, VCD of 13 is shown). VCD exciton couplet signals analyzed for a series of small molecules with two IR active groups lead to the recognition of two appealing prospects for applying the methodology [53, 54]: (i) it bypasses the need for expensive theoretical simulations as current evidence shows that experimental signals can be used for fast analysis of AC even if the overall molecules exhibits various conformations and

3.7 OAc O

MeO MeO AcO

OMe O

Me OMe

RO

AcO

OMe O

Me

0.2

Me

O

OO

0 Δε VCD

OMe AcO

(a)

1786

O

−0.1

Me O

O

−0.2

800

O AcO

O 13

0.1

AcO

O O AcO

O O

95

OH

OAc

MeO OMe

1805

OMe H

OMe

OAc

RO

Ph

Me

Me

Optical Rotatory Dispersion (ORD)

–

400 ε 0 1900 1800 1700 1600 1500 IR

O

(b)

Wavenumber (cm−1)

Figure 3.27 (a) Provides set of structures that are suitable for VCD exciton couplet method. (b) Provides VA and VCD exciton couplet response for compound 13 [53, 54].

(ii) the intrinsically weak VCD signal (e.g., carbonyl band region ∼1750 cm−1 ) is amplified by a factor of ∼20. This further translates into an advantage that the sample amount for the detection of VCD can be lowered by the exciton coupling effect. The approach has been tested for a pool of compounds with known absolute stereochemistries [53], and it is currently [55] one of the novel approaches in the configurational elucidation of new natural products. Overall, the proposed VCD exciton coupling method awaits further validation of its scope with future investigations.

3.7 Optical Rotatory Dispersion (ORD)

Optical rotation is the oldest of the chiroptical methods. Traditionally optical rotation (OR) was measured at the sodium D line (𝜆 = 589 nm) to provide the [𝛼]D values. However, optical rotation can be measured at different wavelengths, and as such, it is referred to as ORD. The specific rotation of a solution is expressed as [𝛼] = 100𝛼/lc, where 𝛼 is the measured optical rotation at a certain 𝜆, l is the path length in dm, and c is the concentration of the sample in gram per 100 ml of solution. The specific rotation is often used to determine the enantiomeric purity of a sample. It has also been used for the AC determination of several molecules using empirical rules. As mentioned for ECD, nowadays it is not recommended to solely rely on empirical rules but rather to compare experimental and theoretically predicted optical rotations. Optical rotation is very easy and quick to measure, with typically 1–10 mg of sample solubilized in about 1 ml of solvent. However, the rather high concentrations employed can favor the formation of solute–solute interactions that may increase the complexity of the analysis. To exclude the presence of this interference, measurements at different concentrations should be performed. The specific rotation at very small concentrations is

96

3 Absolute Configuration and Conformational Analysis of Chiral Compounds

α

nm

Figure 3.28 Hypothetical experimental (black line) and theoretical (dotted line) ORD curves. The theoretical prediction is energetically shifted from the experimental one [56].

called intrinsic rotation [57]. Chiroptical responses at low concentration are principally induced by an individual molecule and therefore those values are appropriate to be compared with the theoretically predicted intrinsic rotation. In the last decades, the development in computational chemistry has considerably improved the reliability in the predicted optical rotations. However, as it often happens in ECD and VCD, certain inaccuracy in the prediction of the energy of the transitions may provide theoretically predicted OR values shifted from the experimental ones. As illustrated in the boxed-in segment of Figure 3.28, when comparing the sign at a single wavelength of theoretical and experimental OR, a misassignment would occur [56]. This is the reason why ORD analysis is strongly recommended instead. Typically, a qualitative comparison between experimental and theoretical ORD curves is based on the overall trend curvatures. When using several wavelengths, an energy shift in the theoretical ORD prediction will not lead to an improper assignment. 3.7.1 Advantages of ORD

• • • •

Presence of UV/Vis-active chromophores is not needed. ORD can be easily implemented in the available ECD spectrometers. Very fast and easy to measure. Not affected by vibronic coupling.

3.7.2 Limitations of ORD

• Theoretical simulation of the spectra needs the prediction of electronic excited states.

• The low signal resolution makes ORD not suitable for flexible molecules with opposite responses for different conformers.

• Between 1 and 10 mg of sample is needed.

3.8

When More than One Method is Needed

Regularly ORD is chosen as a cross-validation method when ECD and/or VCD are not unambiguous. The use of a particular chiroptical method should take into account the nature as well as the amount of material in hand. However, often the use of more than one method is required, or at least recommended, as a crossvalidation for structure determination of challenging chiral molecules.

3.8 When More than One Method is Needed

Despite the fact that each individual method carries the capacity for independent stereochemical structural elucidation, in some cases combination of more than one method is desirable for two key reasons: (i) to increase the confidence level of the AC and conformational assignment and (ii) to bypass limitations of a given method either with respect to certain classes of chiral compounds or the experimental conditions. The text below provides examples of case studies in which tandem application of more than one chiroptical method was desirable and in some cases necessary. 3.8.1 Combination of ECD and VCD

The tripodal cyclotriveratrylene (CTV) (M)-14 and its enantiomer were prepared in a study to perform regioselective additions to C60 (Figure 3.29) [58]. The first assigned AC of (+)-14 was the same as that of a known derivative of a precursor. However, the low energetic barrier isomerization of these CTVs calls for the use of chiroptical methods in order to ascertain the AC assignment [58]. The PES of (+)-14 was explored using the force field MMFF implemented in MacroModel 9.5, followed by the optimization of the non-redundant conformers at the B3LYPT/6-31G(d)//AM1 level of theory (this notation means that first the optimization was performed at the AM1 level, followed by the B3LYPT/6-31G(d) levels of theory). The resulting three conformers are presented in Figure 3.29. The ECD spectrum was measured and simulated using TD-DFT. The Boltzmann-weighted spectra of the three conformers resembles very well the experimental ECD of (M)-14, thereby confirming the AC of (+)-14 as (M)-14. As a cross-validation, the Boltzmann-weighted VCD spectra of all conformers were also found to resemble the experimental one very well, thereby being in agreement with the ECD results [58]. 3.8.2 Combination of ECD and ORD

Oligomers from dimer to hexadecamer were synthesized from enantiopure allenes with known AC, and the ECD as well as ORD intensities showed no linearity with

97

3 Absolute Configuration and Conformational Analysis of Chiral Compounds 20

10

O O

O

O

O

O

O

O

260

280

300

320

340

–10

O

O

O

0

O O O

–20

10%

O

(a)

λ (nm)

(b) 6000

200 B 100 G

5000

D

4000

0 F –100 G

A

C D

–200

3000 2000

B

1000

E

0 –300 –400

(c)

E

F 1500

A C 1100

1300 ν∼ (cm−1)

Figure 3.29 (a) Low-energy conformers of (M)-14 and their relative populations in a Boltzmann ensemble. (b) Experimental ECD spectra (CH2 Cl2 ) of CTV-derived trimalonates (+)-14 (black solid line) and (−)-14 (gray solid line), and the spectrum calculated for (M)14 (TD-B3LYP/6-31G(d)) (black dashed line). (c) Experimental VCD spectra (0.042 M, CCl4 )

–1000

Δ𝜀 ∗ 104 (L mol−1 cm−1)

(M)-14

O

Δε (L mol–1 cm–1)

O O

15%

75%

Δ𝜀 ∗ 104 (L mol−1 cm−1)

98

–2000 900

of (+)-14 (gray solid line) and (−)-14 (gray dashed line), and the VCD trace calculated for (M)-14 (black solid line). The calculated frequencies were scaled by the basis-setspecific factor 0.97. The region between 1200 and 1240 cm−1 is omitted due to intense solvent (CCl4 ) absorption [58].

the number of building blocks. This observed chiral amplification suggested the formation of ordered structures in solution [35]. These alleno-acetylenic oligomers, in addition to the vibronic coupling mentioned above [35], present an additional challenge: the low rotational barriers about the butadiene moieties hamper the definition of a PES. As an alternative, the ECD and ORD spectra of (P,P)-(+)-7 with different conformations about the central single bond were simulated and compared with the experimental ones (Figure 3.30). The ORD analysis, at the HF/6-31G(d) level of theory, suggested that the conformers in solution should have 𝜃 in the 0∘ to +135∘ range. Comparison of the experimental and theoretical ECD spectra allowed narrowing the conformational space to the 0∘ to +45∘ range. ZINDO, HF/6-31G(d), and B3LYP/6-31-G(d) levels of theory provided similar ECD signatures for a particular conformer.

3.8

When More than One Method is Needed

99

200 5000 150

+45 +90

4000 100 3000

–1

cm )

50

2000

Δ𝜀 (M

–1

[𝛼]

0 −50

1000

−100

0

−150

−1000

−200 200

(a)

+135 exp 0

180

−2000 225

250

275 λ (nm)

300

Figure 3.30 (a) CD spectra of (P,P)-(+)7 at 𝜃 = −135∘ , −90∘ , −45∘ , 0∘ , +45∘ , +90∘ , and 180∘ , calculated at the TD HF/6-31G(d) level of theory. Experimental spectrum of (P,P)-(+)-7 (black thick

325

350

145 −90 −135 350

(b)

400

450 500 λ (nm)

line). (b) Calculated ORD and experimental (chloroform, dashed line) traces of (P,P)-(+)-7 at the HF/6-31G(d) level of theory [35].

3.8.3 Combination of VCD and ORD

The chiral dialkynyl(phenyl)-methane (R)-15 was obtained from the resolution of its racemate as a precursor of expanded cubanes [59]. Due to the lack of strong electronic transitions in the UV/Vis region, the ECD signals are very weak and not suitable for the AC determination. Therefore, a combination of VCD and ORD analysis was considered. First, conformational search was performed in order to define the PES. The resulting geometries were optimized at the B3LYP/6-31G(d) level of theory, rendering three main conformers (Figure 3.31). The computed Gibbs free energy of the three conformers was used to determine their relative population in solution. The VCD and ORD spectra of all conformers were calculated at the B3LYP-6-31G(d) as well as B3PW91/6-31G+(d) levels of theory. The VCD simulated spectra of (S)-15 (Boltzmann averaged of all three conformers, Figure 3.31) has been compared with the experimental VCD of (−)-15. Predicted Cotton effects 1 and 2 resemble the experimental ones well. More importantly, these Cotton effects have the same sign for the three conformers, and therefore the average simulated signs do not depend on possible errors in the conformational analysis. Overall, the theoretical spectrum resembles qualitatively the experimental one. Nonetheless, the sign of Cotton effects 3–5 is dependent on the conformation. In order to confirm the AC assignment made by VCD, the ORD of both enantiomers of 15 was measured at four different wavelengths. Now, the comparison of experimental and theoretical ORDs allows to unambiguously assign the AC of (−)-15 as (S), in agreement with the VCD analysis (Figure 3.31) [59]. In Chapter 11 an example of AC determination by a cross-validation of VCD, NMR, and X-ray is also presented.

550

600

20

1.4

15

1.2

4

Si(iPr)3

5

–1

15

0

ε (M

OH

−5

SiMe3

−10

1

1.0 –1

Ph

cm )

10

[α]

60 50 40 30 20 10 0 −10 −20 −30 −40 −50 −60

2

1

0.6 0.4

5 3

0.2

−15

3

5

0.8

4

2

0.0

−20 420

440

460

480

500 520

540

560

580 600

1

0.015

30 20

3

λ (nm)

10

5 –1

cm )

(a)

0

0.010

–1

−10

2

4

−20

Δε (M

1

0.005

−30

3

5

−40

0.000

25%

11%

(b)

1500

(c) Figure 3.31 (a) Experimental ORD curves of (+)-15 (c = 9.6 mM in hexane, triangles, black line) and (−)-15 (c = 12.5 mM in hexane, diamonds, black line). Calculated ORD values at the B3LYP/6-31G(d) level of theory for (R)-15 (squares, gray line) and (S)-15 (circles, gray line). The theoretical values were adjusted by scaling down by a factor of 0.3. (b) Conformers of (R)-15 found at the B3LYP/6-31G(d)

1450

−50

2

4

58%

1400

ε (M–1 cm–1)

3 Absolute Configuration and Conformational Analysis of Chiral Compounds

Δε (M–1 cm–1)

100

1350

1300

1250

−60 1200

–1

ν (cm )

level of theory. The conformer populations (Boltzmann distribution) were determined by using the computed Gibbs free energy at 298.15 K. (c) Calculated IR (dashed line, upper graph), experimental IR (solid line, upper graph), calculated VCD (dashed line, lower graph), and experimental VCD spectrum (solid line, lower graph). Calculated frequencies were shifted by 0.97 [59].

3.9 Concluding Remarks

Each chiroptical method (ECD, VCD, and ORD) has its own unique advantages, and therefore, the choice of a particular method is case dependent. The rapid instrumental, methodological, and theoretical developments in the last years have yielded notable improvements in the reliability of the AC as well as conformational assignments using these methods [3]. Consequently, nowadays one can rely on the use of ECD, VCD, ORD, or a combination of them for structural determination of small and medium -sized organic chiral molecules.

References 1. Barron, L.D. (2004) Molecular

Light Scattering and Optical Activity, Cambridge University Press, New York.

2. Stephens, T.D., Bunde, C.J., and Fillmore,

B.J. (2000) Mechanism of action in thalidomide teratogenesis. Biochem. Pharmacol., 59, 1489–1499.

References 3. Berova, N., Polavarapu, P.L., Nakanishi,

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

K., and Woody, R.W. (2012) Comprehensive Chiroptical Spectroscopy, John Wiley & Sons, Inc., Hoboken, NJ. Alonso-Gómez, J.L., Rivera-Fuentes, P., Harada, N., Berova, N., and Diederich, F. (2009) An enantiomerically pure allenoacetylenic macrocycle: synthesis and rationalization of its outstanding chiroptical response. Angew. Chem. Int. Ed., 48, 5545–5548. Stephens, P.J. and Harada, N. (2010) Review article ECD cotton effect approximated by the Gaussian curve and other methods. Chirality, 233, 229–233. Gaussian Inc. (2003) Gaussian 03 and 09, Gaussian Inc., Wallingford, CT, www.gaussian.com (accessed 18 July 2014). Crawford, T.D., Tam, M.C., and Abrams, M.L. (2007) The current state of ab initio calculations of optical rotation and electronic circular dichroism spectra. J. Phys. Chem. A, 111, 12057–12068. Allinger, N.L., Yuh, Y.H., and Lii, J.H. (1989) Molecular mechanics. The MM3 force field for hydrocarbons. 3. The van der Waals’ potentials and crystal data for aliphatic and aromatic hydrocarbons. J. Am. Chem. Soc., 111, 8551–8566. Góbi, S., Vass, E., Magyarfalvi, G., and Tarczay, G. (2011) Effects of strong and weak hydrogen bond formation on VCD spectra: a case study of 2chloropropionic acid. Phys. Chem. Chem. Phys., 13, 13972–13984. Lin, N., Santoro, F., Zhao, X., Rizzo, A., and Barone, V. (2008) Vibronically resolved electronic circular dichroism spectra of (R)-(+)-3methylcyclopentanone: a theoretical study. J. Chem. Phys. A, 4, 12401–12411. Skomorowski, W., Pecul, M., Sałek, P., and Helgaker, T. (2007) Electronic circular dichroism of disulphide bridge: ab initio quantum-chemical calculations. J. Chem. Phys., 127, 085102. Yanai, T. (2004) A new hybrid exchange? correlation functional using the Coulomb-attenuating method (CAMB3LYP). Chem. Phys. Lett., 393, 51–57. Dev, P., Agrawal, S., and English, N.J. (2013) Functional assessment for predicting charge-transfer excitations of

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

dyes in complexed state: a study of triphenylamine-donor dyes on titania for dye-sensitized solar cells. J. Phys. Chem. A, 117, 2114–2124. Aliev, A.E., Mia, Z.A., Busson, M.J.M., Fitzmaurice, R.J., and Caddick, S. (2012) Diastereomer configurations from joint experimental-computational analysis. J. Org. Chem., 77, 6290–6295. Mennucci, B., Tomasi, J., Cammi, R., Cheeseman, J.R., Frisch, M.J., Devlin, F.J., Gabriel, S., and Stephens, P.J. (2002) Polarizable continuum model (PCM) calculations of solvent effects on optical rotations of chiral molecules. J. Phys. Chem. A, 106, 6102–6113. Polavarapu, P.L. (2007) Renaissance in chiroptical spectroscopic methods for molecular structure determination. Chem. Rec., 7, 125–136. Nicu, V.P., Baerends, E.J., and Polavarapu, P.L. (2012) Understanding solvent effects in vibrational circular dichroism spectra: [1,1′ -binaphthalene]2,2′ -diol in dichloromethane, acetonitrile, and dimethyl sulfoxide solvents. J. Phys. Chem. A, 116, 8366–8373. Kurtán, T., Jia, R., Li, Y., Pescitelli, G., and Guo, Y.-W. (2012) Absolute configuration of highly flexible natural products by the solid-state ECD/TDDFT method: ximaolides and sinulaparvalides. Eur. J. Org. Chem., 2012, 6722–6728. Alonso-Gómez, J.L., Navarro-Vázquez, A., and Cid, M.M. (2009) Chiral (2,5)pyrido[7(4)]allenoacetylenic cyclophanes: synthesis and characterization. Chemistry, 15, 6495–6503. Berova, N., Nakanishi, K., and Woody, R.W. (2000) Circular Dichroism: Principles and Applications, 2nd edn, John Wiley & Sons, Inc., New York. Lightner, D.A. and Gurst, J.E. (2000) Organic Conformational Analysis and Stereochemistry from Circular Dichroism Spectroscopy, John Wiley & Sons, Inc., New York. Berova, N., Di Bari, L., and Pescitelli, G. (2007) Application of electronic circular dichroism in configurational and conformational analysis of organic compounds. Chem. Soc. Rev., 36, 914–931. Bieli¯unas, V., Raˇckauskait˙e, D., Orentas, E., and Stonˇcius, S. (2013) Synthesis,

101

102

3 Absolute Configuration and Conformational Analysis of Chiral Compounds

24.

25.

26.

27.

28.

29.

30.

31.

enantiomer separation, and absolute configuration of 2,6-oxygenated 9azabicyclo[3.3.1]nonanes. J. Org. Chem., 78, 5339–5348. Harada, N. and Nakanishi, K. (1983) Circular Dichroic Spectroscopy Exciton Coupling in Organic Stereochemistry, University Science Books, Mill Valley, CA. Harada, N. and Uda, H. (1982) Angular dependence of the u.v. absorption maximum wavelength in exciton coupling systems. J. Chem. Soc., Chem. Commun., (4), 230–232. Alonso-Gómez, J.L., Schanen, P., Rivera-Fuentes, P., Seiler, P., and Diederich, F. (2008) 1,3-Diethynylallenes (DEAs): enantioselective synthesis, absolute configuration, and chiral induction in 1,1,4,4-tetracyanobuta1,3-dienes (TCBDs). Chem. Eur. J., 14, 10564–10568. Alonso-Gómez, J.L., Petrovic, A.G., Harada, N., Rivera-Fuentes, P., Berova, N., and Diederich, F. (2009) Chiral induction from allenes into twisted 1,1,4,4-tetracyanobuta-1,3-dienes (TCBDs): conformational assignment by circular dichroism spectroscopy. Chem. Eur. J., 15, 8396–8400. Berova, N., Pescitelli, G., Petrovic, A.G., and Proni, G. (2009) Probing molecular chirality by CD-sensitive dimeric metalloporphyrin hosts. Chem. Commun., 22, 5958–5980. Chen, Y., Petrovic, A.G., Roje, M., Pescitelli, G., Kayser, M.M., Yang, Y., Berova, N., and Proni, G. (2010) CD-sensitive Zn-porphyrin tweezer host-guest complexes, part 2: cis- and trans-3-hydroxy-4-aryl/alkyl-betalactams. A case study. Chirality, 22, 140–152. Petrovic, A.G., Chen, Y., Pescitelli, G., Berova, N., and Proni, G. (2010) CD-sensitive Zn-porphyrin tweezer host-guest complexes, part 1: MC/OPLS2005 computational approach for predicting preferred interporphyrin helicity. Chirality, 22, 129–139. Moore, B. and Autschbach, J. (2012) Density functional study of tetraphenylporphyrin long-range exciton coupling. ChemistryOpen, 1, 184–194.

32. Nishizaka, M., Mori, T., and Inoue, Y.

33.

34.

35.

36.

37.

38.

39.

(2011) Axial chirality of donor-donor, donor-acceptor, and tethered 1,1′ binaphthyls: a theoretical revisit with dynamics trajectories. J. Phys. Chem. A, 115, 5488–5495. Geist, J.G., Lauw, S., Illarionova, V. et al (2010) Thiazolopyrimidine inhibitors of 2-methylerythritol 2,4-cyclodiphosphate synthase (IspF) from Mycobacterium tuberculosis and Plasmodium falciparum. ChemMedChem, 5, 1092–1101. Rivera-Fuentes, P., Alonso-Gómez, J.L., Petrovic, A.G., Seiler, P., Santoro, F., Harada, N., Berova, N., Rzepa, H.S., and Diederich, F. (2010) Enantiomerically pure alleno-acetylenic macrocycles: synthesis, solid-state structures, chiroptical properties, and electron localization function analysis. Chem. Eur. J., 16, 9796–9807. Rivera-Fuentes, P., Alonso-Gómez, J.L., Petrovic, A.G., Santoro, F., Harada, N., Berova, N., and Diederich, F. (2010) Amplification of chirality in monodisperse, enantiopure alleno-acetylenic oligomers. Angew. Chem. Int. Ed., 49, 2247–2250. Faulkner, T.R., Moscowitz, A., Holzwarth, G., Hsu, E.C., and Mosher, H.S. (1974) Infrared circular dichroism of carbon-hydrogen and carbondeuterium stretching modes. Calculations. J. Am. Chem. Soc., 96, 252–253. De Gussem, E., Bultinck, P., Feledziak, M., Marchand-brynaert, J., Stevens, V., Herrebout, W., and Stevens, C.V. (2012) Vibrational circular dichroism versus optical rotation dispersion and electronic circular dichroism for diastereomers: the stereochemistry of 3(1’-hydroxyethyl)-1-(3’-phenylpropanoyl)azetidin-2-one. Phys. Chem. Chem. Phys., 14, 8562–8571. Nicu, V.P. and Baerends, E.J. (2009) Robust normal modes in vibrational circular dichroism spectra. Phys. Chem. Chem. Phys., 11, 6107–6118. Nicu, V.P., Debie, E., Herrebout, W., Van der Veken, B., Bultinck, P., and Baerends, E.J. (2009) A VCD robust mode analysis of induced chirality: the case of pulegone in chloroform. Chirality, 21 (Suppl. 1), E287–E297.

References 40. Góbi, S. and Magyarfalvi, G. (2011)

41.

42.

43.

44.

45.

46.

47.

48.

Reliability of computed signs and intensities for vibrational circular dichroism spectra. Phys. Chem. Chem. Phys., 13, 16130–16133. Sadlej, J., Dobrowolski, J.C., Rode, J.E., and Jamróz, M.H. (2006) DFT study of vibrational circular dichroism spectra of D-lactic acid-water complexes. Phys. Chem. Chem. Phys., 8, 101–113. Covington, C.L. and Polavarapu, P.L. (2013) Similarity in dissymmetry factor spectra: a quantitative measure of comparison between experimental and predicted vibrational circular dichroism. J. Phys. Chem. A, 117, 3377–3386. Batista, J.M., Batista, A.N.L., Rinaldo, D., Vilegas, W., Cass, Q.B., Bolzani, V.S., Kato, M.J., López, S.N., Furlan, M., and Nafie, L.A. (2010) Absolute configuration reassignment of two chromanes from Peperomia obtusifolia (Piperaceae) using VCD and DFT calculations. Tetrahedron: Asymmetry, 21, 2402–2407. Wang, F. and Polavarapu, P.L. (2001) Predominant conformations of (2R, 3 R)-(-)-2, 3-butanediol. J. Phys. Chem. A, 105, 6991–6997. Shin, S., Nakata, M., and Hamada, Y. (2006) Analysis of vibrational circular dichroism spectra of (s)-(+)-2-butanol by rotational strengths expressed in local symmetry coordinates. J. Phys. Chem. A, 110, 2122–2129. Longhi, G., Abbate, S., Scafato, P., and Rosini, C. (2010) A vibrational circular dichroism approach to the determination of the absolute configuration of flexible and transparent molecules: fluorenone ketals of 1,n-diols. Phys. Chem. Chem. Phys., 12, 4725–4732. Batista, J.M., Batista, A.N.L., Mota, J.S., Cass, Q.B., Kato, M.J., Bolzani, V.S., Freedman, T.B., López, S.N., Furlan, M., and Nafie, L.A. (2011) Structure elucidation and absolute stereochemistry of isomeric monoterpene chromane esters. J. Org. Chem., 76, 2603–2612. Losada, M., Tran, H., and Xu, Y. (2008) Lactic acid in solution: investigations of lactic acid self-aggregation and hydrogen bonding interactions with water and methanol using vibrational absorption and vibrational circular dichroism

49.

50.

51.

52.

53.

54.

55.

56.

spectroscopies. J. Chem. Phys., 128, 014508. Sadlej, J., Dobrowolski, C., Rode, J.E., Buch, V., and Buck, U. (2010) VCD spectroscopy as a novel probe for chirality transfer in molecular interactions. Chem. Soc. Rev., 39, 1478–1488. Poopari, M.R., Dezhahang, Z., and Xu, Y. (2013) A comparative VCD study of methyl mandelate in methanol, dimethyl sulfoxide, and chloroform: explicit and implicit solvation models. Phys. Chem. Chem. Phys., 15, 1655–1665. Poopari, M.R., Dezhahang, Z., Yang, G., and Xu, Y. (2012) Conformational distributions of N-acetyl-L-cysteine in aqueous solutions: a combined implicit and explicit solvation treatment of VA and VCD spectra. ChemPhysChem, 13, 2310–2321. Merten, C., Amkreutz, M., and Hartwig, A. (2010) Determining the structure of α-phenylethyl isocyanide in chloroform by VCD spectroscopy and DFT calculations—simple case or challenge? Phys. Chem. Chem. Phys., 12, 11635–11641. Taniguchi, T. and Monde, K. (2012) Exciton chirality method in vibrational circular dichroism. J. Am. Chem. Soc., 134, 3695–3698. Wu, T. and You, X. (2012) Exciton coupling analysis and enolization monitoring by vibrational circular dichroism spectra of camphor diketones. J. Phys. Chem. A, 116, 8959–8964. Asai, T., Taniguchi, T., Yamamoto, T., Monde, K., and Oshima, Y. (2013) Structures of spiroindicumides A and B, unprecedented carbon skeletal spirolactones, and determination of the absolute configuration by vibrational circular dichroism exciton approach. Org. Lett., 15, 4320–4323. Petrovic, A.G., Navarro-Vázquez, A., and Alonso-Gómez, J.L. (2010) From relative to absolute configuration of complex natural products : interplay between NMR, ECD, VCD, and ORD assisted by ab initio calculations. Curr. Org. Chem., 14, 1612–1628.

103

104

3 Absolute Configuration and Conformational Analysis of Chiral Compounds 57. Polavarapu, P.L., Petrovic, A., and Wang,

F. (2003) Intrinsic rotation and molecular structure. Chirality, 15 (Suppl), S143–S149. 58. Kraszewska, A., Rivera-Fuentes, P., Rapenne, G., Crassous, J., Petrovic, A.G., Alonso-Gómez, J.L., Huerta, E., Diederich, F., and Thilgen, C. (2010) Regioselectivity in tether-directed remote functionalization – the addition of a cyclotriveratrylene-based trimalonate to C60 revisited. Eur. J. Org. Chem., 2010, 4402–4411.

59. Buschhaus, B., Convertino, V.,

Rivera-Fuentes, P., Alonso-Gómez, J.L., Petrovic, A.G., and Diederich, F. (2010) Optically active trialkynyl(phenyl)methane: synthesis and determination of its absolute configuration by vibrational circular dichroism (VCD) and optical rotatory dispersion (ORD). Eur. J. Org. Chem., 2010, 2452–2456.

105

4 Mass Spectrometry Strategies in the Assignment of Molecular Structure: Breaking Chemical Bonds before Bringing the Pieces of the Puzzle Together Wilfried M.A. Niessen and Maarten Honing

4.1 Introduction

The assessment of molecular structures forms one of the major challenges to organic and especially analytical chemists. A clear relation between the mechanism of chemical synthesis processes and the determination of the “correct” molecular structure are at the basis of many processes and research efforts. In addition, analytical chemists are increasingly focusing on the assessment of the molecular structure of “unknown” chemical entities. This is, for example, the case in environmental and food-safety applications (identification of contaminants such as pesticides and veterinary drug residues) or in the characterization of pharmaceutical products (impurities and degradation products in active pharmaceutical ingredients (APIs) and drug metabolites), base chemicals such as caprolactam, and/or in food product sciences (molecular entities resulting from degradation or decomposition processes). The elucidation of molecular structures is not limited to the assessment of the constitution but also addresses spatial descriptors, conformation, and configuration [1, 2]. The latter aspects are of importance for the correlation of structures with biological or chemical properties [3]. Classically, organic chemists utilized technologies such as nuclear magnetic resonance (NMR), vibrational (IR) spectroscopy, and X-ray diffraction (XRD) and, to a lesser extent, mass spectrometry (MS). In this context, high-resolution MS is only applied for confirmation of the molecular formula. With developments in the hyphenation of MS with gas chromatography (GC) and, more importantly, liquid chromatography (LC), structure elucidation became a key part of the work of the analytical chemist, recently leading to the development and application of advanced multi-instrument platforms, for example, hybrid tandem mass spectrometry (MS–MS) [4, 5] or even complex LC–NMR–MS systems [6]. More recently, a new dimension in the analysis of molecular structures, including the spatial descriptors of importance for small chiral molecules, is added by the implementation of ion-mobility spectrometry within MS–MS systems [7]. Structure Elucidation in Organic Chemistry: The Search for the Right Tools, First Edition. Edited by María-Magdalena Cid and Jorge Bravo. © 2015 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2015 by Wiley-VCH Verlag GmbH & Co. KGaA.

106

4 Mass Spectrometry Strategies in the Assignment of Molecular Structure

This chapter presents a comprehensive overview of current MS-based technologies and methodologies for the structure elucidation of small molecules (typically up to 1 kDa size), illustrated with some typical examples. In many instances, MS is preferred as the initial technology over spectroscopic methods (NMR, IR) because of its sensitivity and the ease of coupling to chromatographic separation technologies and a large variety in experimental design, enabling structure elucidation of compounds in mixtures. The use of MS is based on the ability to ionize intact molecules, providing information on the nominal or accurate molecular mass depending on the instrument applied (Section 4.2.2), and likely elemental composition, and to put energy in the ions to induce structure-specific fragmentation, enabling the recognition of specific building blocks and the reconstruction (putting the puzzle together) of the molecular structure. It is the interpretation of the accurate molecular mass and the isotopic distribution of the compound, which is key in the effective assignment of small molecule structures [8–10]. MS-based structure elucidation discussions have been dominated by the experts using electron ionization (EI, formerly known as “electron impact ionization”), for which a solid understanding of the fragmentation rules is available [11–13]. Identification of unknown compounds using EI in gas chromatography–mass spectrometry (GC–MS) and mass-spectral library searching has become an important tool in analytical laboratories [14–17]. Nowadays, liquid chromatography–mass spectrometry (LC–MS) has become the most important tool in structure elucidation of most classes of small molecules [18]. LC–MS is based on the use of soft ionization, mostly electrospray ionization (ESI), followed by selection of a particular precursor ion, collision-induced dissociation (CID) of the selected ion, and subsequently mass analysis of the resulting product ions in an MS–MS instrument. Unfortunately, the level of understanding of the fragmentation of protonated and deprotonated molecules in CID is far less. After briefly discussing the key technologies important for MS-based structure elucidation, various approaches in putting energy in molecules, mechanisms in breaking molecular bonds, and strategies in confirmation of the molecular identity within different application areas are discussed and illustrated with examples. Altogether, this redefines the crucial position MS has and will continue to have in molecular structure assignment projects.

4.2 Instrumentation and Technology

An MS experiment typically comprises five steps: (1) sample introduction, often by means of and following chromatographic separation, (2) analyte ionization, (3) mass analysis, that is, separation of ions according to their mass-to-charge ratio (m/z), (4) ion detection, and (5) data processing and interpretation of the results (Figure 4.1). In some cases, mainly depending on the ionization technique applied, more complicated multistage mass analysis procedures (MS–MS or MSn )

4.2

Instrumentation and Technology

(5)

(1) Inlet GC or LC

(2)

(3)

Ion source

(3a) MS-1

Select precursor

(4)

Mass analyzer

(3b) CID

Detector

Instrument control & data processing

(3c) MS-2

Analyze products

Figure 4.1 Schematic diagram of the mass spectrometry process.

are applied in step (3), featuring (3a) selection of a particular precursor ion, (3b) fragmentation of the selected ion, and (3c) mass analysis of the resulting product ions. In this section, we discuss fundamental aspects of the technologies important for analyte ionization and (multistage) mass analysis. In order to achieve mass analysis, a high vacuum (pressure ≤ 10 –5 mbar) is required in the mass analyzer and ion detection system. As outlined below, ionization might take place in high vacuum, as in EI, or at atmospheric-pressure ionization, as in ESI. In the latter case, a vacuum interface is needed to transfer ions into the mass analyzer. 4.2.1 Ionization Techniques

A wide variety of analyte ionization techniques, that is, more than 50, are available for MS. Any ionization technique should lead to gas-phase ions, either in high vacuum or transferable to high vacuum, to enable subsequent mass analysis. Ionization techniques can be classified in different ways. From a structure elucidation point of view, a useful classification is based on the difference between hard and soft ionization techniques. In a hard ionization technique, a substantial amount of internal energy is put into the molecule upon generation of the ion. This is the case in EI, where typically a few electron volts internal energy is transferred to the molecular ion, M+⋅ . This internal energy results in insource compound-specific fragmentation (Section 4.3.1). The mixture of intact molecular ions and fragment ions is subsequently mass analyzed. In contrast, in a soft ionization technique, hardly any internal energy is transferred to the ion, which is often a protonated or deprotonated molecule, [M + H]+ or [M − H]− , and no in-source fragmentation occurs. If fragmentation is desirable, it has to be induced by increasing the internal energy of the ion, for instance, by collisions in an MS–MS experiment (Section 4.2.3 and 4.3.2). In between these extremes, other ionization techniques, frequently based on gas-phase chemical ionization (CI), or

107

108

4 Mass Spectrometry Strategies in the Assignment of Molecular Structure

ion activation techniques [19] enable an “intermediate” disposition of energy in a molecule, providing selectivity and, more importantly, mass spectra that exhibit both fragment ions and ions related to the intact analyte molecule. The latter are frequently missing in EI mass spectra. Another classification of analyte ionization techniques can be based on the physical state of the analyte molecule. We distinguish gas-phase, liquid-phase, and solid-phase or surface ionization techniques. EI and CI are examples of gasphase ionization techniques, while ESI is an example of a liquid-phase ionization technique; matrix-assisted laser desorption/ionization (MALDI) and desorption electrospray ionization (DESI) are examples of surface ionization techniques. Gas-phase ionization requires either gas-phase samples or evaporation of the analytes prior to ionization. Surface ionization techniques are frequently the socalled energy-sudden techniques [20], in which intense localized energy is applied to the sample, for example, by means of a laser pulse, to simultaneously ionize and transfer the ion from the solid phase to the gas phase. In liquid-phase ionization, the sample solution, for example, the LC mobile phase, is nebulized into small droplets, from which gas-phase analyte ions are generated, for example, in ESI. A third, and with respect to structure elucidation also highly relevant, classification is based on the type of primary ions generated in the ionization process. As indicated, EI results in molecular ions, M+⋅ , which are odd-electron ions (OE+⋅ ), whereas most soft ionization techniques such as ESI and MALDI result in either positively or negatively charged even-electron ions (EE+ ), often [M + H]+ or [M − H]− . As outlined in Sections 4.3.1 and 4.3.2, the fragmentation of OE+⋅ and EE+ is distinctly different. These three ways in classifying the formation of gaseous ions illustrate the tremendous variety of approaches in transforming a broad spectrum of molecules into ions amenable to MS. Nevertheless, in the context of this chapter, EI and ESI are the most important ionization techniques representing the main approaches in molecular structure assignment of small molecules using MS. EI is based on the interaction of gas-phase molecules with 70 eV electrons in a high-vacuum ion source. The electron energy of 70 eV is generally applied as the standard value, as it provides good sensitivity and robustness and enables the use of EI mass spectral libraries, also based on 70 eV mass spectra. Obviously, at the expense of sensitivity, lower electron energy (10–20 eV) can be applied for particular purposes, especially to observe the molecular ion. One of the interactions occurring is the loss of an electron from the molecule M, resulting in the formation of M+⋅ . Upon ionization, the ion carries up to 5 eV internal energy, which leads to fast in-source fragmentation reactions. In any fragmentation reaction of a single-charge ion, at least two products are generated – that is, an ion with a lower m/z and a neutral molecule or radical, which is lost as it is not observed in the MS. The mass of the neutral may be inferred from the m/z differences between the initial ion and its fragment ion. Typical features of fragmentation in EI are discussed in Section 4.3.1. ESI is a liquid-phase ionization technique, based on the nebulization of a solution, for example, the mobile phase from an LC column, into an atmospheric-pressure ion source. Gas-phase ions are generated in the process

4.2

Instrumentation and Technology

of droplet evaporation and field-induced electrohydrodynamic disintegration of the droplets [21]. Desolvation and collisional cooling of the ions occur when they move through the vacuum interface between atmospheric-pressure ion source and high-vacuum mass analyzer [22]. In most cases, either [M + H]+ or [M − H]− ions are generated, depending on the operating polarity, but other adduct ions such as [M + Na]+ or [M + CH3 COO]− may be generated as well. Although no fragmentation is observed, some structure information may already be deduced from the results of polarity switching (acquiring both positive-ion and negative-ion data). This requires some understanding of proton-transfer reactions in buffered aqueous solutions and in the gas phase [23]. As an example, abundant response in the negative-ion mode may indicate the presence of carboxyl or other acidic functional groups. Abundant [M + Na]+ and [M + K]+ may indicate neighboring aliphatic hydroxyl groups, while [M + CH3 COO]− ions may be the result of weakly basic functional groups. 4.2.2 Mass Analyzers

In a mass analyzer, ions are separated either in space or, in most cases, in time based on their m/z. Mass analysis is always performed in high vacuum (≤10−5 mbar, see Table 4.1). Six different types of mass analyzers are currently in use: quadrupole, ion-trap (IT), time-of-flight (TOF), Orbitrap, Fouriertransform ion-cyclotron resonance (FT-ICR), and sector instruments. Mass analyzers can also be considered the building blocks of MS–MS instrumentation (Section 4.2.3). It is beyond the present discussion to discuss these building blocks and their working principles in detail [24]. Some important features are summarized in Table 4.1. In a basic operation, a mass spectrometer continuously acquires mass spectra; that is, the instrument is operated in full-spectrum single-stage MS mode. For specified applications, especially in routine targeted quantitative analysis, data acquisition is performed in selected-ion monitoring (SIM) mode, which largely improves the sensitivity. In SIM mode, the instrument only acquires the ions at a particular m/z during a preset dwell time, yet losing the detailed information present in the full-spectrum mode. Whether SIM mode is possible in a particular mass analyzer is indicated in Table 4.1. A useful classification divides these building blocks into unit-mass-resolution and high-resolution instruments (Table 4.1). For most instruments, the resolving power can be expressed as the ratio of the m/z and the full-width at half maximum (FWHM) of the peak at the given m/z. Typical values for high-resolution instruments are given in Table 4.1; for unit-mass instruments, the resolving power is not applicable. Unit-mass-resolution instruments allow m/z determination with an accuracy of ±0.1 (nominal-mass determination), whereas with high-resolution mass spectrometry instruments (HRMS) the error in m/z determination will typically be in the third decimal place (accurate-mass determination). Based on the

109

110

4 Mass Spectrometry Strategies in the Assignment of Molecular Structure

Table 4.1 Characteristics and features of different mass analyzers. Analyzer type

Features

Quadrupole

Unit-mass resolution Nominal-mass determination Moderate costs; User-friendly Unit-mass resolution Nominal-mass determination Moderate costs; User-friendly Both cylindrical (3D-IT) and linear ion traps (LIT) are available. HRMS ( 0

L2 L1

HO

Absolute configuration? 298 K

H HO

L2

(S)-MPA

213 K

1H NMR (CS2/CD2CI2)

L1

ΔδT1,T2 L1> 0 ΔδT1,T2 L2> 0

H HO

L2 L1

Absolute configuration? 298 K

213 K

Figure 7.4 Steps to follow and models for the assignment of the absolute configuration of secondary alcohols according to the Δ𝛿 T1 ,T2 signs of their MPA esters.

7.2

Single Derivatization Methods for Mono- and Polyfunctional Compounds

As a result, part of the signals in the 1 H NMR spectrum are shifted to high field (positive Δ𝛿 T1 ,T2 ) and others do so in the opposite sense (negative Δ𝛿 T1 ,T2 ). This behavior allows assigning the position of the substituents (L1 /L2 ) around the asymmetric carbon. In the case of polyfunctional compounds such as sec/sec-1,n-diols [13], four stereochemistries are possible, types A–D, as shown in Figure 7.5. The use of a single derivative and comparison of their NMR spectra at two different temperatures allows the assignment of their relative configuration [13a] (syn/anti), and only in the case of anti-1,n-diols its absolute configuration (type C/D) can be assigned. bis-MPA esters of sec/sec-1,n-diols present a well-defined conformational equilibrium [13b,c] between two NMR-significant conformers: in the most stable conformation, both MPA units are in synperiplanar disposition, while in the less stable conformation they are in antiperiplanar arrangement. A decrease in the NMR probe temperature increases the population of the more stable conformer (sp), as well as its contribution to the average NMR spectrum. It should be noted that not all the protons of the substrate can be used as diagnostic signals. As the shielding/deshielding effects of the carbonyl and phenyl groups of both MPA units affect the CαH protons of the diol moiety, only R1 and R2 are of diagnostic use. In the bis-(R)-MPA ester of syn-1,n-diols, types A and B, the two substituents (R1 /R2 ) of the diol part are shielded in the most stable conformer (both MPA units in sp conformation), as shown in Figure 7.5a,b. When the temperature decreases, the equilibrium moves toward the most stable conformer and the signals corresponding to R1 /R2 are shifted upfield. Therefore, both substituents present syn-1,2-type A

syn-1,2-type B (R)-MPA O

OH R1 +

+ R2

R1

R2

O H (R)-MPA

OH

(a)

+ R2

OH R1 +

R2

R1

O H (R)-MPA

OH

(b) anti-1,2-type D

anti-1,2-type C (R)-MPA OH R1 +

(R)-MPA O H

H

− R2

OH

O Hα(R1) R2 R1 H O (R)-MPA

(c) Figure 7.5 (a) Shielding effects caused by the auxiliaries on the bis-(R)-MPA ester of a syn-1,2-type A sec/sec-diol. (b) Idem for a syn-1,2-type B sec/sec-diol. (c) Idem for a

(R)-MPA OH R1 −

+ R2

OH

O

H

R2 R1 Hα(R2)O (R)-MPA

(d) anti-1,2-type C sec/sec-diol. (d) Idem for a anti-1,2-type D sec/sec-diol. Positive and negative Δ𝛿 T1 ,T2 are indicated by + and − signs respectively.

247

248

7 Simplified NMR Procedures for the Assignment of the Absolute Configuration

a positive Δ𝛿 T1 ,T2 (indicated by + signs in Figure 7.5). The NMR behavior of the two diols (types A and B) is the same and we cannot differentiate between them. However, in the anti-1,n-diols the NMR behavior is different for both substituents (R1 /R2 ) and characteristic of each stereochemistry. In the bis-(R)-MPA ester of an anti-1,n-type C, substituent R1 is shielded in the most stable conformer, and R2 is shielded in the less stable conformer (Figure 7.5c). With decreasing temperature, the signal corresponding to R1 is shifted upfield, while the one corresponding to R2 is shifted downfield. This means that Δ𝛿 T1 ,T2 for R1 is positive and Δ𝛿 T1 ,T2 for R2 is negative (indicated by − sign). In the bis-(R)-MPA ester of an anti-1,n-type D, R2 is shielded in the most stable conformer, and R1 is shielded in the less stable (Figure 7.5d). By applying the same reasoning, the expected NMR behavior is reversed: Δ𝛿 T1 ,T2 for R1 is negative and Δ𝛿 T1 ,T2 for R2 is positive. Figure 7.6 shows the evolution with temperature (298 to 183 K) of the 1 H NMR spectra corresponding to the bis-(R)-MPA esters of the four stereoisomers of heptane-2,3-diol, taken as example. Figure 7.6a,b shows type A and type B diols, in this case where all the signals (Me, Bu) are shielded with decreasing temperature (positive Δ𝛿 T1 ,T2 ); therefore, it is not possible to distinguish between them. In the case of type C (Figure 7.6c), the methyl is shielded, and the butyl is deshielded, positive and negative Δ𝛿 T1 ,T2 , respectively. The opposite happens in the type D diol; the methyl is deshielded and the butyl is shielded, so negative and positive Δ𝛿 T1 ,T2 values are obtained respectively (Figure 7.6d). A series of sec/sec-1,n-diols of diverse structures and known absolute configurations have validated the generality of this correlation. From an experimental standpoint, this method requires (i) preparation of one of the bis-MPA esters, either the bis-(R) or the bis-(S)-MPA, (ii) record of an initial spectrum at room temperature (298 K) and a second spectrum at a lower temperature (213 K is suitable), and (iii) comparison of the two spectra and calculation of Δ𝛿 T1 ,T2 for R1 and R2 . Finally, the absolute configuration is assigned according to the scheme shown in Figure 7.7. prim/sec-1,2-Diols are another group of polyfunctional compounds, whose configuration can be determined by this type of simplified methods[14]. The most stable conformers of each bis-MPA-ester depend on both the configuration of the diol and MPA. Also, each methylene proton experiences different shielding/deshielding effects that are characteristic of the configuration of the diol and the MPA. Evolution with temperature of the signals corresponding to methylene protons allows the assignment of the configuration of the diol [14a]. In this case, the carbonyl of the MPA esterifying the primary alcohol plays an important role. In the bis-(R)-MPA ester of a prim/sec-1,2-diol of type A, in the most stable conformer (Figure 7.8a) both methylene protons are affected by the shielding/deshielding of the carbonyl group. In the most stable conformer of the bis-(R)-MPA ester of the enantiomeric diol (Type B), the methylene proton that resonates at the highest field (pro-S) is subjected to the shielding effect of the two phenyls of both MPA units and also by the effect of the carbonyl. For its part,

7.2

Single Derivatization Methods for Mono- and Polyfunctional Compounds

.

syn-1,2-type A

syn-1,2-type B

(R)-MPA O

(R)-MPA

H

O

H

O H O

(R)-MPA

H

(R)-MPA

T(K) 298 K

183 K (a)

1.0

0.8

0.6

0.4

(b)

0.2

anti-1,2-type C

1.2

0.8

0.6

anti-1,2-type D

(R)-MPA O

1.0

(R)-MPA

H

O

H O

H

H O

(R)-MPA

(R)-MPA

T(K) 298 K

183 K 1.4 (c)

1.2

1.0

0.8

1.2 (d)

1.0 0.8 δ (ppm)

0.6

Figure 7.6 (a) Evolution with temperature (298 to 183 K) of the 1 H NMR spectra of the bis(R)-MPA ester of syn-1,2-type A heptane-2,3-diol. (b) Idem of syn-1,2-type B heptane-2,3-diol. (c) Idem of anti-1,2-type C heptane-2,3-diol. (d) Idem of anti-1,2-type D heptane-2,3-diol.

249

250

7 Simplified NMR Procedures for the Assignment of the Absolute Configuration

Experimental ΔδT1 T2signs 1st spectrum Derivatization

OH R1

2nd spectrum

1H

NMR (CS2/CD2CI2)

R2 OH

OH

OH R2

R1

R2

R1

HO

HO

anti-1,2 type C anti-1,2 type D

Absolute configuration?

OH

OH R2

R1 HO 298 K

213 K

R2

R1 HO

syn-1,2 type A

syn-1,2 type B

Figure 7.7 Steps to follow and models for the assignment of the absolute configuration of sec/sec-1,2-diols according to the Δ𝛿 T1 ,T2 signs of their bis-(R)-MPA esters.

Type A 1,2-diol H O(R)MPA O(R)MPA L

ap-I CH3O H

H O O

pro-RH

298 K Me O

O Hpro-S

OCH3

Average

H

213 K

(a)

sp-I pro-(S) pro-(R) sp-I

δ (ppm)

Type B 1,2-diol (R)MPAO H O(R)MPA L CH3O H

O Me

O pro-RH

(b) Shielding: Deshielding:

298 K

O

H O

OCH3 H

Hpro-S

213 K pro-(R)

sp-II

Figure 7.8 (a) Evolution with temperature (298 to 213 K) of the chemical shifts originated by the pro-R and pro-S methylene protons of the bis-(R)-MPA ester of a type

pro-(S)

δ (ppm) A prim/sec-1,2-diol. (b) Idem of a type B prim/sec-1,2-diol. Shielding and deshielding effects are indicated by arrows.

7.2

Single Derivatization Methods for Mono- and Polyfunctional Compounds

251

the methylene proton that resonates at the lowest field (pro-R) is shielded by the phenyl of one MPA unit and deshielded by the carbonyl (Figure 7.8b). As a consequence of the combination of shielding/deshielding effects from the phenyl and carbonyl groups of the MPA units outlined above, evolution with temperature of the signals of the methylene protons is characteristic of the configuration of the diol: 1) In the bis-(R)-MPA ester of a prim/sec-1,2-diol of type A, at the lower temperature the proton that resonates in the highest field (pro-R) is lightly shielded (Δ𝛿 T1 ,T2 > 0), whereas the proton that resonates at the lowest field (pro-S) is lightly deshielded (Δ𝛿 T1 ,T2 < 0), in both cases by less than 0.1 ppm. 2) In the bis-(R)-MPA ester of a prim/sec-1,2-diol of type B, the methylene proton that resonates at high field shows a strong shift upfield at low temperatures (between 0.2 and 0.3 ppm), whereas the methylene proton that resonates at low field shifts slightly downfield (0.0–0.1 ppm). This behavior has been checked for a series of prim/sec-1,2-diols of known absolute configurations and wide structural variety [14]. The same behavior was observed in the derivatives of (S)-MPA. As a summary (Figure 7.9), the procedure for the assignment of the absolute configuration consists of (i) preparation of either the bis-(R)- or the bis-(S)-MPA derivative; (ii) comparison of its 1 H NMR spectra taken at room temperature and at a lower temperature; (iii) calculation of the Δ𝛿 T1 ,T2 values for the methylene proton that resonates at high field, and (iv) for a bis-(R)-MPA ester, if the Δ𝛿 T1 ,T2 for the high-field proton is 0.10 ppm, then the absolute configuration of the diol is represented by type B. For the bis-(S)-MPA ester, trends in the Δ𝛿 T1 ,T2 values are the opposite: >0.10 ppm for a diol of type A, and 0.1ppm proton

Figure 7.9 Steps to follow and models for the assignment of the absolute configuration of prim/sec-1,2-diols according to the Δ𝛿 T1 ,T2 signs of their bis-(R)-MPA esters.

252

7 Simplified NMR Procedures for the Assignment of the Absolute Configuration

7.2.2 Selective Complexation

The second approach is also based on the controlled shift of the conformational sp/ap equilibrium [18] but caused by selective complexation [15, 16] of one of the two main conformers with a metal ion and permits the assignment of configuration of secondary alcohols and amines based basically on the same grounds as the low temperature method. It works by comparison of the NMR spectrum, taken in MeCN-d3 , of an MPA ester [15] or MPA amide [16] (just a single derivative, the (R)- or the (S)-MPA), before and after the addition of barium perchlorate. Thus, in the case of an (R)MPA ester, the conformational equilibrium has been shown in Section 7.2.1 and addition of Ba(ClO4 )2 produces the selective complexation of the metal ion with the carbonyl and methoxy oxygens of the MPA part indicated in Figure 7.10. The chelate of the sp conformer is more stable than that of the ap conformer in MPA esters and therefore, addition of the metal salt to the NMR tube shifts the conformational equilibrium in favor of the sp conformer and as a consequence, the spectral signals also experience the shift. This addition has therefore the same effect in MPA esters of alcohols as lowering the temperature: the L1 /L2 substituent located in front of the phenyl ring of the MPA in the sp conformer is the one that gets more shielded by addition of Ba2+ while the protons located in the other side will show deshielding (more shielded in absence of barium salt). Comparison of the shifts for the protons of L1 /L2 is quantitatively expressed as Δ𝛿 Ba (the difference between the chemical shift in the absence of Ba2+ minus the chemical shift in the presence of Ba2+ ); a positive Δ𝛿 Ba in an (R)-MPA ester means that the specified group is on the same side as the phenyl ring in the sp Ba2+

Shielded group

O H

O (R)-MPA

H

Ba2+

X OMe

L2 L1

MeO

H X

H

L2 L1

Shielded group

X= NH, O ap In the absence of the Ba2+ salt In the presence of the Ba2+ salt

Major conformer (amides) Minor conformer (esters) Decreased population (amides & esters)

sp Major conformer (amides) Mayor conformer (esters) Increased population (amides & esters)

Figure 7.10 Controlled shift of the conformational ap/sp equilibrium in MPA amides and esters caused by selective complexation of Ba2+ with the carbonyl and methoxy groups of MPA.

7.2

Single Derivatization Methods for Mono- and Polyfunctional Compounds

O 4′ O 2′ 1′ H O O H 5′ O O 6′ O

H(1′)

H(5′) H(6′)

H(2′)

MeO

253

H(4′)

H Ba2+

ΔδBa < 0 O

O

O

H Ba2+

O O

Me

H

O

O

Ba2+

ΔδBa > 0

O 6.0

4.5

4.0

3.5

δ (ppm)

H

Figure 7.11 Application of the method based on the selective complexation with Ba2+ to diacetone D-glucose (a secondary alcohol).

conformation and that it moves upfield when barium is added. A negative value means that the specified group is in the same side as the phenyl ring in the ap conformation and that it moves downfield upon addition of the barium perchlorate. Figure 7.11 illustrates the application of this method to a secondary alcohol (diacetone D-glucose). Protons H(4′ ), H(5′ ), and H(6′ ) are shielded in the most stable conformer of the (R)-MPA ester (sp), while protons H(1′ ) and H(2′ ) are shielded in the less stable conformer (ap). After addition of barium perchlorate, the population of the sp conformer increases and protons H(4′ ), H(5′ ), and H(6′ ) are further shielded (positive Δ𝛿 Ba ). Protons H(1′ ) and H(2′ ) are deshielded due to the decrease in the population of the conformer ap (negative Δ𝛿 Ba ). In practice [15], the assignment requires taking the NMR spectrum of the MPA ester in MeCN-d3 ; then solid Ba(ClO4 )2 is added to the NMR tube and a new spectrum is taken after some shaking. Comparison of the chemical shifts gives the Δ𝛿 Ba signs necessary to place L1 /L2 in their spatial location around the asymmetric carbon. A series of secondary alcohols with diverse structures and known configuration have validated the generality of that correlation [15]. Figure 7.12 illustrates the steps to be followed for the assignment and a graphical model showing the correlation Δ𝛿 Ba sign/spatial location of L1 /L2 . In exactly the same way as for secondary alcohols, the addition of barium salt can be used for the assignment of absolute configuration of amines [16], the only difference being in the conformational composition of MPA amides [19] with respect to the MPA esters just discussed. As in MPA amides the main conformer is the ap

254

7 Simplified NMR Procedures for the Assignment of the Absolute Configuration

1st spectrum

2nd spectrum

Experimental

Absolute configuration

Derivatization

H L2

HX

(R)-MPA

Addition of Ba2+

L1

H

ΔδBaL1 > 0 ΔδBaL2 < 0

L2 L1

HX

Absolute configuration?

H HX

L2

(S)-MPA

L1

Addition of Ba2+

ΔδBaL1 < 0 ΔδBaL2 > 0

H HX

L2 L1

Absolute configuration? X= O, NH Figure 7.12 Steps to follow and models for the assignment of the absolute configuration of secondary alcohols and primary amines according to the Δ𝛿 Ba signs of their MPA esters and amides.

and not the sp; therefore, the shift of the conformational equilibrium by selective chelation of the sp increases the population not of the most stable one but of the second one in abundance. In this way, the shielding effects act in exactly the same way as in alcohols with the same chirality: a positive Δ𝛿 Ba means that the L group concerned is on the same side as the phenyl ring in the sp conformer. Thus, there is a correlation between the barium shifts and the spatial position of the L1 /L2 groups that has been validated with a large series of representative amines and can be used for assignment. Figure 7.12 shows the steps to follow for the assignment and a graphical model showing the correlation between the Δ𝛿 Ba sign and the spatial location of L1 /L2 in the amine. 7.2.3 Esterification Shifts

The esterification shifts procedure [17] to determine the absolute configuration of a secondary alcohol is a “single derivative” method that involves the comparison of the NMR spectrum of a single derivative (the (R)- or the (S)-9-AMA ester) of a secondary alcohol with the spectrum of the alcohol without derivatization. This approach is technically simpler than the previous ones (i.e. selective complexation, low temperature) because neither addition of a barium salt nor the use of

7.2

Single Derivatization Methods for Mono- and Polyfunctional Compounds

uncommon solvents (e.g. MeCN-d3 , CS2 /Cl2 CD2 ) is necessary. 9-AMA must be used as auxiliary reagent in this procedure. As stated before, the method consists in the comparison of the chemical shifts for L1 /L2 in the “free” alcohol and in one, the (R)- or the (S)-9-AMA ester derivative. Again, the differences in the chemical shift of L1 /L2 are originated from the conformational composition of the 9-AMA ester, which leaves the anthryl group oriented to produce selectively a high aromatic shielding effect on the substituent (L1 , Figure 7.13) located on the same side as the anthryl group in the sp conformation. In practice, this comparison means that while the protons of one of the substituents (L1 ) suffer an intense shielding with respect to their resonance in the alcohol, the protons of the other substituent (L2 ) resonate at very close shifts in both the alcohol and its 9-AMA derivative (Figure 7.13). In consequence, knowing the conformation of the 9-AMA ester derivative of the sec-alcohol and the spatial location of the anthryl group of the auxiliary (its R/S configuration), comparison of the chemical shifts informs on the identity of the protons that reside under the shielding cone of the anthryl group and therefore on their spatial location. In this way, the L1 /L2 substituents can be placed one just in front of the anthryl ring and the other at the opposite side of the plane bisecting the sp conformer. Alcohol

L2

L1

L2 H

L1 OH

(a)

(R)-9-AMA ester L2 L1

H O

L2

L1

O H

MeO δ(ppm) ΔδAR

(b)

L2

ΔδAR

L1

ΔδAR L2 Δ𝛿AS L1 L2

L1 O (S)-AMA

Figure 7.14 Selection of chiral secondary alcohols and their esterification shift values.

7.3

1st spectrum

Resin-Bound Chiral Derivatizing Agents (Mix and Shake Method)

2nd spectrum

Experimental

Absolute configuration

Derivatization

H

H L2

HO

(R)-9AMA

L1

ΔδAR L2 > ΔδAS L1

HO

L2 L1

Absolute configuration?

Figure 7.15 Steps to follow and models for the assignment of the absolute configuration of secondary alcohols according to Δ𝛿 AR and Δ𝛿 AS values.

shifts within the L1 /L2 substituents: in the (R)-9-AMA ester derivatives, the most intensely shielded protons are located at the right hand substituent (L1 is the substituent located in front of the anthryl group in the sp conformation), while those that are only slightly shielded are located at the left hand substituent (L2 ); thus Δ𝛿 AR L1 ≫ Δ𝛿 AR L2 and the reverse occurs in the (S)-9-AMA esters where Δ𝛿 AS L1 ≪ Δ𝛿 AS L2 . This correlation has been validated with a series of secondary alcohols of known absolute configuration [17]. When MPA is used the same distribution is obtained but the magnitude of the shielding is clearly smaller, close in some cases to the experimental error, leaving 9-AMA as the reagent of choice. The protocol to assign the absolute configuration of a secondary alcohol by this method is summarized in Figure 7.15. It comprises its derivatization with either (R)- or (S)-9AMA, comparison of the chemical shifts for the protons in the alcohol and in the 9-AMA ester, and calculation of Δ𝛿 (Δ𝛿 AS or Δ𝛿 AS ). Next, a molecular model of the 9-AMA derivative in its sp conformation is made and the substituent on the same side as the anthryl group identified as the one suffering the strong shielding (the greatest Δ𝛿). 7.3 Resin-Bound Chiral Derivatizing Agents (Mix and Shake Method)

A second way to simplify the classical NMR procedures for the assignment of absolute configuration involves the use of the auxiliary CDAs anchored to polymer

257

258

7 Simplified NMR Procedures for the Assignment of the Absolute Configuration

resins [20] (“mix and shake” method) and leads to significant progress because no bench work is necessary to prepare the derivatives – just mix and shake for some minutes the substrate and the CDA-linked resin in the NMR tube. This method is based on polystyrene-bound CDAs (CDA-resins) specifically designed to achieve a high-yield formation of the required derivatives by fast formation of the covalent linkage (amide, thioester, or ester bonds) between the substrate (alcohol, amine, thiol, cyanohydrin, diols, triols, amino alcohols) and the chiral auxiliary within the NMR tube, at room temperature and using the deuterated NMR solvent (CDCl3 , CD3 CN, CS2 /CD2 Cl2 ) as the reaction solvent. In this way, just mixing and shaking the resin-bound CDA with the substrate is necessary to get the derivative that is obtained in the NMR tube ready for recording the spectra because the polystyrene does not interfere. Although several different resins and linkages with the CDA have been examined, in practice the most efficient one was demonstrated to be a benzoic acid functionalized polystyrene that can be easily derivatized with the standard MPA, MTPA, BPG, and 9-AMA auxiliary reagents through the formation of a mixed anhydride. This resin-linked auxiliary swells in typical NMR solvents and acts as an electrophile through the benzoic acid carboxy group, allowing efficient attack by the substrate nucleophile (Figure 7.16). In the case of amines [20a], the reaction takes 5 min for the total conversion, liberating the corresponding amide to the solution while the resin-benzoate leaving group floats in the tube. Overall, this approach allows the assignment of absolute configurations of chiral primary amines, primary and secondary alcohols, cyanohydrins, thiols, diols, triols, and amino alcohols, using adequate resin bound-CDA [20]. The single procedure described before for amines, by complexation with Ba2+ , can also be adapted to the resin procedure by using MeCN-d3 as solvent [16]. H L2 L1

HX

H HX

Unknown configuration! Mix, shake and measure

O

O

L2 L1

Configuration assigned!

X

O R1

R2

R1 = H R2 = OMe R1 = CF3 R2 = OMe R1 = H R2 = NHBoc X = NH, O

(Resin: floating) H

O Ar

X R1 R2

L2 L1

(CDA-substrate: in solution) Figure 7.16 “mix and shake” method for secondary alcohols and primary amines based on the use of chiral derivatizing agents (CDAs) anchored to polymer resins.

7.3

Resin-Bound Chiral Derivatizing Agents (Mix and Shake Method)

259

OMe H HO

CH2CH3 CH3

1st spectrum 1H

14

1′

NMR Ph 2

(R)-MPA

3

DMAP DMAP MPA

SO3H NH2

1H

SO3

DMAPH

NH3

MPA

2nd spectrum

1′

Ph

8.0

7.0

NMR

14

OMe 3

2

6.0

5.0

3.4 δ (ppm)

3.0

Figure 7.17 Application of the “mix and shake” method to (S)-butan-2-ol followed by the use of sulfonic acid and amine polystyrene resins as scavengers.

As the hydroxy group of alcohols is a weaker nucleophile than the amino group, the mix and shake procedure for assigning the configuration of hydroxycontaining compounds is slower than with amines, but this can be very efficiently surpassed by adding DMAP followed by sequential addition of sulfonic acid and amine polystyrene resins that act as scavengers and clean the NMR solution; so a good quality spectrum is obtained without traces of the reagents in a few minutes (Figure 7.17) [20b]. The advantages of these CDA-resins [20a, 20b], when compared to the standard coupling procedures, seem clear: (i) very easy preparation of the CDA-resins that are stable for months, (ii) no external reaction flasks (other than the NMR tubes), coupling agents (i.e., DCC or EDC), solvents, filtrations, chromatographic separations, or bench manipulations are required; (iii) undesired by-products (i.e., ureas) are not produced; and (iv) the transformations take place at room temperature in high yields, and the whole process to get the spectra takes from 5 up to 60 min. In addition, the procedure is so clean that it can be carried out at a microscale level (

0

HO

H OH (c)

OH

R α O

0

R β

OH

HO H

H

R O

Figure 7.19 (a) Steps to follow to determine the absolute configuration of hydroxyl acids by formation of a mixed borate with BINOL. (b) Mixed borate between (R)- and (S)-1,1′ -binaphthalene-2,2′ -diol (BINOL) and

OH O

ΔδRS < 0

R

OH

H OH O ΔδRS > 0

an α-hydroxy acid. (c) Models to assign the absolute configuration of α-hydroxy acids from the Δ𝛿 RS signs of their borate complexes with (R)- and (S)-BINOL. (d) Idem for β-hydroxy acids.

This procedure, although of scope limited to α- and β-hydroxy acids, presents the advantage of simplicity (just mixing) and less time (around 30 min) required to get the assignment.

7.5 Tandem HPLC-NMR: Simultaneous Enantioresolution and Configurational Assignment

A particularly interesting case for assignment appears when the substrate of unknown configuration is presented not as a pure single enantiomer but contaminated with a certain amount of the other enantiomer or when we are directly dealing with the mixture of enantiomers. This situation is frequently found in fields related to asymmetric synthesis (i.e., the assay of new asymmetric catalysts) or the systematic analyses of mixtures of enantiomers of interest in pharmaceutical and medical applications, where the need for automation is high and the amount of sample is limited.

7.5

Tandem HPLC-NMR: Simultaneous Enantioresolution and Configurational Assignment

It is in this context that directly coupled HPLC-NMR has been successfully used for the separation and configurational assignment of the enantiomeric components of mixtures of secondary alcohols [8, 23] (including racemates). The procedure requires the use of 9-AMAA [(R)- or (S)-9-AMA)] as CDA and can be carried out in microgram scale. The basis for this application lies in the experimental observation that the (R)and (S)-9-AMA ester derivatives of a chiral secondary alcohol are easily separated by HPLC with standard columns, both in reverse and normal phases [23a] (MPA or MTPA showed no such ability for separation). In this way, 9-AMA is a very efficient reagent to allow the separation of enantiomeric secondary alcohols and if the exit of the HPLC column is connected to an NMR apparatus, the spectra of the two peaks containing the (R)- and (S)-9-AMA ester derivatives can be obtained and assigned [23a]. For the sake of simplicity, reverse phase is preferred because it allows using the same solvent for the HPLC separation (deuterated MeCN-D2 O-formic acid) and the NMR measurement. Normal phase HPLC can also be used for tandem HPLCNMR, being very convenient if preparative separation is sought. There are two situations where this methodology can be successfully applied, depending on the composition of the substrate: (i) mixture of enantiomers that can be racemic and (ii) a single enantiomer. In both cases, the procedure involves the simultaneous HPLC separation of 9AMA esters, the recording of the NMR spectra, and the assignment of the absolute configuration of the secondary alcohol/s [23a]. In the first case, the sample constituted by a mixture of enantiomeric alcohols is derivatized with a single pure enantiomer of the CDA, that is, the (R)-9-AMA and the mixture injected to the HPLC-NMR leading to two peaks that correspond to the (R)-9-AMA esters (Figure 7.20a). The NMR spectra of the two peaks are recorded, and the signals corresponding to L1 /L2 assigned. Next, the Δ𝛿 1,2 are calculated for L1 and L2 in the following manner: Δ𝛿 1,2 L = 𝛿L (compound with the lowest retention time) − 𝛿L (compound with the highest retention time). Finally, the configuration is assigned by comparison of the experimental Δ𝛿 1,2 for L1 and L2 with those shown in Figure 7.20b,c. In the second case, the sample is constituted by a single enantiomer that can carry some impurities. This sample is now derivatized with an uneven mixture (i.e., 3 : 1) of (R)- and (S)-9-AMA, and the resulting mixture of 9-AMA diastereomers submitted to tandem HPLC-NMR, which will show two peaks in the selected 3 : 1 ratio that allow us to identify which peak corresponds to the (R)-9-AMA ester and which to the (S)-9-AMA ester. The resulting NMR spectra of the (R)- and (S)-9-AMA derivatives are compared and the Δ𝛿 RS for L1 and L2 are calculated as usual (Figure 7.21). This technique, apart from representing a significant simplification because the same CDA and solvent were used for both HPLC separation and NMR configurational assignment, offers the possibility of its automatization to a series of compounds at microscale level.

263

264

7 Simplified NMR Procedures for the Assignment of the Absolute Configuration

H

H HO

L1 L2

+ HO

L2 L1

Derivatization (R)-9-AMA

(a)

1H

NMR

1H

HPLC

Mixture of (R)-9-AMA esters

Experimental

1

Δδ1,2 L1 Δδ1,2 L2

NMR

2 Time

Absolute configuration

Experimental

Absolute configuration

Experimental

H Δδ1,2

L1 < 0 Δδ1,2 L2 > 0

RO

H Δδ1,2

L2

L1 > 0 Δδ1,2 L2 < 0

L1

RO

L1 L2 H

H RO 1 (b)

L1

RO

L2

1

2 Time

(c)

L2 L1

2 Time

Figure 7.20 Steps to follow (a) and models (b,c) for the simultaneous enantioresolution and configurational assignment of a mixture of enantiomeric alcohols by tandem HPLC-NMR of their (R)-9-AMA esters.

7.6 Assignment Based on the Chemical Shifts from the Auxiliaries

Regardless of the reduction in the number of diastereomeric derivatives that have to be prepared, the simplification of the experimental work involved, and the possibilities for automatization, major difficulties may arise with certain substrates related to the rigorous assignment of the NMR signals of L1 and L2 . In these cases, the application of the standard methodologies may be tedious and hindered by either the presence of multiplets or the accidental coincidence of chemical shifts. This is particularly important in the case of polyfunctional substrates [4a] that frequently produce complex NMR spectra. In order to solve this problem, some results have been published describing approaches based on the use of diagnostic signals that are simpler to analyze. Thus, in the case of sec/sec-1,n-diols [4a, 13] and sec/sec-1,n-amino alcohols [4a, 24] the assignment of the configuration can be carried out by comparison of the chemical shifts of the methine protons directly bonded to the two chiral centers of the substrate. Similarly, for prim/sec-1,2-diols [4a, 14], a single derivatization procedure has been developed using the methylene protons as signals for

7.6

Assignment Based on the Chemical Shifts from the Auxiliaries

H HO

L1 L2 Experimental

(R)-9-AMA ester

Derivatization (R)-9-AMA/(S)-9-AMA 3:1

1H

NMR

(S)-9-AMA ester 1H

HPLC Mixture of (R)-9-AMA esters

1

2

ΔδRS L1 < 0 ΔδRS L2 > 0

Absolute configuration H

L2 L1

HO

NMR

H

ΔδRS L1 > 0 ΔδRS L2 < 0

HO

L1 L2

Time Figure 7.21 Configurational assignment of a single alcohol from the Δ𝛿 RS signs obtained by tandem HPLC-NMR of an uneven mixture of its (R) and (S)-9-AMA esters.

265

266

7 Simplified NMR Procedures for the Assignment of the Absolute Configuration

diagnosis. In the most complex substrate, prim/sec/sec-1,2,3-triols [25], assignment requires the identification and comparison of H(2′ ) and H(3′ ) signals. Particularly interesting examples of diagnostic signals that are easy analyzed, thus making assignment much simpler, are found in the cases of prim/sec [26] and sec/prim-1,2-amino alcohols [26]. In the bis-MPA derivatives of these substrates, the diagnostic protons are located on the auxiliary reagent (MPA) and not on the substrate part. This is so because in the bis-MPA derivatives, one of the MPA units acts as “active reagent” pointing the shielding cone to the other MPA unit that acts as “substrate.” This “reagent–substrate” role of the two MPA units allows the use of the easily identified OMe and CαH singlets to correlate with the stereochemistry of the amino alcohol [26]. Thus, for example, in the case of the bis-(R)-MPA derivative of the (S)-2aminopropan-1-ol (a sec/prim-1,2-amino alcohol, Figure 7.22), the MPA amide acts as a “reagent” and shields the CαH and OMe of the MPA ester. However, the MPA ester does not “affect” the MPA amide (Figure 7.22a). In the bis-(S)-MPA derivative, the MPA ester acts as a “reagent” and shields the CαH and OMe of the MPA amide, while the MPA amide does not “affect” the MPA ester (Figure 7.22b). This means that the Δ𝛿 RS of the CαH and OMe of the MPA ester are negative, whereas the Δ𝛿 RS of the CαH and OMe of the MPA amide are positive. This trend can be seen in all amino alcohols in which the spatial disposition of the substituents is the same as in the case of the (S)-2-aminopropan-1-ol. The opposite is seen where the spatial disposition of the groups is the opposite of this. In practice [26b], it is not necessary to identify the OMe and CαH signals for the MPA ester and MPA amide parts or calculate their Δ𝛿 RS values because the direct inspection of the separation of the signals in the bis-(R)- and the bis-(S)MPA (Δ𝛿 R and Δ𝛿 S , respectively) is enough to establish the correlation chemical shifts–stereochemistry. For a sec/prim-amino alcohol with the configuration shown in Figure 7.23a, in the bis-(R)-MPA the signals corresponding to the MPA ester (CαH and OMe) are shielded by the MPA amide, while those of the MPA amide are not affected by the MPA ester. In the bis-(S)-MPA, the opposite happens; the MPA amide signals are shielded by the MPA ester, while those of the MPA ester are not affected by the MPA amide. Therefore, the separation of CαH and OMe signals of the MPA units have to be lower in the bis-(R)-than in the bis-(S)-MPA derivative: Δ𝛿 R ≪ Δ𝛿 S . For bis-(R)-MPA

CH3O H

H Me N

H H O

OCH3

O H

O

bis-(S)-MPA

“Substrate”

H

H Me N

CH3O Shieding on: Me(3’)

H H O O H

H

“Reagent” OCH3 H

O

“Reagent” “Substrate” (a)

(b) Figure 7.22 (a) Main shielding effects in the bis-(R)-MPA derivative of a sec/prim-1,2-amino alcohol [(S)-2-aminopropan-1-ol]. (b) Idem for the bis-(R)-MPA derivative.

7.6

Assignment Based on the Chemical Shifts from the Auxiliaries

CαH

L

H NHMPA OMPA

MPA ester

MPA amide

OMe MPA MPA ester amide

ΔδR

ΔδR> ΔδS

NHMPA OMPA

bis-(R)-MPA bis-(S)-MPA

(b)

4.80

4.60

Figure 7.23 (a) Assignment of the absolute configuration of a sec/prim-amino alcohol [(S)-2-aminopentan-1-ol] from comparison of Δ𝛿 R and Δ𝛿 S values of its bis-MPA

3.40

3.20

derivatives. (b) Idem for a sec/prim-amino alcohol with the opposite configuration [(R)2-amino-3-methylbutan-1-ol].

a sec/prim-amino alcohol with the opposite configuration, the trend observed in the NMR behavior is the opposite: Δ𝛿 R ≫ Δ𝛿 S (Figure 7.23b). As in the previous case, it is possible to formulate a similar simplified method to assign the absolute configuration of the prim/sec-1,2-amino alcohols. Thus, in both cases, the procedure is reduced to the preparation of the two MPA derivatives and comparison of the NMR spectra, analyzing only the signals of the CαH and OMe of both MPA units. The separations of the signals, Δ𝛿 R and Δ𝛿 S , are calculated and compared. If Δ𝛿 R ≪ Δ𝛿 S , then the configuration of the sec/prim1,2-amino alcohol corresponds to that shown in Figure 7.24a (Figure 7.24c, in the case of prim/sec-1,2-amino alcohol). On the contrary, if Δ𝛿 R ≫ Δ𝛿 S , then the configuration of the amino alcohol corresponds to that shown in Figure 7.24b (Figure 7.24d, in the case of prim/sec-1,2-amino alcohol). Assignment of these substrates can also be carried out using a single derivatization procedure [26a]. It consists of the derivatization of the sec/prim-1,2-amino alcohol (or prim/sec-1,2-amino alcohol) with either (R)- or (S)-MPA and analyses of the bis-MPA derivative of the amino alcohol and the recording of two 1 H NMR spectra at two different temperatures. The evolution of the singlets due to the CαH

267

268

7 Simplified NMR Procedures for the Assignment of the Absolute Configuration

Derivatization

1H

NMR

L NH2 OH

L

(R)-MPA

or

NH2 (S)-MPA Absolute configuration?

Figure 7.24 (a) Assignment of the absolute configuration of a sec/prim-1,2-amino alcohol with the configuration shown in the figure from Δ𝛿 R and Δ𝛿 S values of CαH and OMe groups of its bis-MPA derivatives. (b) Idem for a sec/prim-1,2-amino alcohol with

L

ΔδR ΔδS ΔδR/ΔδS > 1

(b)

H OMPA NHMPA

L

H OMPA NHMPA

CαH, OMe (MPA)

CαH, OMe (MPA)

ΔδR > ΔδS ΔδR/ΔδS > 1

the opposite configuration. (c) Idem for a prim/sec-1,2-amino alcohol with the configuration shown in the figure. (d) Idem for a prim/sec-1,2-amino alcohol with the opposite configuration.

of the MPA auxiliaries allows inference of the absolute configuration of the amino alcohol. The conformational equilibrium of these two systems (sec/prim- and prim/secamino alcohols) consists of two well-defined conformers: in the most stable, the MPA ester is in the sp conformation, while the MPA amide is in the ap conformation. In the least stable conformer, the MPA ester is in ap conformation while the MPA amide is in the sp conformation [26]. Taking the bis-(R)-MPA amidoester of (S)-2-aminopropan-1-ol as a model compound, in the most stable conformation, the MPA amide acts as a “reagent” and shields the signals of the MPA ester, which takes the role of “substrate” although in the least stable conformation the roles “reagent/substrate” are reversed. A reduction in temperature produces an increase in the population of the most stable conformation, and the number of molecules in the least stable conformation decreases. Lowering the temperature, the signal corresponding to the MPA ester shifts upfield (Figure 7.25a) because there is an increase in the number of molecules in which the MPA ester signals are shielded. The signal corresponding to the MPA amide shifts downfield with decreasing temperature (Figure 7.25a). Once more, there is a decrease in the number of molecules in which the MPA amide signals are shielded. Therefore, the Δ𝛿 T1 ,T2 CαH (MPA ester) is positive, and the Δ𝛿 T1 ,T2 CαH (MPA amide) is negative.

7.6

(a) H Me CH3O ap N H

Assignment Based on the Chemical Shifts from the Auxiliaries

H H O sp OCH 3

O

H Me H N

H

H

O

H H

H

O ap

H

MeO sp O

O

OMe CαH MPA amide

CαH MPA ester

298 K 233 K

(b)

L

213 K

H NH2 OH

183 K 4.60

ΔδR(298) >> ΔδR(Low temp)

4.50

4.40

δ (ppm)

(c) H

OCH3 ap H N H H O O Me

O

MeO sp OCH3

H N H H

O Me

H

H

H sp

H CαH MPA ester

ΔδR(298)

O

H O ap OMe CαH MPA amide

298 K 233 K

(d)

L

H NH2 OH

213 K

ΔδR(183)

183 K 4.80

4.70

4.60

4.50

4.40

4.30

δ (ppm)

ΔδR(298) > ΔδR(Low temp)

ΔδR(298) ΔδS(Low temp)

(a)

(b)

OH L

Absolute configuration?

H OH

H OH

NH2 298 K

213 K

L

NH2

L

NH2

ΔδR(298) ≥ ΔδR(Low temp)

ΔδR(298) distance that separates the two nuclei involved, and the other is the molecular tumbling rate that the species experiences in the solution. The molecular tumbling is characterized by a parameter termed the correlation time, 𝜏 c , which is defined as the time required for the molecular species to rotate 1 radian in any direction (Figure 9.2a). The correlation time is related with the size of the molecular species. For small organic molecules free in solution, 𝜏 c is small (typically from hundreds of picoseconds to a few nanoseconds) and the detectable NOEs are small, slow, and positive in sign (Figure 9.2b). A different situation occurs for large molecular species in which 𝜏 c is considerably larger (e.g., several nanoseconds or beyond), the detectable NOEs being strong, fast, and negative in sign (Figure 9.2b). The relationship between NOE intensity and the r−6 distance has been established in a rigorous manner [8, 9] and it can be applied to deduce the conformation of molecules at different levels of complexity. In molecules containing many protons (and/or other NMR active nuclei), the most precise theory for the interpretation of NOE intensities to deduce internuclear distances, and thus the conformation, is the full relaxation matrix approach [9]. For a given conformation of the molecule it considers simultaneously the cross-relaxation effects within the complete network of nuclei (e.g., all the protons). The interpretation of NOE is more complex for flexible molecules that, instead of a single conformer, contain several conformations in exchange equilibrium. While NOE intensities are very sensitive to the exact population of conformers, the measurement of a sufficient number of key NOEs may be required to estimate the actual equilibrium of conformers in solution. In the following two sections, NOE experiments are described for the study of ligands that are in fast transient association equilibrium with a macromolecular receptor (e.g., protein) as represented in Figure 9.1.

327

328

9 NMR Techniques for the Study of Transient Intermolecular Interactions

NOE spectrum Small molecule, small τc Small & slow positive NOEs NOE

HA

r HB

HA

HB

Large specie, large τc Large & fast negative NOEs (a) τc

HA

HB (b) Figure 9.2 (a) The NOE between a pair of nuclei is sensitive to the r−6 distance among them and the correlation time, 𝜏 c , of the molecular species in which the nuclei reside. (b) For a given distance between the pair of

nuclei, the sign and magnitude of the NOE observed for a proton Ha when a nearby proton Hb is perturbed drastically depends on the correlation time, 𝜏 c , of the molecular species.

9.2.2 Transferred NOE

The TR-NOE, which was discovered by Bothner-By [10] and extensively employed by Feeney and coworkers [11] and other scientists [12], permits assessment of the bioactive conformation of a small ligand molecule in its interaction with the binding site of a macromolecular receptor. Depending on its architecture, the ligand and the binding site may or may not change their conformation upon binding to the receptor. The knowledge of the bioactive conformation of a small ligand that interacts with its biological target has key implications for structurally based drug design.

9.2

Nuclear Overhauser Effect

As in basic NOESY, a TR-NOESY spectrum displays information on spatially close protons of the small ligand molecule and, therefore, it provides key conformational information. Experimentally, the TR-NOESY is performed with exactly the same standard NOESY pulse sequence, but it is applied not to a sample of a pure molecule in solution but to a sample that contains a mixture of the ligand and the receptor in dynamic exchange as represented by the equilibrium of Figure 9.1. Very frequently, in such a sample, the ligand is present in large excess with respect to the receptor. If the equilibrium exchange rate is fast in the chemical shift time scale and the chemical shifts are averaged, then, due to the excess of ligand, the TR-NOE cross-peaks appear at the same chemical shifts of the free ligand and therefore are straightforward to assign. However, given the very different correlation time of the ligand when it forms part of the complex species (large 𝜏 c ) with respect to the free ligand in solution (small 𝜏 c ), the TR-NOEs generated for the ligand in the bound state are of opposite signs and have stronger magnitude than those corresponding to the ligand in the free state (see explanation in Section 9.2). Thus, despite the excess of ligand in the sample in its free state, under suitable conditions that are described below, the TR-NOEs corresponding to the bound state may prevail over those generated in the free state (Figure 9.3). The conditions for the applicability of the TR-NOE experiment depends critically on the dissociation rate of the protein–ligand complex and the molar fractions of free and protein-bound species: kon

−−−−−−− → Protein + Ligand(excess) ← − Protein− Ligand

(9.2)

pbound 𝜎 bound > pfree 𝜎

(9.3)

koff free

koff >> 𝜎 bound

(9.4)

where pbound and pfree are the fractions of bound and free ligand, 𝜎 bound and 𝜎 free the cross-relaxation rates for the bound and the free ligand, respectively, and k off is the off-rate constant. For small molecules in their bound state, cross-relaxation rates in the presence of the protein (𝜎 bound ) are negative and opposite in sign to those of the free state (positive, 𝜎 free ) (as illustrated by the NOE cross-peak H1–H-2 in Figure 9.3). Obviously, the value of 𝜎 bound for a particular proton pair will depend on the interproton distances, the spectrometer frequency, and on the correlation time of the complex. Equation 9.3 indicates that the balance between the molar fractions and the respective cross-relaxation rates must be favorable to the ligand in the bound state. From Equation 9.4 it may be appreciated that the rate of the exchange process must be fast on the relaxation time scale. Because of the relatively low values of cross-relaxation rates (𝜎) in diamagnetic systems ( 15 kDa) at low concentration (10−6 –10−8 M) and one or a pool of small test compounds (ratio receptor – ligand 1 : 10 up to 1 : 1000) two experiments are recorded (optimally in an interleaved fashion): (i) 1D 1 H-NMR under conditions of thermal equilibrium, the so-called reference spectrum or STDoff experiment and (ii) a second 1 H-NMR experiment, the STDon experiment, in which some protons of the receptor are selectively irradiated with low-power radiofrequency during a certain period (saturation time) that can be varied typically in the range of several seconds. If the conditions of irradiation are adequately chosen, it is possible to saturate very efficiently only protons of the protein, but not those of the ligand (Figure 9.5a). In this situation, if binding occurs, magnetization from the receptor protons will be transferred to ligand protons that are close in space in the bound state (Figure 9.5b). As in the bound state the hydrodynamic properties of both ligand and receptor are driven by the largest molecule, transfer of magnetization in the STDon experiment leads to a significant reduction in signal intensities for the ligand (negative intermolecular NOE for big, slowly tumbling molecules) [8]. For transient interactions in fast exchange, this perturbation of ligand polarization in the bound state is transferred to the free state (bulk solution), where saturation accumulates during the saturation time of the experiment. This process results in the detection of the saturation transfer on the free ligand NMR signals in the spectrum STDon . Since signals are reduced in comparison to the corresponding STDoff experiment, subtraction of both experiments (STDoff − STDon ) leads to positive difference signals for the molecule/s affected by intermolecular magnetization transfer (Figure 9.5c). For each ligand signal, an STD intensity can be obtained by measuring the corresponding signal intensity in the STDon and STDoff spectra and applying equation Equation 9.6 (analog of Equation 9.1). STD =

STDoff - STDon STDoff

(9.6)

For a non-binding molecule in the mixture, all its intensities in the STDon and STDoff spectra remain the same, which correspond to a null STD intensity for all of its signals. On the other hand, a binding molecule that satisfies the condition of fast exchange (Equation 9.4) may have some of its signals with an STD intensity different from null [46].

9.3

Saturation Transfer Difference NMR

337

NOE NOE

H

H

H

H

H

H

H

H

H

H H H

H

H

H

H

H H H

H

H H H

H

H

H

R

H

H H

H

H

H

H H H

H

H H H

H H H

H H H

(a) STDON

H

H

H

H

H

H

H

H H H

H1

Koff L

H H

NOE H1

H

H H

H H H

H

R

H

(b)

H

H

H2

L

Kon

H H

H2

H H H H Free state (detected by NMR)

Bound state

STDOFF (1H spectrum) H1

H2

Scan 1 – Scan 2 Sca

n1

R

STDOFF – STDON

H–1 H–2 STDON H1

R H2

H H H

H

H

H H

H

H

H H

H H

H

H

H H H

H

R

H

H H

H

H

H H

H

H

H

H

H

H H

NOE NOE

H

R

H

H

H H H

n2

Sca

R

(c) Figure 9.5 (a–c) Principle of the STD experiment (see text for explanation).

9.3.1 STD NMR Applications 9.3.1.1 Ligand Screening

This is probably the most useful application from the pharmaceutical industry viewpoint [52]. In this type of application, STD experiments are recorded in the presence of several potential ligands and a single target receptor, using experimental conditions that make them compete for the binding site and therefore for the transfer of magnetization [53, 54]. The signals from the ligand that interacts with the receptor will appear in the difference STDoff − STDon experiment (Figure 9.5c) while those from the non-interacting ones will be canceled.

338

9 NMR Techniques for the Study of Transient Intermolecular Interactions

One of the strengths of the STD methodology for ligand screening is that, it is considerably robust and the spectra are free for false positives. However, STD does not prevent the occurrence of false negatives. The latter can occur due to a number of situations, for instance, the possibility of strong binding (i.e., the condition of Equation 9.4 is not met) and scarcity of protons of the ligand and/or in the receptor binding site. These situations would cause the non-observance of STD responses for the corresponding ligand. However, for the pharmaceutical industry, generally, the possibility of false negatives is considered less problematic than false positives, and in this sense, the STD experiment is a complementary method of screening. Additional advantages of this technique are that the protein requirements are low: samples are at low concentration, the needlessness of isotopic labeling, and the absence of a high molecular weight limit. The fact that the ligands are competing for the same binding site also exacerbates the competing nature of this experiment. This has made STD NMR spectroscopy widely applicable in the pharmaceutical industry in the first stages of the development of new drugs [1, 4, 5]. 9.3.1.2 Epitope Mapping

In an STD NMR experiment, the amount of transference of magnetization is, among other factors, due to the 1 H– 1 H intermolecular NOE in the bound state, which is proportional to the inverse of the sixth power of the distance between the nuclei. This property can be exploited to analyze the binding mode of the ligand. Thus, in a first approximation, it can be assumed that the STD intensity of a given proton of the ligand (Equation 9.6) is related to their proximity to some protons of the receptor at the binding site. Thus, the largest STD intensities correspond to those protons of the ligand in closest contact with the receptor, while on the contrary the absence of STD will correspond to parts of the ligand far from the receptor protons. To facilitate the comparison, the set of STD intensities obtained for a ligand are expressed as relative STD percentages (%) by normalizing to 100% the most intense one (relative STD) [55]. Those protons with the maximum STD percentage are the most relevant for the interaction. The use of STD percentages also facilitates the comparison of the STD results between a series of ligands that bind the same receptor. The method is called ligand epitope mapping and reveals the structural features required in the ligand that are important for the binding interaction. A problem that may introduce errors for the determination of the binding epitope is the potential T1 longitudinal relaxation bias in the STD intensities [55, 56]. It causes a relative overestimation in the STD intensity for protons of the ligand with long T1 with respect to those with shorter T1 that are underestimated. The reason for the overestimation is the longer time that saturation is accumulated in the free state of the ligand for those protons with long T1 with respect to others with short T1 , while the latter relax faster toward equilibrium (Figure 9.5). This so-called T1 bias is proportional to the duration of the saturation time of the STD experiment and may cause problems for the interpretation of the STDs such as in determining the ligand-binding epitope, especially when the ligand protons have substantially different T1 . A typical case of T1 bias in STD occurs

9.3

Saturation Transfer Difference NMR

when there are aromatic protons (long T1 ) and methylene protons (short T1 ) in the same ligand. This situation leads to an overestimation of the STD for the aromatic protons proportional to the saturation time. The problem of T1 bias can be avoided by using the STD initial build-up rate method proposed by Mayer and James [55]. The method is as follows: instead of measuring just a single STD experiment at a certain saturation time, a number of STD experiments are acquired at a series of saturation times. For a given signal of the ligand, its initial STD buildup rate (STD0 ) is obtained by fitting the experimental STD build-up curve in which the STD obtained with Equation 9.6 (STDobs ) is represented at each saturation time (t sat ) and the curve is fit to the following monoexponential equation (Equation 9.7). STDobs (tsat ) = STDmax ⋅ (1 − e(−ksat

⋅ tsat )

)

(9.7)

where STDmax is the maximum STD intensity reachable when long saturation times are used and k sat stands for the observed saturation rate constant. Multiplication of k sat and STDmax yields the slope of the curve at zero saturation time or the initial build-up rate (STD0 ). This slope is proportional to the STD intensity in the absence of T1 bias while the proportionality constant is the same for every proton of the ligand (see example in Figure 9.6) [55]. This method has been used to analyze and quantify dual binding mode in some lectins [58]. 9.3.1.3 Quantitative Structural Analysis: CORCEMA-ST

The quantitative interpretation of STD in combination with molecular modeling tools has been used to deduce the structure of the ligand–receptor complex. The laboratory of Prof. N. R. Krishna has provided the theoretical framework for the quantitative analysis of STD-NMR experiments. It is based on a modification of the method known as COmplete Relaxation and Conformational Exchange MAtrix [59] described for the transferred NOE experiments of Section 9.3. The theory developed for the STD experiment is known as CORCEMA-ST (COmplete Relaxation and Conformational Exchange MAtrix-Saturation Transfer) [60–62] and allows the prediction of the STD signal intensities given the coordinates of the protein–ligand complex, using some kinetic and thermodynamic values (k on and dissociation constant) and some NOE-related parameters, such as the rotational correlation times of the receptor and ligand, and the protein proton directly saturated by the applied low-power radiofrequency. In this way, for a model of the complex that could be obtained from different techniques (e.g., X-ray crystallography, NMR, docking simulations), CORCEMA-ST provides the theoretical quantitative STDs. Experimental STD build-up curves can be compared with predictions. The agreement between the molecular model and the experimental NMR data can be quantified by the so-called R-NOE factor (Equation 9.8): √ ΣWk (STDexp,k − STDcal,k ) R-NOE = (9.8) ΣWk (STDexp,k )

339

340

9 NMR Techniques for the Study of Transient Intermolecular Interactions

Cl

100% 69.4%

b′

c′

a′

d′

100%

69.4% 69.4%

CO

f N

e

53.0%

a CH3 55.8%

H3CO

c

d

b

59.6% (a)

54.5%

HOOC

STDoff a′d′ b′c′

9.5

9.0

8.5

8.0

7.5

d

cfe

7.0

6.5

6.0

5.5

(b)

5.0 4.5 f1 (ppm)

4.0

3.5

3.0

a

b

2.5

2.0

1.5

1.0

0.5

0.0

1.0

0.5

0.0

STDoff − STDon a′d′ b′c′

9.5

9.0

8.5

8.0

7.5

c f e

7.0

a

b

6.5

6.0

5.5

5.0

(c)

Figure 9.6 (a) Structure of indomethacin showing the STD0 percentages (%) obtained from the STD study of the mixture indomethacin: zein 50 : 1. (b) A pair of STDoff and STDoff-on spectra of the mixture showing the assignment of indomethacin signals. The STDoff-on spectrum was obtained by irradiation of the

4.5

4.0

3.5

3.0

2.5

2.0

1.5

f1 (ppm)

aliphatic signal of the zein that is indicated with an arrow and the saturation time was 2 s. A series of STDoff-on spectra were obtained varying the saturation time and the STD intensities obtained were fitted to Equation 9.7 to determine the STD0 values that are shown. (Reprinted with permission from Ref. 56).

9.3

Saturation Transfer Difference NMR

where STDexp,k and STDcal,k are the experimental and calculated STD intensities of proton k, respectively. A low R-NOE factor indicates a good fit between experimental and theoretical data. In this way, different structural models derived, for example, from different docking runs, can be ranked according to how well they explain the experimental STD NMR data. A procedure for optimization of the bound conformation has been developed for models originating from computational docking or for cases where the crystallographic structure of the protein receptor deviates from the solution one. This STD NMR intensity-restrained CORCEMA optimization (SICO) [63] procedure uses a hybrid structure refinement protocol that includes CORCEMA calculations and simulated annealing simulation to refine the bound conformation. The R-NOE factor [63] (Equation 9.8) is calculated for the starting structure and all the intermediate structures after each cycle of refinement in order to compare the goodness of the procedure. The protocol minimizes the R-NOE factor of the STD, yielding the optimum ligand geometry and position within the binding pocket. Some examples have been recently published [31, 64]. The molecular models of the complexes of the anti-HIV-1 antibody 2G12 with a disaccharide and a tetrasaccharide were obtained from published X-ray data, and the complex with a trisaccharide from docking simulations. From these structural models the theoretical STD intensities were predicted by CORCEMA-ST, and the resulting low R-NOE factors corroborated that the binding modes of the ligands in solution were similar to those observed in the solid state [65, 66]. This quantitative approach has been successfully applied to several cases of protein–carbohydrate interactions [63, 67, 68]. This methodology has even permitted the detection of cases of multiple binding modes of a carbohydrate ligand into the same binding pocket [58]. Figure 9.7 summarizes an STD NMR study of the molecular recognition of oligomannoside ligands by antibody s2G12 [31]. 9.3.1.4 Binding Constants from STD NMR

From the analysis of the experiment it is obvious that the STD intensities are dependent on the protein–ligand complex concentration in solution. A simple conversion by multiplying the absolute STD intensities by the molar excess of ligand over protein yields a magnitude, the saturation transfer difference amplification factor (STD-AF) (Equation 9.9): STD-AF = STD × [L0 ]∕[R0 ]

(9.9)

where [L0 ] and [R0 ] are the total concentration of the ligand and receptor, respectively. Since STD-AF is proportional to the fraction of bound protein, in principle it should be possible to obtain the apparent binding constant by adjusting these values to a Langmuir type equation, after titration of the ligand onto the protein sample. However, initial attempts to extract directly the binding constant using this method were unsuccessful, as the values obtained depended strongly on the saturation time, monitored signal, and relative concentration of species. See, for example, in Figure 9.8, the variation of the apparent dissociation constant, K D , with the saturation time (K D corresponds graphically to the concentration of

341

342

9 NMR Techniques for the Study of Transient Intermolecular Interactions OH

100–65%

A

OH O

HO HO

C

OH O

45–35%

HO HO

B

O

B

OH O

16–15%

HO HO

A O

(a) 5

(b)

NH2

5

A B C

H1 H2 H3 H4

4 3 2 1

A B C

H1 H2 H3 H4

4 STD (%)

STD (%)

C

O

3 2 1

0

0 0.5

1.0

1.5 2.0 2.5 Saturation time (s)

(c)

3.0

0.5

(d)

Figure 9.7 Molecular recognition of linear oligomannosides by the anti-HIV-1 2G12 antibody, studied by STD NMR in solution. (a) Trisaccharide Man 1-2 Man 1.2 Man.

1.0

1.5 2.0 2.5 Saturation time (s)

3.0

(b) Structure of the calculated (docking) derived structural models. (c) Experimental STD build-up curves. (d) Predictions from CORCEMA-ST based on b).

3000 HE3 HZ2 HD1 HA

O H2N

CH C CH2

OH H𝜀3

H𝛿1 H𝜁3

HN

H𝜂2

Dissociation constant, KD

BSA + Tryptophan 2500 2000 1500 1000 500

H𝜁2

Initial slopes

KD (calorimetry)

0 0 (a)

(b) Figure 9.8 (a,b) Plot of KD calculated from the STD intensity values, showing the dependence with the saturation time and monitored proton,

1

2 3 Saturation time (s)

4

for tryptophan binding to BSA, compared with the value obtained from calorimetry [69]. Reprinted with permission from Ref. 69

9.3

Saturation Transfer Difference NMR

ligand when normalized STD-AF is 0.5). This figure reveals that the apparent K D values increase monotonically with the saturation time [69, 70]. Similarly, other factors such as receptor concentration, signal intensity, and so on have been demonstrated to have similar spurious effects [69, 70]. Thus, until recently, the method of choice for determining binding constants by STD NMR using competition experiments with another inhibitor of known KD value has been the use of the Cheng and Prusoff equation, which determines the relative binding constants [71, 72]. The origin of these discrepancies can be found in the processes of fast rebinding of previously saturated ligand molecules to the protein-binding site during the experimental saturation time. If a ligand molecule binds the protein before its perturbed magnetization has not completely returned to equilibrium it will not have the same capacity to gain all the magnetization available from the receptor. Consequently, the observed bulk STD signal is reduced when the lifetime of the free state is shorter than the T 1 relaxation time of the proton considered due to incomplete polarization recovery in the free state. The probability of such rebinding processes is higher for larger saturation times, higher fraction of bound ligand (low ligand concentrations), higher affinity, and higher concentration of receptor [69]. After a study of the artifacts introduced by the different experimental parameters of the STD NMR experiment, it was concluded that [69]: (i) the value of K D obtained by STD NMR spectroscopy is always greater than, or equal to, the true thermodynamic value; (ii) the bias introduced is greatest for ligand protons showing the largest STD intensities; and (iii) the deviations are larger at larger protein concentrations, that is, at higher complex concentrations. The determination of absolute dissociation constants requires the removal of all the effects from fast protein–ligand rebinding in solution. These effects are cancelled out at t sat = 0, where no saturation has been transferred, and any STD is hence zero. However, in analogy with the STD build-up curve method described above, in Figure 9.8 the trend can be calculated by fitting the STD-AF build-up curve (Equation 9.10) and calculating the slope at zero saturation time (STD-AF0 ) (Equations 9.10 and 9.11) STD-AFobs (tsat ) = STD-AFmax ⋅ (1 − e(−ksat

( limtsat →0

⋅ tsat )

)

) d STD-AF = ksat ⋅ STD-AFmax = STD-AF0 dt

(9.10)

(9.11)

Next, the binding isotherms are obtained by representing graphically STD-AF0 as a function of the added ligand concentration. Finally, the K D value is obtained by fitting this association curve to a Langmuir equation. The method is summarized in Figure 9.9 [69].

343

9 NMR Techniques for the Study of Transient Intermolecular Interactions

STD-AF0 = STD-AFmax (1-exp(−ksattsat)) 18 0.2 mM 0.4 mM 0.6 mM 0.8 mM 1.0 mM

STD-AF

12

6

STD-AF0 = STD-AFmax ksat 0

0

1

(a)

2 Saturation time (s)

Ligand concentration STD-AFmax (mM)

(b)

3

4

ksat

STD-AF0

(s−1)

(STD-AFmax × ksat)

0.2

6.8 (± 0.2) 0.68 (± 0.04)

4.6 (± 0.4)

0.4

12.3 (± 0.7) 0.44 (± 0.05)

5.5 (± 0.9)

16 (± 1.0)

0.6

0.43 (± 0.07)

7.0 (± 1.5)

0.8

21 (± 1.0)

0.34 (± 0.04)

7.1 (± 1.2)

1.0

25 (± 1.5)

0.30 (± 0.03)

7.2 (± 1.5)

8 7 6 STD-AF0

344

Y = Bmax X/(KD + X)

5 4 3

KD = 0.210 (0.05)

2 1

(c)

0 0.0

0.2

0.4 0.6 0.8 1.0 1.2 Ligand concentration (mM)

Figure 9.9 Method for the calculation of binding constants from STD data. (a) Building of the STD-AF build-up curve and fitting to Equation 9.10. (b) Calculation of the initial

1.4

growing rate, STD-AF0 using Equation 9.11 (this should be done for each titration point). (c) Average binding isotherm used to determine the dissociation constant K D .

9.4

Diffusion NMR

9.4 Diffusion NMR

NMR diffusion experiments allow the characterization of supramolecular interactions such as ligand–protein interactions and the determination of relevant parameters related with the structure, size, shape, and binding affinity of these complexes. In this part of the chapter, the basic principles for the interpretation of the NMR diffusion data in the presence of binding interactions are outlined. Examples covering a range of diffusion experiments for the study of binding transient interactions will be presented. 9.4.1 Diffusion and Molecular Structure

The diffusion coefficient measures the speed of translation that any molecular species, either a single molecule or a supramolecular complex, experiences in solution as a result of random Brownian motions. It is related with a number of features that include size, shape, and molecular mass of the molecular species together with other experimental aspects, such as viscosity and temperature of the solution. The simplest relation of diffusion with molecular size and shape is given by the Debye equation (Equation 9.12): D=

kB T f

(9.12)

where D is the diffusion coefficient, k B is the Boltzmann constant, T is the temperature, and f is the friction coefficient. Different expressions for the friction coefficient have been proposed, depending on the approximations used to treat the solvent and solute. For instance, for a spherical molecule the friction parameter f is given by Equation 9.13 and the full equation is known as the Stokes–Einstein equation (Equation 9.14). f = 6π𝜂 r

(9.13)

where 𝜂 is the viscosity of the solvent and r the effective hydrodynamic radius of the molecule. D=

kB T 6π𝜂r

(9.14)

9.4.2 Measuring Diffusion with NMR

NMR experiments relying on diffusion only require spectrometers capable of producing pulse field gradients (PFGs), typically along the z-axis, which are standard today. The experiments provide an NMR spectrum in which the signal integral (or intensity) is conveniently modulated by the diffusion coefficient of the corresponding species.

345

346

9 NMR Techniques for the Study of Transient Intermolecular Interactions

There are numerous NMR experiments available for measuring diffusion. The choice of the appropriate experiment is conditioned by the type of sample and the required sensitivity. A thorough description of the most common experiments can be found elsewhere [7, 73, 74]. Special care should be taken with the experimental parameters to avoid systematic errors [75, 76]. The possibility of temperature gradients in the sample may cause convection and increased diffusion coefficients that are erroneously measured with the experiment. This is one of the most common sources of error when determining diffusion coefficients by NMR, especially for less viscous solvents. Convection can be alleviated by the use of reduced samples volume with Shigemi tubes and/or small diameter coaxial capillary tubes or by spinning the sample at special rates [77]. Specific NMR diffusion experiments were also designed to compensate for the artifacts caused by lamellar convection [78]. DOSY (diffusion ordered spectroscopY) is one of the most popular NMR experiments to measure diffusion coefficients of either single molecules or mixtures of compounds without the need to separate them physically. A DOSY spectrum can be seen as a series of 1D NMR spectra in which each spectrum in the series is acquired with a certain value of the strength of the PFG used to encode the diffusion in the signal intensity of each NMR signal. Stejskal and Tanner deduced an expression that relates the signal intensity seen in a given 1D NMR spectrum with the strength of the PFG applied, and the diffusion coefficient of the molecular specie that generates the signal [79, 80]. There are actually different versions of these so-called Stejskal–Tanner equations depending on the exact diffusion pulse sequence and the type of shape used for the gradient pulses applied to encode diffusion. The two most basic DOSY pulse sequences are known as the stimulated echo (STE) and the gradient spin echo (SE) and the two most common shapes used for the gradient pulses that encode the diffusion are rectangular and halfsinusoidal. DOSY experiments based in STE and SE use the same form of the Stejskal–Tanner equation. For rectangular and half-sinusoidal shaped gradients the relationship between the diffusion coefficient and signal intensity is given by Equations 9.15 and 9.16, respectively. ( ) I(G) 𝛿 = −𝛾 2 G2 D𝛿 2 Δ − (9.15) ln I(0) 3 ( ) I(G) 4Δ − 𝛿 ln = −𝛾 2 G2 D𝛿 2 (9.16) I(0) π2 where I(G) and I(0) are the intensity of the signal upon application of the PFG and the initial intensity, respectively. 𝛾 is the magnetogyric constant (for 1 H is 26751 rad G−1 s−1 ), G is the power of the gradient (G cm−1 ), D is the diffusion coefficient (cm2 s−1 ), 𝛿 is the duration of the gradient (about 1 ms), and 𝛥 is the duration of the gradient echo or stimulated echo. To determine the diffusion coefficients, a series of experiments are performed in which either G, 𝛿, or 𝛥 is varied. However, to guarantee that the contribution to the signal attenuation caused by relaxation is the same, the duration of all the events in the DOSY pulse sequence should be constant for each point recorded in the

9.4

Diffusion NMR

347

Gr

ad

ien

tp

ow

er

diffusion dimension. Normally, the only parameter that is incremented is the gradient power G, and all other parameters in Equation 9.15 or 9.16 remain constant. The gradient power is conveniently varied (e.g., linearly or exponentially) from the minimum to the maximum allowed. The number of spectra that are obtained in which the gradient is varied will affect the precision of the determined diffusion coefficient per second. The nonlinear fitting of the signal intensity to Equation 9.15 or 9.16 provides D, and there are special processing algorithms to represent such information as a 2D plot correlation with a diffusion dimension. An example of DOSY spectrum can be seen in Figure 9.10.

6.0

5.5

5.0

4.5

4.0

3.5 1H

3.0

2.5

2.0

1.5

1.0

0.5

0.0 –0.5

(ppm) DOSY processing (ILT)

MeOH 1E−05

H2O

nBuOH

Diffusion (cm2 s−1)

1E−04

TEG

1E−06 6.0

5.5

5.0

4.5

4.0

3.5

3.0

1H

(ppm)

2.5

2.0

1.5

1.0

0.5

0.0 –0.5

Figure 9.10 1 H DOSY spectrum for a mixture of methanol, triethylene glycol (TEG), and n-butanol in D2 O. 1 H NMR signals of the same compound appear at the same position in the vertical diffusion dimension.

348

9 NMR Techniques for the Study of Transient Intermolecular Interactions

Signal overlap, as often occurs in the analysis of complex mixtures of compounds, cause problems in determining the individual diffusion coefficient of the species with the monoexponential equations Equation 9.15 or 9.16. In such cases, special algorithms for processing the diffusion dimension are required, for instance, bi-exponential fitting [81], MaxEnt [82], DECRA [73], and SCORE [83] to provide individual diffusion coefficients. Nevertheless, in practice these methods are limited to a maximum of three or four overlapping components that have enough signal sensitivity and with relatively different diffusion coefficients. Another possible solution to reduce signal overlap is to increase the dimensionality of the NMR experiment, although at the cost of extra measurement time. Some of the experiments proposed are 3D DOSY-J-resolved [84, 85], 3D DOSY-COSY [86], 3D DOSY-TOCSY [81], and 3D DOSY-HSQC [82, 87]. Improved hybrid experiments have been developed more recently in which the DOSY dimension is incorporated internally (iDOSY) into the sequence of another experiment and provides enhanced sensitivity. Some examples are 2D J-IDOSY [88], 3D COSY-iDOSY [89], 3D DQF-COSY iDOSY [86], and 3D HSQC-iDOSY [90]. 9.4.3 Diffusion Coefficient in the Presence of Chemical Exchange

Consider the bimolecular association equilibrium between a small molecule (L, ligand) and a large molecule (R, receptor) that can be described as a two-site exchange system (see Figure 9.1). If the size of the two molecules is very different, the diffusion coefficient in the bound state (Dbound ) is approximately the same as that of the macromolecule in the free state. The influence of exchange in the DOSY spectra of a two-site system has been considered and analyzed in detail [91–94]. For the analysis of diffusion NMR data, there are three different regimes to consider. The regime depends on the relationship between the global exchange rate of the association equilibrium (k ex )2) and the diffusion NMR time scale, which is given by the diffusion delay time Δ.

• Fast exchange regime: Δ ≪ 1/k ex In this regime the observed diffusion coefficient (Dobs ) is related to the diffusion of the free and bound species (Dfree and Dbound ). The observed diffusion coefficient (Dobs ) is the average of the diffusion coefficient of the species that generates the signal in the free and bound states, Dfree and Dbound , respectively, weighted by their respective molar fractions, p, where pfree + pbound = 1 (Equation 9.17): Dobs = pfree Dfree + pbound Dbound = (1 − pbound ) Dfree + pbound Dbound (9.17) In this regime Dobs can be determined from the mono-exponential fit of the signal intensity to the Stejskal–Tanner equation (Equation 9.15 or 9.16). 2) k ex is related to koff by k ex = k on [Prot]free + k off , which, in the typical conditions of the experiments reported here, could be assimilated to k off as [Prot]free goes to zero.

9.4

Diffusion NMR

• Intermediate-exchange regime: 𝛥 ∼ 1/k ex In this regime the observed diffusion coefficient (Dobs ) is related to the diffusion of the free and bound species (Dfree and Dbound ). However, unlike the fast regime, Dfree and Dbound are not related by a simple relationship; the weight of each parameter depends on the power of the PFG and therefore is not constant along the traces of diffusion experiment. In general, in this regime it is difficult or not possible to determine Dfree and Dbound from the fit to the Stejskal–Tanner equation (Equation 9.14 or 9.15). • Slow exchange regime: 𝛥 ≫ 1/k ex In this regime the observed diffusion coefficient (Dobs ) is completely independent for the free and bound species. In principle, if there is no signal overlap among these two species, a mono-exponential fit of the signal intensity to the Stejskal–Tanner equation (Equation 9.14 or 9.15) would provide either Dfree or Dbound . However, if there is signal overlapping, a bi-exponential fit to the Stejskal–Tanner equation would provide both Dfree and Dbound . 9.4.4 Diffusion NMR Applications 9.4.4.1 Diffusion NMR Screening

Diffusion-edited NMR has been used for screening mixtures of compounds for testing in drug discovery programs in the pharmaceutical industry [94]. These methods are based on the fact that the apparent size or shape of a small molecule can be altered by complexation with a partner in solution. In fact, when a small molecule is in transient binding to a large receptor, as in a ligand binding to a protein, its diffusion coefficient may decrease by more than one order of magnitude (Figure 9.11). This means that at least for some time the small molecule will have the diffusion coefficient of the large receptor. If the association of the small molecule occurs in the fast exchange regime in the diffusion time scale, Equation 9.17 applies. Thereby the identification of ligands from mixtures is possible because the diffusion coefficient of a small molecule is altered by the complexation with a receptor; for this reason, this methodology has also been called “affinity NMR.” Diffusion editing can be combined with other NMR experiments that allow the structural identification of the interacting molecule without the need of prior separation of the components. 9.4.4.2 Diffusion NMR in the Study of Non-covalent Transient Intermolecular Interactions

DOSY can be a useful technique for the qualitative study of the relative strength of specific non-covalent interactions in solution, such as hydrogen bonds and ionpairing, and even to study solvation. It has been shown that the relative decrease in the diffusion coefficient of a particular molecule in a mixture of molecules, which interact by H-bond with a common H-bond acceptor or donor, can be interpreted in terms of the tendency of the molecules in a mixture to be involved in association by H-bonds with the

349

9 NMR Techniques for the Study of Transient Intermolecular Interactions

250

200 Dligand/Dprotein

350

50

00

50

0 100

101

102

103

104

105

106

107

MWprotein/MWligand Figure 9.11 Ratio Dligand /Dprotein plotted against MWprotein /MWligand . Notice that with increasing MWprotein /MWligand, Dlig /Dprot increases as well, that is, the effective diffusion coefficient of the ligand decreases dramatically.

H-bond donor or acceptor [92, 95]. With proper experimental design, to account for changes in viscosity of the solutions, the determined diffusion values can be interpreted in terms of changes in the hydrodynamic radius of the interacting molecules [92, 95]. There are numerous examples in the literature where diffusion NMR data has been used to study ion-pairing, both from a qualitative and a quantitative point of view [96, 97]. As an example, for two ions of very different size, if the diffusion of the anion and the cation can be determined separately, the determination of the same diffusion coefficient for both ions is an indication of a complete ion-pairing. 9.4.4.3 Diffusion NMR in the Study of Self-aggregation

Molecular self-assembly is a particular case of association equilibrium and some molecules are able to form high order self-aggregates. Its formation is promoted by the establishment of a number of favorable non-covalent intermolecular interactions (π–π stacking, hydrophobic, ionic, etc.). Self-assembly may introduce changes in the NMR observables such as chemical shift, relaxation times, and/or diffusion coefficients. Diffusion NMR is a convenient way to study self-aggregation phenomena [98–101]. Unlike chemical shifts, diffusion NMR does not require particularly well-resolved lineshapes. While relaxation times are sensitive to both the global and internal molecular dynamics, only the former contributes to the diffusion measurements. The structure and properties of a self-aggregate depends on the exact experimental conditions such as temperature, solvent, and concentration, among others. The aggregation number (N), namely, the average number of units constituting the supramolecule, can be determined if the hydrodynamic size of the elemental

9.4

Diffusion NMR

building blocks is known (rH 0 ). The determination of rH 0 is straightforward from the diffusion coefficient measured under the experimental conditions in which the supramolecule completely disaggregates, normally very diluted solutions or with different solvents. Hydrodynamic radii and volume of a self-aggregate are usually determined from diffusion data assuming a spherical supramolecular system, although other shapes can be considered as well [91–99, 101].2 Diffusion NMR has been used to study self-aggregates in a variety of systems [100, 102, 103]. An example is the case of surfactants, which are amphiphilic molecules with a rich variety of self-assembly properties [93]. A diffusion NMR titration study can provide information on micellar size, structure, ion binding, and solubilization [104, 105] (Figure 9.12). The point in the titration where the diffusion coefficient abruptly drops to lower values indicates the presence of aggregates in solution, that is, the so-called critical micelle concentration; see Figure 9.11. Assuming spherical shapes for the monomer and micelle, the ratio of their diffusion coefficients is inversely proportional to the cubic root of their molecular weight and the aggregation number can be determined at each point in the titration (figure adapted from Ref. [96]). 9.4.4.4 Diffusion NMR to Determine the Equilibrium Binding Constant

Diffusion NMR can provide access to equilibrium dissociation constant (K D = K on /K off ) of association binding equilibria [106]. Assuming the association equilibrium of Figure 9.1 and that the system is in the fast exchange regime of diffusion, the starting point for the diffusion-based determination of the association constant is the mathematical treatment to get K D from Dobs . The method in principle is analogous to any other NMR observable in the fast regime whose value is modulated by the concentration of the species in the equilibrium, such as chemical shifts or relaxation times [107]. However, if the difference in size between the ligand and the receptor is large enough, it can be assumed that the diffusion coefficient of the receptor or host is not greatly modified by the binding of a small ligand molecule so that the diffusion of the complex, Dbound RL , is the same as the diffusion of the large receptor in the free state, Dfree R (Figure 9.13), this reduces one unknown and facilitates the calculation of K D . Assuming that the approximation holds and that the diffusion coefficients of the free species have already been determined for the ligand and the receptor, Dfree R and Dfree L , respectively, then it is possible to calculate the association constant for the mixture of ligand and receptor with a single experiment in which the apparent diffusion coefficient of the ligand, Dobs L , is measured. The method saves considerably time for the determination of K D since there is no need to perform a titration study exploring several concentrations. The deduction of the equation to determine the K D with diffusion coefficients for the equilibrium of Figure 9.12 is straightforward. It starts with the usual definition of the dissociation constant K D (Equation 9.18).

351

9 NMR Techniques for the Study of Transient Intermolecular Interactions SO3Na

SO3Na SO3Na

NaO3S

O

O

O

O

n

(a)

Monomer

Micelle

2.5 × 10−6 Dobs (cm2.s−1)

352

2 × 10−6 cmc = 0.32 mM −6

1.5 × 10

10−6 5 × 10−7

0.1

(b)

1

10

[SC4TH]/mM

Figure 9.12 Study of the micellization of p-sulfocalixarene-based surfactant (SC4TH). (a) Structure of SC4TH, (b) self-aggregation equilibrium of SC4TH promotes the formation of a micelle, and (c) DOSY titration curve of SC4TH at 25 ∘ C.

KD =

[R] ⋅ [L] [RL]

(9.18)

Under fast exchange equilibrium Equation 9.16 holds. It can be rearranged with respect to the molar fraction of the bound ligand pL bound (Equation 9.19) and all the parameters can be directly measured with DOSY diffusion experiments.

pLbound =

DLobs − DLfree DRL − DLfree bound

(9.19)

9.4

Diffusion NMR

The usual definition of molar fractions in the equilibrium of Figure 9.12 is given by Equations 9.20–9.25: [RL] , [L0 ] [L] , = [L0 ]

pLbound =

(9.20)

pLfree

(9.21)

pLbound + pLfree = 1

(9.22)

[RL] , [R0 ] [R] , = [R0 ]

pRbound =

(9.23)

pRfree

(9.24)

pRbound + pRfree = 1

(9.25)

where L0 and R0 are the total concentrations of the ligand L and receptor R, respectively. Substituting Equations 9.20–9.25 in Equation 9.18 gives the following expression for the dissociation constant K D (Equation 9.26). ) ) ( ( pRfree [R0 ] ⋅ 1 − pLbound [L0 ] pRfree [R0 ] ⋅ 1 − pLbound (9.26) KD = = pLbound [L0 ] pLbound In the previous equation pR free can be expressed by the known parameter pL bound using the relationships of Equations 9.20–9.25 (Equation 9.27) ( ) pL [L0 ] 1 − bound [R0 ] ⋅ (1 − pLbound ) ([R ] − pL [L ]) ⋅ (1 − pLbound ) [R0 ] 0 bound 0 KD = = pLbound pLbound (9.27) The main limitation of this methodology is the binding between small molecules. In these cases the approximation of Figure 9.13 in which Dbound RL is the same as Dfree R does not hold. This is usually the situation in most host–guest chemistry studies and typical medium-sized host molecules, such as cyclodextrins. It has been shown that a data treatment, which takes into account the H R

+

DfreeR

L

DfreeL

H R

L

Kd

DboundRL ~ DfreeR

Figure 9.13 Diffusion coefficients of the species for the bimolecular association equilibrium between a large receptor (R) and a small ligand molecule (L).

353

354

9 NMR Techniques for the Study of Transient Intermolecular Interactions

diffusion of all species, is needed for accurate results. This treatment involves, however, the determination of the diffusion coefficients of a series of solutions with different molar ratios (titration study) [1–3, 5, 106] and is therefore justifiable only when other potentially much faster NMR methods are not possible, for instance, when the chemical shift change of the guest molecule is very small.

9.5 Conclusions

Due to its primary nature, NMR is capable of acquiring structural information for each of the individual atoms of the molecule because each signal in the spectrum corresponds to an individual atom, even in complex macromolecules. In addition, NMR is very sensitive to dynamic phenomena and in the case of the existence of equilibrium the parameters obtained from the spectrum reflect the species present in it. Depending on the kinetics, the signal(s) and the parameter(s) measured from them could account for all the populated states either as an average or as a series of single conformations. This property makes NMR an extraordinary tool for the study of transient interactions. In this chapter, we have reviewed the main tools for the study of these interactions when the kinetics is fast enough in the NMR time scale to yield averaged parameters: Transferred NOESY, saturation transfer difference spectroscopy, and diffusion. We have made an effort to discuss the theoretical bases of each particular technique and shown some examples explaining the differences and the different parameters that can be extracted from each technique.

References 1. Pellecchia, M., Bertini, I., Cowburn,

D., Dalvit, C., Giralt, E., Jahnke, W., James, T.L., Homans, S.W., Kessler, H., Luchinat, C., Meyer, B., Oschkinat, H., Peng, J., Schwalbe, H., and Siegal, G. (2008) Perspectives on NMR in drug discovery: a technique comes of age. Nat. Rev. Drug Discovery, 7, 738–745. 2. Calle, L.P., Canada, F.J., and Jimenez-Barbero, J. (2011) Application of NMR methods to the study of the interaction of natural products with biomolecular receptors. Nat. Prod. Rep., 28, 1118–1125. 3. Roldós, V., Cañada, F.J., and Jiménez-Barbero, J. (2011) Carbohydrate–protein interactions: a 3D view by NMR. ChemBioChem, 12, 990–1005.

4. Pellecchia, M., Sem, D.S., and Wuthrich,

5.

6.

7.

8.

K. (2002) NMR in drug discovery. Nat. Rev. Drug Discovery, 1, 211–219. Meyer, B. and Peters, T. (2003) NMR spectroscopy techniques for screening and identifying ligand binding to protein receptors. Angew. Chem. Int. Ed., 42, 864–890. Lepre, C.A., Moore, J.M., and Peng, J.W. (2004) Theory and applications of NMR-based screening in pharmaceutical research. Chem. Rev., 104, 3641–3675. Johnson, C.S. (1999) Diffusion ordered nuclear magnetic resonance spectroscopy: principles and applications. Prog. Nucl. Magn. Reson. Spectrosc., 34, 203–256. Neuhaus, D. and Williamson, M.P. (2000) The Nuclear Overhauser Effect in

References

9.

10.

11.

12.

13.

14.

15.

16.

Structural and Conformational Analysis, Wiley-VCH Verlag GmbH, New York. London, R.E., Perlman, M.E., and Davis, D.G. (1992) Relaxation-matrix analysis of the transferred nuclear Overhauser effect for finite exchange-rates. J. Magn. Reson., 97, 79–98. Bothnerby, A.A. and Noggle, J.H. (1979) Time development of nuclear Overhauser effects in multispin systems. J. Am. Chem. Soc., 101, 5152–5155. Albrand, J.P., Birdsall, B., Feeney, J., Roberts, G.C.K., and Burgen, A.S.V. (1979) The use of transferred nuclear Overhauser effects in the study of the conformations of small molecules bound to proteins. Int. J. Biol. Macromol., 1, 37–41. Arepalli, S.R., Glaudemans, C.P.J., Daves, G.D., Kovac, P., and Bax, A. (1995) Identification of protein-mediated indirect Noe effects in a disaccharide-Fab? Complex by transferred ROESY. J. Magn. Reson., Ser. B, 106, 195–198. Bevilacqua, V.L., Thomson, D.S., and Prestegard, J.H. (1990) Conformation of methyl beta-lactoside bound to the ricin-B-chain - interpretation of transferred nuclear Overhauser effects facilitated by spin simulation and selective deuteration. Biochemistry, 29, 5529–5537. Canales, A., Rodriguez-Salarichs, J., Trigili, C., Nieto, L., Coderch, C., Andreu, J.M., Paterson, I., Jimenez-Barbero, J., and Diaz, J.F. (2011) Insights into the interaction of discodermolide and docetaxel with tubulin. Mapping the binding sites of microtubule-stabilizing agents by using an integrated NMR and computational approach. ACS Chem. Biol., 6, 789–799. Siebert, H.C., Andre, S., Lu, S.Y., Frank, M., Kaltner, H., van Kuik, J.A., Korchagina, E.Y., Bovin, N., Tajkhorshid, E., Kaptein, R., Vliegenthart, J.F.G., von der Lieth, C.W., Jimenez-Barbero, J., Kopitz, J., and Gabius, H.J. (2003) Unique conformer selection of human growth-regulatory lectin galectin-1 for ganglioside GM(1) versus bacterial toxins. Biochemistry, 42, 14762–14773. Kitov, P.I., Sadowska, J.M., Mulvey, G., Armstrong, G.D., Ling, H., Pannu,

17.

18.

19.

20.

21.

22.

23.

N.S., Read, R.J., and Bundle, D.R. (2000) Shiga-like toxins are neutralized by tailored multivalent carbohydrate ligands. Nature, 403, 669–672. Clavel, C., Canales, A., Gupta, G., Santos, J.I., Canada, F.J., Penades, S., Surolia, A., and Jimenez-Barbero, J. (2007) NMR studies on the conformation of oligomannosides and their interaction with banana lectin. Glycoconjugate J., 24, 449–464. Asensio, J.L., Canada, F.J., Bruix, M., Rodriguez-Romero, A., and Jimenez-Barbero, J. (1995) The interaction of hevein with Nacetylglucosamine-containing oligosaccharides. Solution structure of hevein complexed to chitobiose. Eur. J. Biochem., 230, 621–633. Haselhorst, T., Espinosa, J.F., Jimenez-Barbero, J., Sokolowski, T., Kosma, P., Brade, H., Brade, L., and Peters, T. (1999) NMR experiments reveal distinct antibody-bound conformations of a synthetic disaccharide representing a general structural element of bacterial lipopolysaccharide epitopes. Biochemistry, 38, 6449–6459. Poveda, A. and Jimenez-Barbero, J. (1998) NMR studies of carbohydrateprotein interactions in solution. Chem. Soc. Rev., 27, 133–143. Canales, A., Matesanz, R., Gardner, N.M., Andreu, J.M., Paterson, I., Díaz, J.F., and Jiménez-Barbero, J. (2008) The bound conformation of microtubulestabilizing agents: NMR insights into the bioactive 3D structure of discodermolide and dictyostatin. Chem. Eur. J., 14, 7557–7569. Penalver, P., Marcelo, F., Jimenez-Barbero, J., and Vicent, C. (2011) Carbohydrate recognition at the minor-groove of the self-complementary duplex d(CGCGAATTCGCG)(2) by a synthetic glyco-oligoamide. Chem. Eur. J., 17, 4561–4570. Gouda, H., Sunazuka, T., Hirose, T., Iguchi, K., Yamaotsu, N., Sugawara, A., Noguchi, Y., Saito, Y., Yamamoto, T., Watanabe, T., Shiomi, K., Omura, S., and Hirono, S. (2010) NMR spectroscopy and computational analysis of interaction between Serratia marcescens

355

356

9 NMR Techniques for the Study of Transient Intermolecular Interactions

24.

25.

26.

27.

28.

29.

chitinase B and a dipeptide derived from natural-product cyclopentapeptide chitinase inhibitor argifin. Bioorg. Med. Chem., 18, 5835–5844. Asensio, J.L., Espinosa, J.F., Dietrich, H., Canada, F.J., Schmidt, R.R., Martin-Lomas, M., Andre, S., Gabius, H.J., and Jimenez-Barbero, J. (1999) Bovine heart galectin-1 selects a unique (Syn) conformation of C-lactose, a flexible lactose analogue. J. Am. Chem. Soc., 121, 8995–9000. Weimar, T., Stoffer, B., Svensson, B., and Pinto, B.M. (2000) Complexes of glucoamylase with maltoside heteroanalogues: bound ligand conformations by use of transferred NOE experiments and molecular modeling. Biochemistry, 39, 300–306. Garcia-Herrero, A., Montero, E., Munoz, J.L., Espinosa, J.F., Vian, A., Garcia, J.L., Asensio, J.L., Canada, F.J., and Jimenez-Barbero, J. (2002) Conformational selection of glycomimetics at enzyme catalytic sites: experimental demonstration of the binding of distinct high-energy distorted conformations of C-, S-, and O-glycosides by E-coli beta-galactosidases. J. Am. Chem. Soc., 124, 4804–4810. Santos, J.I., de Souza, A.C., Canada, F.J., Martin-Santamaria, S., Kamerling, J.P., and Jimenez-Barbero, J. (2009) Assessing carbohydrate-carbohydrate interactions by NMR spectroscopy: the trisaccharide epitope from the marine sponge microciona prolifera. ChemBioChem, 10, 511–519. Montero, E., Vallmitjana, M., Perez-Pons, J.A., Querol, E., Jimenez-Barbero, J., and Canada, F.J. (1998) NMR studies of the conformation of thiocellobiose bound to a beta-glucosidase from Streptomyces sp. FEBS Lett., 421, 243–248. Espinosa, J.F., Montero, E., Vian, A., Garcia, J.L., Dietrich, H., Schmidt, R.R., Martin-Lomas, M., Imberty, A., Canada, F.J., and Jimenez-Barbero, J. (1998) Escherichia coli beta-galactosidase recognizes a high-energy conformation of C-lactose, a nonhydrolyzable substrate analogue. NMR and modeling studies

30.

31.

32.

33.

34.

35.

36.

37.

of the molecular complex. J. Am. Chem. Soc., 120, 1309–1318. Ni, F. (1994) Recent developments in transferred NOE methods. Prog. Nucl. Magn. Reson. Spectrosc., 26, 517–606. Enríquez-Navas, P.M., Marradi, M., Padro, D., Angulo, J., and Penadés, S. (2011) A solution NMR study of the interactions of oligomannosides and the anti-HIV-1 2G12 antibody reveals distinct binding modes for branched ligands. Chem. Eur. J., 17, 1547–1560. Siebert, H.C., Jimenez-Barbero, J., Andre, S., Kaltner, H., and Gabius, H.J. (2003) Describing topology of bound ligand by transferred nuclear Overhauser effect spectroscopy and molecular modeling. Methods Enzymol., 362, 417–434. Poveda, A., Asensio, J.L., MartinPastor, M., and JimenezBarbero, J. (1997) Solution conformation and dynamics of a tetrasaccharide related to the Lewis(x) antigen deduced by NMR relaxation measurements. J. Biomol. NMR, 10, 29–43. Jimenez-Barbero, J., Dragoni, E., Venturi, C., Nannucci, F., Arda, A., Fontanella, M., Andre, S., Canada, F.J., Gabius, H.J., and Nativi, C. (2009) Alpha-O-linked glycopeptide mimetics: synthesis, conformation analysis, and interactions with viscumin, a galactoside-binding model lectin. Chem. Eur. J., 15, 10423–10431. Martin-Pastor, M., De Capua, A., Alvarez, C.J.P., Diaz-Hernandez, M.D., Jimenez-Barbero, J., Casanueva, F.F., and Pazos, Y. (2010) Interaction between ghrelin and the ghrelin receptor (GHSR1a), a NMR study using living cells. Bioorg. Med. Chem., 18, 1583–1590. Sattler, M., Schleucher, J., and Griesinger, C. (1999) Heteronuclear multidimensional NMR experiments for the structure determination of proteins in solution employing pulsed field gradients. Prog. Nucl. Magn. Reson. Spectrosc., 34, 93–158. Garcia-Aparicio, V., Sollogoub, M., Bleriot, Y., Colliou, V., Andre, S., Asensio, J.L., Canada, F.J., Gabius, H.J., Sinay, P., and Jimenez-Barbero, J. (2007) The conformation of the C-glycosyl

References

38.

39.

40.

41.

42.

analogue of N-acetyl-lactosamine in the free state and bound to a toxic plant agglutinin and human adhesion/growthregulatory galectin-1. Carbohydr. Res., 342, 1918–1928. Mikkelsen, L.M., Hernaiz, M.J., Martin-Pastor, M., Skrydstrup, T., and Jimenez-Barbero, J. (2002) Conformation of glycomimetics in the free and protein-bound state: structural and binding features of the C-glycosyl analogue of the core trisaccharide alpha-D-Man(1 - > 3)-[alpha-D-Man-(1 - > 6)]D-Man. J. Am. Chem. Soc., 124, 14940–14951. Asensio, J.L., Siebert, H.C., von der Lieth, C.W., Laynez, J., Bruix, M., Soedjanaamadja, U.M., Beintema, J.J., Canada, F.J., Gabius, H.J., and Jimenez-Barbero, J. (2000) NMR investigations of protein-carbohydrate interactions: studies on the relevance of Trp/Tyr variations in lectin binding sites as deduced from titration microcalorimetry and NMR studies on hevein domains. Determination of the NMR structure of the complex between pseudohevein and N,N′ ,N′′ ’-triacetylchitotriose. Proteins, 40, 218–236. Jimenez-Barbero, J., Canales, A., Northcote, P.T., Buey, R.M., Andreu, J.M., and Diaz, J.F. (2006) NMR determination of the bioactive conformation of peloruside a bound to microtubules. J. Am. Chem. Soc., 128, 8757–8765. Revuelta, J., Vacas, T., Torrado, M., Corzana, F., Gonzalez, C., Jiménez-Barbero, J., Menendez, M., Bastida, A., and Asensio, J.L. (2008) NMR-based analysis of aminoglycoside recognition by the resistance enzyme ANT: the pattern of OH/NH3+ substitution determines the preferred antibiotic binding mode and is critical for drug inactivation. J. Am. Chem. Soc., 130, 5086–5103. Potenza, D. and Belvisi, L. (2008) Transferred-NOE NMR experiments on intact human platelets: receptor-bound conformation of RGD-peptide mimics. Org. Biomol. Chem., 6, 258–262.

43. Angulo, J., Langpap, B., Blume, A., Biet,

44.

45.

46.

47.

48.

49.

50.

51.

T., Meyer, B., Krishna, N.R., Peters, H., Palcic, M.M., and Peters, T. (2006) Blood group B galactosyltransferase: insights into substrate binding from NMR experiments. J. Am. Chem. Soc., 128, 13529–13538. Johnson, M.A. and Pinto, B.M. (2002) Saturation transfer difference 1DTOCSY experiments to map the topography of oligosaccharides recognized by a monoclonal antibody directed against the cell-wall polysaccharide of group A streptococcus. J. Am. Chem. Soc., 124, 15368–15374. Sanchez-Pedregal, V.M., Reese, M., Meiler, J., Blommers, M.J.J., Griesinger, C., and Carlomagno, T. (2005) The INPHARMA method: protein-mediated interligand NOEs for pharmacophore mapping. Angew. Chem. Int. Ed., 44, 4172–4175. Mayer, M. and Meyer, B. (1999) Characterization of ligand binding by saturation transfer difference NMR spectroscopy. Angew. Chem. Int. Ed., 38, 1784–1788. Forsen, S. and Hoffman, R.A. (1963) Study of moderately rapid chemical exchange reactions by means of nuclear magnetic double resonance. J. Chem. Phys., 39, 2892–2901. Hyde, E.I., Birdsall, B., Roberts, G.C.K., Feeney, J., and Burgen, A.S.V. (1980) Proton nuclear magnetic-resonance saturation transfer studies of coenzyme binding to lactobacillus-casei dihydrofolate-reductase. Biochemistry, 19, 3738–3746. Nagaraja, C.S. (2006) Heteronuclear saturation transfer difference (HSTD) experiment for detection of ligand binding to proteins. Chem. Phys. Lett., 420, 340–346. Diercks, T., Ribeiro, J.P., Cañada, F.J., André, S., Jiménez-Barbero, J., and Gabius, H.-J. (2009) Fluorinated carbohydrates as lectin ligands: versatile sensors in 19F-detected saturation transfer difference NMR spectroscopy. Chem. Eur. J., 15, 5666–5668. Kover, K.E., Groves, P., Jimenez-Barbero, J., and Batta, G. (2007)

357

358

9 NMR Techniques for the Study of Transient Intermolecular Interactions

52.

53.

54.

55.

56.

57.

58.

59.

60.

Molecular recognition and screening using a N-15 group selective STD NMR method. J. Am. Chem. Soc., 129, 11579–11582. Pellecchia, M., Becattini, B., Crowell, K.J., and Fattorusso, R. (2004) NMRbased techniques in the hit identification and optimisation processes. Expert Opin. Ther. Targets, 8, 597–611. Politi, M., Chavez, M.I., Canada, F.J., and Jimenez-Barbero, J. (2005) Screening by NMR: a new approach for the study of bioactive natural products? The example of Pleurotus ostreatus hot water extract. Eur. J. Org. Chem., 2005, 1392–1396. McCoy, M.A., Senior, M.M., and Wyss, D.F. (2005) Screening of protein kinases by ATP-STD NMR spectroscopy. J. Am. Chem. Soc., 127, 7978–7979. Mayer, M. and James, T.L. (2004) NMR-based characterization of phenothiazines as a RNA binding scaffold. J. Am. Chem. Soc., 126, 4453–4460. Yan, J.L., Kline, A.D., Mo, H.P., Shapiro, M.J., and Zartler, E.R. (2003) The effect of relaxation on the epitope mapping by saturation transfer difference NMR. J. Magn. Reson., 163, 270–276. Sousa, F.F.O., Luzardo-Alvarez, A., Blanco-Mendez, J., and Martin-Pastor, M. (2012) NMR techniques in drug delivery: application to zein protein complexes. Int. J. Pharm., 439, 41–48. Angulo, J., Diaz, I., Reina, J.J., Tabarani, G., Fieschi, F., Rojo, J., and Nieto, P.M. (2008) Saturation Transfer Difference (STD) NMR spectroscopy characterization of dual binding mode of a mannose disaccharide to DC-SIGN. ChemBioChem, 9, 2225–2227. Moseley, H.N.B., Curto, E.V., and Krishna, N.R. (1995) Complete Relaxation and Conformational Exchange Matrix (CORCEMA) analysis of NOESY spectra of interacting systems; twodimensional transferred NOESY. J. Magn. Reson., Ser. B, 108, 243–261. Jayalakshmi, V. and Krishna, N.R. (2004) CORCEMA refinement of the bound ligand conformation within the protein binding pocket in reversibly forming weak complexes using STD-NMR intensities. J. Magn. Reson., 168, 36–45.

61. Jayalakshmi, V., Biet, T., Peters, T., and

62.

63.

64.

65.

66.

67.

68.

Krishna, N.R. (2004) Refinement of the conformation of UDP-galactose bound to galactosyltransferase using the STD NMR intensity-restrained CORCEMA optimization. J. Am. Chem. Soc., 126, 8610–8611. Krishna, N.R. and Jayalakshmi, V. (2008) Quantitative analysis of STD-NMR spectra of reversibly forming ligandreceptor complexes. Top. Curr. Chem., 273, 15–54. Jayalakshmi, V. and Krishna, N.R. (2005) Determination of the conformation of trimethoprim in the binding pocket of bovine dihydrofolate reductase from a STD-NMR intensity-restrained CORCEMA-ST optimization. J. Am. Chem. Soc., 127, 14080–14084. Szczepina, M.G., Bleile, D.W., and Pinto, B.M. (2011) Investigation of the binding of a carbohydrate-mimetic peptide to its complementary anticarbohydrate antibody by STD-NMR spectroscopy and molecular-dynamics simulations. Chem. Eur. J., 17, 11446–11455. Calarese, D.A., Lee, H.K., Huang, C.Y., Best, M.D., Astronomo, R.D., Stanfield, R.L., Katinger, H., Burton, D.R., Wong, C.H., and Wilson, I.A. (2005) Dissection of the carbohydrate specificity of the broadly neutralizing-anti-HIV-1 antibody 2G12. Proc. Natl. Acad. Sci. U.S.A., 102, 13372–13377. Calarese, D.A., Scanlan, C.N., Zwick, M.B., Deechongkit, S., Mimura, Y., Kunert, R., Zhu, P., Wormald, M.R., Stanfield, R.L., Roux, K.H., Kelly, J.W., Rudd, P.M., Dwek, R.A., Katinger, H., Burton, D.R., and Wilson, I.A. (2003) Antibody domain exchange is an immunological solution to carbohydrate cluster recognition. Science, 300, 2065–2071. Yuan, Y., Wen, X., Sanders, D.A.R., and Pinto, B.M. (2005) Exploring the mechanism of binding of UDP-galactopyranose to UDPgalactopyranose mutase by STD-NMR spectroscopy and molecular modeling. Biochemistry, 44, 14080–14089. Wen, X., Yuan, Y., Kuntz, D.A., Rose, D.R., and Pinto, B.M. (2005) A combined STD-NMR/molecular modeling

References

69.

70.

71.

72.

73.

74.

75.

76.

77.

protocol for predicting the binding modes of the glycosidase inhibitors kifunensine and salacinol to Golgi alpha-mannosidase II. Biochemistry, 44, 6729–6737. Angulo, J., Enriquez-Navas, P.M., and Nieto, P.M. (2010) Ligand-receptor binding affinities from Saturation Transfer Difference (STD) NMR spectroscopy: the binding isotherm of STD initial growth rates. Chem. Eur. J., 16, 7803–7812. Angulo, J. and Nieto, P.M. (2011) STD-NMR: application to transient interactions between biomolecules-a quantitative approach. Eur. Biophys. J., 40, 1357–1369. Cheng, Y. and Prusoff, W.H. (1973) Relationship between inhibition constant (K1) and concentration of inhibitor which causes 50 per cent inhibition (I50) of an enzymatic-reaction. Biochem. Pharmacol., 22, 3099–3108. Mayer, M. and Meyer, B. (2001) Group epitope mapping by saturation transfer difference NMR to identify segments of a ligand in direct contact with a protein receptor. J. Am. Chem. Soc., 123, 6108–6117. Antalek, B. (2002) Using pulsed gradient spin echo NMR for chemical mixture analysis: how to obtain optimum results. Concepts Magn. Reson., 14, 225–258. Price, W.S. (1998) Pulsed-field gradient nuclear magnetic resonance as a tool for studying translational diffusion: part II. Experimental aspects. Concepts Magn. Reson., 10, 197–237. Connell, M.A., Bowyer, P.J., Adam Bone, P., Davis, A.L., Swanson, A.G., Nilsson, M., and Morris, G.A. (2009) Improving the accuracy of pulsed field gradient NMR diffusion experiments: correction for gradient non-uniformity. J. Magn. Reson., 198, 121–131. Sørland, G.H. and Aksnes, D. (2002) Artefacts and pitfalls in diffusion measurements by NMR. Magn. Reson. Chem., 40, S139–S146. Esturau, N., Sanchez-Ferrando, F., Gavin, J.A., Roumestand, C., Delsuc, M.A., and Parella, T. (2001) The use of sample rotation for minimizing convection effects in self-diffusion NMR

78.

79.

80.

81.

82.

83.

84.

85.

86.

87.

88.

measurements. J. Magn. Reson., 153, 48–55. Jerschow, A. and Müller, N. (1997) Suppression of convection artifacts in stimulated-echo diffusion experiments. Double-stimulated-echo experiments. J. Magn. Reson., 125, 372–375. Sinnaeve, D. (2012) The Stejskal–Tanner equation generalized for any gradient shape—an overview of most pulse sequences measuring free diffusion. Concepts Magn. Reson. A, 40A, 39–65. Kuchel, P.W., Pagès, G., Nagashima, K., Velan, S., Vijayaragavan, V., Nagarajan, V., and Chuang, K.H. (2012) Stejskal–tanner equation derived in full. Concepts Magn. Reson. A, 40A, 205–214. Nilsson, M., Connell, M.A., Davis, A.L., and Morris, G.A. (2006) Biexponential fitting of diffusion-ordered NMR data: practicalities and limitations. Anal. Chem., 78, 3040–3045. Delsuc, M.A. and Malliavin, T.E. (1998) Maximum entropy processing of DOSY NMR spectra. Anal. Chem., 70, 2146–2148. Nilsson, M. and Morris, G.A. (2008) Speedy component resolution: an improved tool for processing diffusionordered spectroscopy data. Anal. Chem., 80, 3777–3782. Lucas, L.H., Otto, W.H., and Larive, C.K. (2002) The 2D-J-DOSY experiment: resolving diffusion coefficients in mixtures. J. Magn. Reson., 156, 138–145. Cobas, J.C. and Martín-Pastor, M. (2004) A homodecoupled diffusion experiment for the analysis of complex mixtures by NMR. J. Magn. Reson., 171, 20–24. Newman, J.M. and Jerschow, A. (2007) Improvements in complex mixture analysis by NMR: DQF-COSY iDOSY. Anal. Chem., 79, 2957–2960. Jerschow, A. and Müller, N. (1996) 3D diffusion-ordered TOCSY for slowly diffusing molecules. J. Magn. Reson., Ser. A, 123, 222–225. Nilsson, M., Gil, A.M., Delgadillo, I., and Morris, G.A. (2004) Improving

359

360

9 NMR Techniques for the Study of Transient Intermolecular Interactions

89.

90.

91.

92.

93.

94.

95.

96.

97.

98.

pulse sequences for 3D diffusionordered NMR spectroscopy: 2DJIDOSY. Anal. Chem., 76, 5418–5422. Nilsson, M., Gil, A.M., Delagadillo, I., and Morris, G.A. (2005) Improving pulse sequences for 3D DOSY: COSYIDOSY. Chem. Commun., 1737–1739. McLachlan, A.S., Richards, J.J., Bilia, A.R., and Morris, G.A. (2009) Constant time gradient HSQC–iDOSY: practical aspects. Magn. Reson. Chem., 47, 1081–1085. Johnson, C.S. (1993) Effects of chemical exchange in diffusion-ordered 2D NMR spectra. J. Magn. Reson., Ser. A, 102, 214–218. Cabrita, E.J. and Berger, S. (2001) DOSY studies of hydrogen bond association: tetramethylsilane as a reference compound for diffusion studies. Magn. Reson. Chem., 39, S142–S148. Lucas, L.H. and Larive, C.K. (2004) Measuring ligand-protein binding using NMR diffusion experiments. Concepts Magn. Reson. A, 20A, 24–41. Cozzolino, S., Sanna, M.G., and Valentini, M. (2008) Probing interactions by means of pulsed field gradient nuclear magnetic resonance spectroscopy. Magn. Reson. Chem., 46, S16–S23. Kapur, G.S., Cabrita, E.J., and Berger, S. (2000) The qualitative probing of hydrogen bond strength by diffusion-ordered NMR spectroscopy. Tetrahedron Lett., 41, 7181–7185. Pregosin, P.S. (2006) Ion pairing using PGSE diffusion methods. Prog. Nucl. Magn. Reson. Spectrosc., 49, 261–288. Macchioni, A., Ciancaleoni, G., Zuccaccia, C., and Zuccaccia, D. (2008) Determining accurate molecular sizes in solution through NMR diffusion spectroscopy. Chem. Soc. Rev., 37, 479–489. Monteiro, C., Maechling, C., and Hervé du Penhoat, C. (2002) Monitoring the non-specific interactions of catechin through diffusion measurements based on pulsed-field gradients. Magn. Reson. Chem., 40, S110–S114.

99. Söderman, O., Stilbs, P., and Price,

100.

101.

102.

103.

104.

105.

106.

107.

W.S. (2004) NMR studies of surfactants. Concepts Magn. Reson. A, 23A, 121–135. Krause-Heuer, A.M., Wheate, N.J., Price, W.S., and Aldrich-Wright, J. (2009) Diffusion-based studies on the self-stacking and nanorod formation of platinum(ii) intercalators. Chem. Commun., 1210–1212. Pacheco, V., Ma, P., Thielmann, Y., Hartmann, R., Weiergraeber, O.H., Mohrlueder, J., and Willbold, D. (2010) Assessment of GABARAP selfassociation by its diffusion properties. J. Biomol. NMR, 48, 49–58. Pérez-Méndez, M., Berenguel, R.M., Garrido, L., and Martín-Pastor, M. (2003) Self-association and stereoselectivity in a chiral liquid-crystal colesteric polymer formed under achiral conditions. Macromolecules, 36, 8049–8055. Phani Kumar, B.V.N., Umayal Priyadharsini, S., Prameela, G.K.S., and Mandal, A.B. (2011) NMR investigations of self-aggregation characteristics of SDS in a model assembled tri-block copolymer solution. J. Colloid Interface Sci., 360, 154–162. Basilio, N., García-Río, L., and Martín-Pastor, M. (2010) Counterion binding in solutions of p-sulfonatocalix[4]arene. J. Phys. Chem. B, 114, 7201–7206. Basilio, N., García-Río, L., and Martín-Pastor, M. (2010) NMR evidence of slow monomer − micelle exchange in a calixarene-based surfactant. J. Phys. Chem. B, 114, 4816–4820. Cameron, K.S. and Fielding, L. (2002) NMR diffusion coefficient study of steroid-cyclodextrin inclusion complexes. Magn. Reson. Chem., 40, S106–S109. Thordarson, P. (2011) Determining association constants from titration experiments in supramolecular chemistry. Chem. Soc. Rev., 40, 1305–1323.

361

10 Analysis of Molecular Interactions by Surface Plasmon Resonance Spectroscopy Eva Muñoz and Daniel Ricklin

10.1 Introduction

Surface plasmon resonance (SPR) is a label-free optical biosensing technology that, within the last decade, has emerged as a leading tool for the study of biomolecular interactions. Essentially, an SPR biosensor monitors the interaction between a molecule immobilized to the surface of a gold-coated sensor chip (referred as to the ligand) and a second molecule free in solution (referred as to the analyte). For newcomers to the field the SPR sensing principle is easy to understand if we compare this type of sensor to a nanobalance that measures the mass of the analyte specifically recognized by the immobilized ligand. Figure 10.1 shows the simplest SPR experiment, during which the analyte solution is injected at a constant flow rate to the surface of the sensor chip. Binding of the analyte to the ligand is monitored in real time by means of SPR response, which is directly associated to mass changes nearby the sensor surface. Association and equilibrium steps are registered during sample injection and, when the injection finishes, dissociation of the complex is monitored through decay of the SPR signal over time. The resulting graph of SPR response vs time is referred to as the “sensorgram” (Figure 10.1b). A complete SPR-binding assay, which usually consists of a set of sensorgrams obtained after analyte injection at different concentrations, provides robust kinetic and affinity data of the ligand–analyte interaction. In addition, structural, thermodynamic, and mechanistic information can be extracted when careful experimental setup and data analysis are performed. It has been over 30 years since the SPR phenomenon was used for the first time for biosensing purposes [1]. Since then, the technique has experienced enormous progress in many aspects concerning the development of experimental and analytical protocols, sensor chip design, and SPR equipment sensitivity and performance [2]. As a consequence, SPR biosensors have become essential tools in the fields of biomolecular recognition analysis and analyte detection and quantification, with competence in a wide range of applications [3]. Structure Elucidation in Organic Chemistry: The Search for the Right Tools, First Edition. Edited by María-Magdalena Cid and Jorge Bravo. © 2015 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2015 by Wiley-VCH Verlag GmbH & Co. KGaA.

362

10

Analysis of Molecular Interactions by Surface Plasmon Resonance Spectroscopy (II) A + L

AL

(I) A + L

AL (III) A + L

AL

SPR response (RU)

90 Analyte

Ligand Au chip

70 Injection end 50 30 10 Injection start −10 0

(a)

(b) Figure 10.1 Schematic representation of the simplest SPR experiment. (a) Au-coated SPR chip with immobilized ligand and analyte solution flowing over the surface. (b)

50

100

150 200 Time (s)

250

300

350

Sensorgram of the ligand–analyte interaction where association (I), equilibrium (II), and dissociation (III) steps are registered.

The present chapter provides an overview of the SPR technology, focusing on theoretical and experimental aspects that must be considered for proper design, execution, and evaluation of SPR assays. Thus, the primary goal is to provide general information and practical advice to assist inexperienced researchers in the understanding of SPR sensing and its applications. Moreover, specialized literature has been cited throughout the chapter that allows for extended insight into key aspects of this fascinating and powerful method.

10.2 General Aspects of the Surface Plasmon Resonance Principle

Surface plasmons (SPs) are propagating electron density waves occurring at the interface between a metal and a dielectric. The phenomenon of SPR consists in the excitation of SPs by a beam of p-polarized light, in conditions of total internal reflection, hitting the metal layer at the interface between the dielectric and an aqueous solution. In an SPR sensor this phenomenon is generated on the surface of the sensor chip, which is made of a glass slide (dielectric) coated with a thin layer of gold (the metal) of approximately 50 nm that is in contact with the aqueous solution. As a consequence of the excitations of the SPs, the reflected light experiences a decrease in intensity, observed as a minimum or “dip” in a diagram of intensity versus angle of incident light. This arrangement, visualized in Figure 10.2, is called the Kretschmann configuration, and is the most utilized configuration in SPR biosensors [4]. Now, how can SPR biosensors measure mass changes nearby the gold surface? The answer to this question is in the evanescent electrical field associated with

Ligand Gold Glass

Light beam

(a)

Sensor chip

Prism Reflected light

The SPR Experiment

363

Reflected light intensity

10.3

(b)

σR

Incident angle

Figure 10.2 (a,b) Typical configuration for an SPR sensor based on Kretschmann configuration.

the SPs, which propagates ∼300 nm into the aqueous solution that is in contact with the gold (where the ligand is attached) and establishes a dependence of the SPs’ resonant frequency with the refractive index (RI) of the aqueous medium. SPR biosensors measure changes in the RI of the aqueous solution by monitoring changes in the angle or intensity of reflected light. When a change in mass occurs nearby the sensor surface, for example, via complex formation of the analyte with the immobilized ligand, a concomitant change in RI happens that is registered in terms of variations in the SPR signal, expressed in resonance units (RU). Correlation between RI changes and mass changes occurring on the sensor surface is established through the sample-dependent RI increment parameter (dn/dc), which relates variations in RI (dn) to variations in sample concentration (dc). For most proteins 1 RU equals a concentration nearby the sensor surface of 1 pg mm−2 . The major strengths of SPR biosensing rely on the ability to perform real time, label-free analysis of biorecognition events with low sample consumption and fast response times. Moreover, state-of-the-art SPR instruments offer exceptional sensitivity, with extremely low background noise (≤0.1 RU) and a wide range of measurable binding affinities. On the other hand, it is important to keep in mind that SPR measures the overall RI changes nearby the sensor surface, not only those coming from mass variations. Therefore, RI changes from other sources must be minimized or eliminated through careful experimental design and data analysis.

10.3 The SPR Experiment

The standard SPR experiment consists in three sequential steps that involve (1) sensor surface design and preparation, (2) binding experiment (monitoring of the ligand–analyte interaction), and (3) data analysis. In this section, a description of steps 1 and 2 is provided while data analysis is described in a subsequent section of the chapter.

364

10

Analysis of Molecular Interactions by Surface Plasmon Resonance Spectroscopy

10.3.1 Sensor Surface Design and Preparation

The SPR sensor chip and the microfluidic system form at least two channels or flow cells (FCs). Essentially, sensor surface preparation consists of the immobilization of the ligand on one or more FC areas of the sensor chip (one FC typically remains unmodified to act as a reference surface). Theoretically, this could be achieved via passive ligand deposition on the gold surface or through the formation of Au–S bonds when the ligand contains thiol groups. However, it is more frequent to use sensor chips coated with a self-assembled monolayer (SAM) or a polymeric matrix carrying some type of functionalization that enables ligand immobilization. Surface coating with the SAM or polymer matrix often maintains hydration and prevents denaturation of the ligand, avoids potential non-specific binding of the analyte to the gold, and increases the number of functional groups available for ligand attachment to the sensor chip. With regard to the ligand attachment, there is a broad spectrum of available coupling strategies that are commonly classified into covalent and non-covalent immobilization approaches [5]. 10.3.1.1 Covalent Immobilization

This approach consists in the establishment of a stable covalent bond between the ligand and the sensor chip. The choice of the coupling chemistry primarily depends on the availability of a suitable functional group in the ligand. Potential effects of the reaction conditions on ligand stability and binding activity also need to be considered. There are several established coupling protocols based on covalent attachments, with demonstrated utility in a wide variety of applications (Table 10.1).

Table 10.1 Common methods of covalent immobilization of ligands. Method

Type of Covalent Bond

Type of ligand

O Amine coupling

Ligand

Proteins

S S Ligand

Proteins

N H

Thiol coupling

O S

Ligand Proteins

Maleimide coupling

O

O Aldehyde coupling

NH N

CH Ligand

Carbohydrates glycoproteins

and

10.3

O HO

O

N O

O

The SPR Experiment

Ligand

O

HN

O

Ligand

S

NHS/EDC

NH2

Activation

Coupling S

S

Au chip Figure 10.3 Amine coupling protocol, consisting in the formation of NHS-active esters on the sensor chip followed by ligand coupling through amide bond formation.

The most popular covalent method is the “amine coupling” [6], recommended as the first choice to immobilize proteins and, in general, ligands containing primary amino groups. The amine coupling protocol establishes an amide bond between –NH2 groups of the ligand and –COOH groups of the sensor chip. As depicted in Figure 10.3, the first step consists in the activation of carboxylic groups with a mixture of N-hydroxysuccinimide (NHS) and 1-ethyl-3-(3-dimethylaminopropyl) carbodiimide (EDC) to yield reactive succinimide esters. Next, a solution of the ligand is passed through the activated surface with the spontaneous formation of an amide group between –NH2 and –COO–NHS. Finally, deactivation of the remaining active groups is achieved with a solution of a blocking reagent such as ethanolamine, which is, by far, the most commonly used agent. A prerequisite for successful amine coupling is that a sufficient number of ligand molecules approach close enough to the activated surface. This is achieved through electrostatic attractive interactions between negatively charged carboxylate groups that were not activated and positively charged amine groups. To ensure the net positive charge of the ligand (typically a protein), the pH of the buffer solution must be at least 0.5 lower than the isoelectric point (pI) of the ligand. Therefore, acidic ligands with a pI at or below 4 are often not amenable to amine coupling. Another important aspect to consider throughout the design of the sensor surface is the degree of ligand immobilization that, when using amine coupling, can be controlled in several ways: (i) during activation by modifying the NHS/EDC concentration and/or the activation time and (ii) during ligand injection by modifying the pH of the solution, the ligand concentration, or the injection time. Finally, it is imperative that none of the buffers used during the procedure contain any primary amines, thereby excluding Tris or glycine. Amine coupling is by far the most common protocol for covalent immobilization as it is easy to perform and often ensures high coupling yields. A potential disadvantage of this strategy, however, is the random orientation of the ligand on the sensor chip, with a concomitant retention of the activity of a percentage of the

365

366

10

Analysis of Molecular Interactions by Surface Plasmon Resonance Spectroscopy

ligand molecules. Alternative coupling chemistries are used when amine coupling is not possible, using specific functional groups within the ligand such as thiol or aldehyde (Table 10.1). The complete description of these methods is beyond the scope of this chapter and it has been already covered in previous works [5]. 10.3.1.2 Non-covalent Immobilization

Non-covalent immobilization methods require the presence of a capture molecule on the sensor chip that establishes specific, highly stable non-covalent interactions with the ligand [5]. While an oriented immobilization through capturing often increases the overall activity of the ligand surface, it may also introduce drawbacks concerning surface capacity and surface stability (i.e., “bleeding” of the ligand from the capture molecule). The most popular capturing method is the stable binding of biotinylated ligands to sensor chips coated with streptavidin or neutravidin, proteins that form strong complexes with biotin (equilibrium dissociation constant, K D ∼ 10−15 M) and ensure rapid ligand loading and high surface stability during the SPR experiment [7]. Other common capturing methods involve the use of ligand- or tag-specific antibodies, nickel-loaded nitrilotriacetic acid (NTA) to capture 6His-tagged ligands, and protein A, protein G, or anti-Fc antibodies for capturing monoclonal antibodies. Non-covalent methods are often used when covalent attachment is arduous. For instance, negatively charged ligands such as DNA or glycosaminoglycans (GAGs) are hardly attracted to a carboxylated surface due to electrostatic repulsion, which renders amine coupling extremely difficult. In contrast, biotinylated DNA and GAGs are easily bound to streptavidin/neutravidin surfaces [8]. Yet, even for proteins, site-specific biotinylation may be a valuable alternative to amine coupling if an appropriate functional group (e.g., a single free cysteine) is available. One disadvantage of capturing methods is that the achievable surface densities are usually lower when compared to covalent coupling; this may be particularly limiting for small molecule assays that are dependent on high-density surfaces to generate sufficient signal intensity. Capturing strategies are therefore predominantly used for the assessment of interactions between macromolecules, which are more susceptible to immobilization-induced heterogeneity and may thereby benefit most from an oriented ligand presentation. Tip The choice of sensor chip and immobilization method greatly depends on the specific application and ligand characteristics. Prior to the experiment, it is important to get as much information as possible on the ligand structure and stability under the coupling conditions proposed. Start with the best-suited method according to the information collected and, if necessary, modify experimental conditions to achieve an optimized sensor surface. The following working scheme can be used as a guideline for an SPR sensor-surface preparation

10.3

The SPR Experiment

Sensor-chip # 1 + Immobilization method # 1

Immobilization sucess? YES

NO

Ligand–analyte binding test

SPR binding response? YES

NO

Change immobilization method and/or

Perform complete binding experiment

Change sensor chip.

10.3.2 The Binding Experiment

The basic SPR experiment consists in monitoring the ligand–analyte interaction when an analyte solution of known concentration is injected over the sensor chip. Subsequently, dissociation is monitored for a reasonable period of time, depending on how fast the analyte leaves the surface (Figure 10.1). For a standard SPR assay, it is recommended to repeat this experiment for at least five different concentrations that span a concentration range 10-fold below and above the expected K D of the complex. Typically, the binding signal must return to baseline before the next analyte injection (this does not apply for kinetic titrations; see below). In cases where baseline conditions are not reached within a suitable time frame, which is often the case for strong interactions, a regeneration step is required to remove analyte molecules that are still bound to the surface (Figure 10.4). The selection of appropriate regeneration solution(s) depends on the nature of the interaction and must be experimentally determined to ensure complete removal of analyte while maintaining the stability/activity of the ligand. Typical regeneration solutions are based on high salt (e.g., 2 M NaCl), acidic (e.g., 10 mM HCl), basic (e.g., 50 mM NaOH), or chaotropic conditions (e.g., 6 M guanidine-HCl). Obtaining high-quality sensorgrams is critical to getting trustable information of the binding event. Consequently, experimental conditions must be carefully adjusted in order to avoid or minimize undesired artifacts prone to perturbing the shape of the sensorgram. In this context, it is worth dedicating some lines to mass transport limitation effects, an artifact frequently observed in SPR experiments [9]. Analyte molecules need to be transported from the bulk solution to the

367

368

10

Analysis of Molecular Interactions by Surface Plasmon Resonance Spectroscopy

100

SPR response

80 60

Regeneration Binding

40 20 0 −20

C1

−40 0

C2 500

C3 1000

C4 1500

2000

C5 2500

Baseline 3000

Time Figure 10.4 Consecutive binding and regeneration cycles, during which the analyte is injected at five different concentrations (C1–C5).

sensor surface in order to bind the ligand. If the rate of transport is slower than the rate of analyte association with the ligand, the observed binding (i.e., the shape of the sensorgram) will be influenced by the rate of analyte transport. Hence, the kinetic information of the binding event extracted from those sensorgrams will be “contaminated” by the effect of mass transport. When present, mass transport effects can be minimized or even eliminated by increasing the flow rate and/or decreasing the ligand density of the sensor surface.

Tip The design of successful SPR-binding assays always requires an optimization of various experimental parameters: (i) Preferred analyte flow rates typically range between 20 and 100 μl min−1 . Lower rates increase the probability of mass transport effects and are primarily recommended for ligand immobilization purposes (e.g., 5 μl min−1 ). (ii) Ideally, the analyte injection time should be long enough, so that the curve reaches a steady state in order to monitor association and equilibriums steps. Exceptions are made in cases where association is very slow and reaching the equilibrium needs too long injection times. (iii) The dissociation time period should be long enough to monitor the decrease of at least 20% of the SPR response reached at the end of the analyte injection. Exceptions are made in cases where the dissociation is extremely slow. (iv) The analyte concentration range should oscillate between 0.1 and 10 times the K D value of the interaction. (v) The regeneration conditions should completely remove the analyte from the sensor surface without damaging the ligand. To determine the success of the regeneration, it is highly recommended that consecutive duplicate injections of the analyte solution be performed at the same concentration as test for reproducibility.

10.4

The Information Contained in the SPR Experiment

10.4 The Information Contained in the SPR Experiment

Properly designed SPR experiments with carefully acquired sensorgrams contain a wealth of valuable information about the molecular interaction, both qualitative and quantitative, that just waits to be harvested. It is always advisable to start an SPR experiment with a good perception about what information is expected and is of most value for the underlying scientific question, as this largely influences the assay design and choice of evaluation methods. The following sections provide a brief overview about the low-hanging fruits and hidden treasures that can be found in an SPR data set. 10.4.1 Qualitative Information

Normalized SPR response (RU/MW)

The basic observation whether an analyte injection results in a binding signal or not, sometimes referred to as “yes/no binding,” is the simplest information that can be extracted. In many cases, it also provides a starting point for subsequent design of quantitative assays, as it allows obtaining feedback about detection limits, suitable assay conditions, and even the quality of the sample and the complexity of the interaction. For this purpose, both the intensity of the signal and the shape of the sensorgram should be observed and critically evaluated. Importantly, even a simple qualitative assay may be used to collect valuable functional information; for example, changes in signal intensity upon addition or removal of certain buffer components such as metal ions may identify an essential cofactor in the binding event (e.g., Ca2+ for C-type lectins or Mg2+ for certain enzymes). Moreover, qualitative assays are often used for the initial screening of analyte libraries or a panel of protein mutants in order to obtain first information about structure–function relation and select candidates for further analysis. In this case, it is particularly important to remember that the SPR response depends on both

(a)

A3 (100 KDa)

SPR response (RU)

SPR response (RU)

A1 (200 KDa)

A1 (20 KDa)

Time (s)

(b)

A1

A2 A3

(c)

A1

A2 A3

Figure 10.5 SPR ranking experiment (a) with equilibrium responses of three analytes with distinct masses plotted (b) and normalized for molecular weight (c).

369

370

10

Analysis of Molecular Interactions by Surface Plasmon Resonance Spectroscopy

the analyte size and concentration. When relying on signal intensities in a screening/ranking experiment, analytes should therefore be injected at equimolar concentrations and the resulting signal intensities should be normalized by the molecular weight of each analyte (Figure 10.5). Tip Looks can be deceiving. Although informative and easy to perform, qualitative experiments should be planned and evaluated particularly critically, as a single injection contains little guidance on whether a signal is specific or not. Be aware that SPR is a label-free technology that detects any changes around the sensor surface that are not necessarily limited to the target–analyte interaction and may also involve non-specific binding or aggregation, to name a few. Always try to involve positive and negative controls, if available, repeat the interaction at different analyte concentrations, and validate whether signal intensity and shape are within expectations. 10.4.2 Binding Affinity and Kinetics

Despite the versatility of SPR in performing functional and screening assays, the acquisition of quantitative information about a molecular interaction remains the prime application of SPR. While binding affinity (commonly expressed as the equilibrium dissociation constant K D ) provides information about the quality or overall strength of a ligand–analyte complex, a full kinetic profile adds dynamic aspects and describes how easily a complex is formed (association rate constant, k a ) and how stable it is (dissociation rate constant, k d ). These three essential interaction parameters are correlated through the following equation: K D = k d /k a . The binding affinity can be determined either by steady state analysis or from a kinetic evaluation using the equation above. Both cases rely on a series of analyte injections at different concentrations (be aware that the accuracy of the binding parameters is only as good as the accuracy of your concentration measurement). As the signal at the binding equilibrium (Req ) is directly proportional to the injected concentration (C), the affinity can be calculated by plotting Req versus C and fitting the resulting binding isotherm to the appropriate binding equation (Figure 10.6a,b). Importantly, this approach can only be applied if all injections reach a steady state. In addition, the plot needs to cover an adequate concentration range to accurately describe the fit; while it is not always possible to reach full saturation, the highest concentration should at least exceed the calculated K D value. The steady state fit will also return the maximum saturation response (R ( ) max ); comparison with the theoretical Rmax (calculated as Rmax theor =

MWligand

MWanalyte

⋅ Rimmobilization ⋅ V ; where Rimmobilization is the response of

ligand immobilization (i.e., ligand density) and V is the ligand valency, that is, number of analyte binding sites per ligand) not only offers a convenient way

10.4

The Information Contained in the SPR Experiment

Steady state

150 100 50 0

(a)

100

200

200

150

150

100

100

50

300

400

Time (s)

500

600

104

(b)

KD = kd /ka

50

KD

0

0

Sample injection

0

Association phase (ka & kd) Dissociation phase (kd)

Rmax

200 Analyte concentration

SPR response (RU)

200

371

10

4

4

10

10

4

Log concentration (M)

10

4

0

(c)

100

200

300

400

Time (s)

Figure 10.6 Quantitative evaluation of an SPR binding experiment with several analyte injection spanning a wide concentration range (a), steady state affinity plot (b), and kinetic evaluation based on a 1 : 1 Langmuir model (c).

of validating the quality of the assay, but may also provide information about the stoichiometry. Steady state analysis is less sensitive to certain effects such as mass transport or analyte rebinding, yet contains far less information than kinetic analysis; it is therefore recommended to aim for a full kinetic evaluation whenever possible. After defining injection start and end points, the evaluation software mathematically fits both the association and dissociation phases of the interaction to established kinetic models. Importantly, global fitting of the entire sensorgram set is required for a robust evaluation to yield high-quality data (Figure 10.6c) [10]. It has to be noted that during association, ligand binding and release occur at the same time, and this phase therefore contains information about both k a and k d , the former being concentration dependent (the unit of k a is M−1 s−1 for a 1 : 1 binding model). The dissociation phase, on the other hand, only shows dissociation of the ligand–analyte complex and is independent of the analyte concentration (the unit of k d is s−1 for a 1 : 1 model). The analysis software also provides derived parameters such as K D and Rmax . Importantly, a kinetic fit should always be evaluated visually before reporting rate constants; software tools such as deviation parameters (e.g., 𝜒 2 ) and residual plots can assist in this validation step. The example of a typical SPR assay in Figure 10.4 requires that the signal returns to baseline before the next analyte injection can be performed; this, in some cases, can be experimentally challenging and often time consuming. The introduction of single cycle kinetic methods (also referred to as “kinetic titration”), in which several consecutive injections are performed without a complete dissociation phase and the entire injection cycle is analyzed at once, has largely influenced the field and increased the throughput of kinetic analyses [11]. The ProteOn instrument platform (Bio-Rad) follows an alternative approach (one-shot kinetics), in which up to six analyte concentrations are injected in parallel over a perpendicular ligand surface, thereby obtaining a full kinetic profile without the need for dissociation/regeneration [12].

500

600

372

10

Analysis of Molecular Interactions by Surface Plasmon Resonance Spectroscopy

Tip Software for the evaluation of binding data usually includes various distinct fitting models for describing 1 : 1 binding (Langmuir model), surface heterogeneity, mass transport effects, bivalent analytes, or conformational changes. Resist the impulse to try all models and pick the one with the best fit without further validation. The majority of interactions are expected to follow a simple 1 : 1 model, but factors such as impurities, immobilization heterogeneity, or other artifacts may lead to deviations. Advanced models often lead to a better fit since they contain additional parameters, but they may mask an issue that needs to be addressed by optimizing the assay itself. If a mass transport model shows improved results, experiments should be performed to confirm this observation (e.g., by increasing the flow rate). Only propose a more complex model (e.g., conformational change) if there is indeed support for such a binding mode from orthogonal assays or structural analyses. The binding and conversion of complement factor B to the opsonin C3b is an example of a welldocumented structural transition for which a conformational change model showed improved fitting [13].

10.4.3 Concentration Analysis

The association phase of a sensorgram is directly correlated to the analyte concentration and can therefore be utilized for concentration analysis. There are several ways to obtain accurate concentration information from an SPR experiment [14]. Similar to other detection methods, a calibration standard (i.e., analyte of certified concentration) can be used in a direct binding assay to generate a calibration curve by plotting either the response at a specific time point or, preferably, the initial binding rates. In an adaptation of this approach, competition or inhibition assay formats can be used in which the analyte (or an analog thereof ) is immobilized and the binding of a competing molecule is measured at increasing analyte concentrations in solution; this method is particularly useful for determining concentrations of small molecule analytes and is, for example, used in commercial kits for the detection of vitamin B12 in food products [15]. Finally, the calibration-free concentration assay (CFCA) format is an intriguing approach for performing concentration analysis without the need for a standard [14, 16]. In a CFCA, the analyte is injected at two different flow rates (e.g., 10 and 100 μl min−1 ) and a variant of the kinetic mass transport model is used to extract the concentration. While taking full advantage of the SPR principle and thereby offering a unique advantage over orthogonal techniques, the method requires knowledge about the analyte’s diffusion coefficient, is restricted to interactions with detectable mass transport limitation, and has a limited dynamic range (K D ∼ 1–50 nM) [14].

10.5

SPR Applications: From Large to Small Molecules

10.4.4 Thermodynamics

Isothermal titration calorimetry (ITC) is considered the gold standard for the acquisition of thermodynamic data of a molecular interaction. However, SPR offers a valuable alternative for obtaining information about enthalpy (𝛥H), entropy (𝛥S), and binding free energy (𝛥G), and may even offer advantages concerning sample consumption over ITC. The affinity (i.e., equilibrium dissociation constant, K D ) thereby offers the key to unlock thermodynamic information through the following mathematical correlation: 𝛥G = −R ⋅ T ⋅ ln KD = 𝛥H – T ⋅ 𝛥S, with R = universal gas constant, T = Temperature While K D is readily available from an SPR experiment, 𝛥H can be obtained from a van’t Hoff analysis [17]. For this purpose, the same interaction experiment is conducted at different temperatures (e.g., typically six steps between 4 and 40 ∘ C) and ln K D is plotted against the reciprocal temperature value (1/T) to obtain 𝛥H/R (slope) and −𝛥S/R (intercept) via regression analysis. Comparative studies between thermodynamic properties determined by SPR and ITC revealed a high level of correlation between the two methods [18].

10.5 SPR Applications: From Large to Small Molecules 10.5.1 Working with SPR and Large Molecules

SPR instruments do not discriminate between analyte classes and can detect proteins, nucleotides, carbohydrates, lipids, and drug molecules. Yet, as the SPR signal depends on the analyte size, assays involving medium and large ligands (MW > 500 g mol−1 ) usually feature favorable signal-to-noise ratios and are more forgiving concerning certain artifacts. However, while small molecule analysis often requires the preparation of high-density ligand surfaces to boost signal generation (Section 10.5.2.), the opposite may be true for many large molecule assays. If the binding signals become too large, the quality of kinetic analyses may be negatively affected and it is recommended to keep Rmax below ∼200 RU (which may be achieved by adapting the ligand density). Other recommendations are more specific for certain molecular classes and are discussed in the following paragraphs. 10.5.1.1 Protein–Protein/Peptide Interactions

Protein–protein interactions still constitute a majority of assay systems and include a large and highly diverse spectrum of applications in life science, food, and drug discovery research. Moreover, proteins may be composed from just

373

374

10

Analysis of Molecular Interactions by Surface Plasmon Resonance Spectroscopy

20 building blocks, but often feature highly distinct characteristics regarding size, stability, flexibility, and functional properties. Consequently, assay development is similarly diverse and there is no single approach. Nevertheless, there are some common points that need to be considered. Before starting a protein interaction experiment, it is recommended that as much information be collected about the binding partners as possible, including molecular weight, pI, stability and, if possible, a rough estimate of the affinity from an orthogonal technique (e.g., enzyme-linked immunosorbent assay (ELISA)). Protein analytes need to be purified and the concentration needs to be determined as accurately as possible to allow for a quantitative assessment of the interaction. Although the purity is important (see box below), it is the activity of both binding partners that needs to be validated most carefully. Activity tests should be performed before starting to design the SPR assay; thereby, you may avoid troubleshooting of an interaction assay that could not work a priori due to inactivity of one of the binding partners. Immobilization of proteins via amine coupling, although often convenient due to the availability of primary amines in lysine residues and at the N-terminus, typically leads to random orientation of the ligand and may significantly impact its activity (this effect is often more pronounced when looking at protein analytes rather than small molecule analytes due to the involvement of larger binding areas that may be partially masked). If feasible, different immobilization (e.g., aldehyde coupling of glycoproteins), capturing (e.g., using an antibody against a domain that is not involved in analyte binding), or labeling approaches (e.g., biotinylation of single free cysteine as in the case of albumin or thioester proteins) may be evaluated. It may be a good idea to reverse the assay format (i.e., immobilizing the original analyte) in order to validate the interaction and determine the ideal assay design. As mentioned above, an immobilization density should be targeted that results in a maximum analyte response value of ∼200 RU or below, especially when performing kinetic analyses. Buffers should be compatible with the proteins (typically, phosphate and HEPES buffer systems at physiological pH and ionic strength), and should contain a surfactant to prevent protein adsorption (e.g., 0.005% Tween-20) and all cofactors needed for the binding (e.g., calcium salts for C-type lectins). Ensure that protein analytes remain stable during the time of analysis (adjust the autosampler temperature if possible or prepare samples shortly before injection if stability at room temperature is an issue). Heavily charged proteins and certain analytes such as lectins may be susceptible to interactions with the sensor chip matrix, which is often carbohydrate-based and contains charged functional groups. Although an adjustment of buffer conditions (e.g., change of pH and ionic strength or addition of soluble matrix components such as carboxymethyl dextran) may alleviate those issues, they need to be considered with care as they could also impact the specific binding event itself. The use of sensor chips with reduced charge levels and/or shorter matrix (e.g., Biacore CM4, Bio-Rad GLC) or reversal of the assay format may be a suitable alternative as well.

10.5

SPR Applications: From Large to Small Molecules

Tip The question about required sample purity is asked particularly often in the case of protein assays, yet it is one that remains difficult to answer. Even an impurity of 1% may interfere with an assay if it binds to the ligand or the matrix; on the other hand, contaminations of 10% or more may be unnoticed if they do not participate in any interaction event. Be aware, however, that even though latter impurities may not interfere directly, they may nevertheless affect other parameters such as concentration measurement during sample preparation and, consequently, quality of the assay. It is therefore of high importance to aim for the highest sample purity possible and subject samples to sensitive analytical methods before using them in an SPR assay (this advise also holds true for commercially obtained proteins). If a potential contaminant cannot be removed, the influence on the SPR quality needs to be carefully investigated (deviations from a 1 : 1 model and/or signals that exceed the theoretical Rmax are all indications for potential interference). In some cases, a change in assay conditions (e.g., changing the buffer system, adding ethylenediaminetetraacetic acid (EDTA) or higher surfactant concentrations) may improve selectivity.

Owing to the ready availability of soluble, full-length proteins, SPR assays have been particularly popular in biological networks that primarily involve plasma proteins, as, for example, certain innate immunity pathways such as the complement system [19]. Assays involving membrane-bound proteins (e.g., receptors, regulators) are more challenging to establish, but several options have evolved in recent years [20]. The recombinant expression of extracellular domains is a suitable and efficient strategy in many cases (e.g., for proteins that are anchored to the membrane via glycosyl phosphatidylinositol linkers), as the resulting proteins can then be treated as ligands or analytes using the standard assay protocols. However, this approach does not work for integral membrane proteins, the activity of which depends on them being embedded in a bilayer. Given their importance for drug discovery, a special effort has been made to make G protein-coupled receptors (GPCRs) amenable to SPR assays. One option is to generate membrane preparations or embed the receptor into liposomes that can be captured on lipidcapturing sensor chips (e.g., Biacore L1 chip; Figure 10.7a) [21]. Integral Molecular developed a system in which GPCRs can be displayed at high density on the surface of a lipoparticle; these can either be captured on a chip or used in competition assays (Figure 10.7b) [20a, 22]. In some cases, it was possible to immobilize or capture certain GPCRs directly on the chip surface in the presence of lipids, which reconstituted a membrane environment (Figure 10.7c) [23]. Since this procedure is not possible for all GPCRs, recent approaches have focused on the generation of thermally stabilized GPCRs that can be tethered to the chip without membrane support (Figure 10.7d) [24].

375

376

10

Analysis of Molecular Interactions by Surface Plasmon Resonance Spectroscopy

= receptor

(a)

= analyte

(b) Figure 10.7 Examples of strategies for measuring membrane receptor interactions (e.g., GPCR). (a) Capturing of receptor-containing liposome on L1 chip; (b) competition experiment with receptor

(c)

(d) lipoparticle and a helper molecule bound to the sensor surface; (c) reconstitution of membrane environment of immobilized receptor; and (d) direct capturing of thermo-stabilized GPCR.

10.5.1.2 Antibody–Antigen Interactions

Although technically belonging to the protein category, antibody assays bear a few unique features and applications that warrant special discussion. Due to the large size and relative stability of antibodies and the high affinity of most antibody–antigen interactions, antibody systems have been among the first to be described using SPR biosensors [25]. Yet, this relative simplicity sometimes lets users forget that there are several key points that have to be considered when planning antibody experiments. It starts with the assay design; while it is tempting to use antibodies as analytes due to their size, this typically leads to highly complex binding behavior and avidity effects as the two antigen-recognition sites bind simultaneously to the immobilized antigen (Figure 10.8). Although kinetic models have been developed to consider bivalent analyte binding, they should not be used routinely. Rather, bivalent proteins such as antibodies should be avoided as analytes and instead be immobilized to the surface. In this way, analyte binding to the two sites occurs independently, typically resulting in a single set of affinity and kinetic parameters (although at a valency of 2; Figure 10.8). It has to be considered, although, that the direct immobilization often leads to a partial masking of binding sites that will likely affect Rmax and may introduce some heterogeneity due to conformational effects [26]. One way of circumventing this problem is a capturing approach, in which an antibody-binding protein (e.g., an anti-Fc antibody) is immobilized first and used to capture the antibody of interest in an oriented manner that does not interfere with antigen binding. Although this approach may lead to comparatively low capacities and requires a strong capturing molecule to avoid surface drift, it also allows for the regeneration of the surface and reloading with the same or a different set of antibodies. This strategy is therefore ideally suited for the characterization of hybridomas and antibody

10.5

SPR Applications: From Large to Small Molecules

Independent binding

Coordinated binding

Langmuir model, valency 2

Bivalent analyte model, avidity effects

(a)

(b)

Figure 10.8 Binding configuration of an antibody–antigen interaction with the antibody being the ligand (a) or the analyte (b).

libraries as well as epitope mapping at high throughput, which has been further facilitated with the introduction of parallelized SPR instruments [27]. 10.5.1.3 Oligonucleotides

From early on in their development and commercialization, SPR instruments have been utilized to detect protein–DNA and DNA–DNA binding, and also to monitor DNA manipulation steps (e.g., hybridization, strand separation, enzymatic cleavage) [28]. Meanwhile the methodology has been further improved and applied to cases such as elucidation of protein–RNA interactions [29], small molecule binding to nucleotides [8], regulation of bacterial replication [30], telomere elongation [31], or monitoring of PCR reactions [32], to name a few [33]. In addition, SPR has also been used for the selection of aptamers, which conversely can act as ligands for interaction studies of protein biomarkers [34]. In many oligonucleotide assays, the method of choice is to immobilize biotinylated DNA, RNA, or aptamers probes on streptavidin-coated sensor chips and use proteins or other oligos as analytes [33b]. Typically, HEPES, MES, or Tris-based buffer systems are used [8, 33b]. While high-salt solutions usually work well for the regeneration of oligonucleotide interactions, intense change in pH may cause denaturation and should be used with care. One of the most common complications in this assay format is that many oligonucleotide-binding proteins are positively charged and may therefore non-specifically bind to the sensor chip matrix. While an increase in salt concentration is expected to influence the interaction event as well, selection of a different chip or assay format may be considered [33b]. Of note, DNA hybridization has not only found its way to SPR application as a subject of various studies but it is also increasingly used as a regenerable capturing method. For example, Biacore offers a “Biotin CAPture Kit” that consists of a sensor chip that is pre-immobilized with an ssDNA oligo and streptavidin that is labeled with the complementary strand; this allows the study of interactions (between a biotinylated ligand and its analyte) that are challenging to regenerate since the streptavidin can be completely removed and reloaded for each cycle. The memLayer kit by LayerLab follows a similar approach for capturing liposomes; a neutravidin/streptavidin chip is saturated

377

378

10

Analysis of Molecular Interactions by Surface Plasmon Resonance Spectroscopy

with a biotinylated DNA strand while the complementary strand is inserted into liposomes via a cholesterol membrane anchor [35]. 10.5.1.4 Larger Structures

In principle, SPR is able to detect any type of binding event at the sensor chip surface and is not restricted to large proteins and nucleotides. However, the exponential decay of the evanescence wave and the microfluidics driving most of the SPR instruments put some limits to the practicality of measuring very large structures. As mentioned above, liposomes and lipoparticles are routinely used in SPR applications. Several papers also described the measurement of virus particles. Yet, while assays with larger cells have occasionally been attempted, other labelfree technologies such as photonic crystal sensors (Section 10.6) are considered more suitable for cell-based applications. 10.5.2 Working with SPR and Small Molecules

Two decades ago, direct SPR assays had been primarily developed for the study of macromolecular interactions that involved large to medium-sized molecules [36]. Conversely, the use of small analytes (MW ≤ 500 g mol−1 ) was challenging due to the inherent low mass and, consequently, an SPR response that was too poor in intensity and quality. As an alternative, indirect SPR competition experiments were established as an ordinary method to study ligand–small analyte systems [37]. Here, the interaction between a secondary larger analyte (e.g., a protein) and the immobilized ligand is first monitored (Figure 10.9a). Next, the same experiment is reproduced in the presence of varying amounts of the small molecule that competes with the large analyte for complex establishment with the ligand. As a consequence, a displacement of the large analyte from the surface occurs that leads to a decrease in the SPR response (Figure 10.9b). The indirect competitive method has been applied to a variety of small molecules including hormones, toxins, drugs, and explosives among others [38]. It offers steady state information and serves to determine binding affinities and/or the amount of analyte present in the sample. Nevertheless, this approach does not yield kinetic data, and it relies on the availability of a large molecule analyte that competes for the same binding area on the ligand, which is not always feasible. In contrast, direct SPR assays provide real-time monitoring of the specific interaction, yielding kinetic information of the binding event. Moreover, they eliminate recognition steps typical of indirect methods, reduce the assay times and the total sample volume, permit sample recovery, and enable the use of an array format. Alternatively, methods based on signal amplification using helper molecules such as antibodies or conjugated gold nanoparticles have been proposed [39]. Direct SPR assays with small molecules can be achieved with good sensitivity if the small molecule is immobilized to the sensor surface instead of the larger partner. A large molecule acting as the analyte leads to notable amplification of

10.5

SPR Applications: From Large to Small Molecules

Secondary analyte

379

No inhibition

90 70 60 30

Ligand

10 −10

(a)

0

50 100 150 200 250 300 350

Small analyte No inhibition

90 70 60

Inhibition

30

Ligand (b)

10 −10 0

50

100 150 200 250 300 350

Figure 10.9 (a,b) Schematic representation of an indirect competitive method.

the SPR response. Although this approach is very attractive, it implies difficulty in coupling a small molecule to the gold surface for which the presence of a specific functional group in the molecule structure (e.g., carboxylic acid, thiol, aldehyde) is required. If the small molecule already contains a suitable functionality in its structure, we have to make sure that it is not involved in the binding to the analyte and, if the functional group has to be introduced, the structural modification must not interfere with the ligand–analyte recognition. Unfortunately, the probability that minor structural modifications of the small molecule will affect its binding abilities is high and implies an important drawback in performing direct SPR experiments in such format. Recent developments in the area of instrument sensitivity, assay, and analysis protocols are now making possible accurate, direct kinetic evaluation of small ligand–analyte complexes, and state of the art equipment (e.g., Biacore T200, ProteOn XPR36, and Reichert SR7500DC) permits reliable evaluation of analytes with molecular mass below 200 g mol−1 . With this potential, direct SPR analysis of small molecules has rapidly gained attraction in pharmaceutical applications with particular relevance in the field of fragment-based drug screening [40]. The last part of this chapter provides an overview of useful experimental considerations to successfully perform direct SPR detection of small analytes. 10.5.2.1 Starting Up

Direct SPR studies of small analytes follow the same protocol as for larger analytes, but there are specific requirements to be considered that set the basis for a successful binding experiment: 1) The sensitivity of the SPR instrument will take an essential role as it is directly related with the detection limit that will be achieved. Moreover, high-capacity sensor chips, formed of highly packed polymer hydrogels with

380

10

Analysis of Molecular Interactions by Surface Plasmon Resonance Spectroscopy

Table 10.2 Common drawbacks of direct SPR detection of small analytes. Source

Drawback

High capacity surface

Steric hindrance Mass transport limitation Matrix effects Matrix effects Bulk refractive index Poor solubility Changes of refractive index increments

Small analyte

multiple attachment points, are indispensable to immobilize a large number of ligand molecules and thereby acquire stronger SPR responses. In the last years, several SPR companies have launched specialized high-capacity sensor chips for such applications, for example, HC1000 (Xantec Bioanalytics), CM7 (Biacore), and GLH (Bio-Rad) chips. 2) With the appropriate equipment and sensor chip, ligand immobilization and binding experiments are carried out as explained in Section 10.3. At this time, one needs to be conscious of potential problems related to the small size of the analyte and the use of a high-capacity surface. In Table 10.2 and in the following paragraphs, a brief description of the most common drawbacks of direct SPR detection of small analytes is provided, together with experimental tips to overcome them. 10.5.2.2 Steric Hindrance

When working with small analytes, it is highly recommended that large amounts of the ligand be immobilized to the sensor surface to achieve good SPR signal intensities. However, highly packed ligand surfaces do not always show the expected performance and the observed SPR signal capacity may be significantly lower than the theoretical Rmax value. This outcome is normally due to an excessive ligand packing and concomitant profound steric hindrance that renders a fraction of the ligand sites on the surface inaccessible for analyte binding [41].

Tip In order to exploit the full potential of high-capacity surfaces, it is recommended that a test be made in which the ligand is immobilized at various densities and the percentage of active ligand is tested by means of the comparison Rmax-exp /Rmax-theor . Figure 10.10 shows a model example where three ligand densities were tested with ligand densities corresponding

10.5

SPR Applications: From Large to Small Molecules

40

(b) High ligand density

Rmax-exp

30

20

(c) High ligand density with increased steric hindrance

10 (a) Low ligand density 0 0

10

20

30

40

Rmax-theor (immobilization degree) Figure 10.10 Relationship between ligand density and the steric hindrance effects.

to Rmax-theor of 10, 30, and 40 RU, and a calculated Rmax-exp of 7, 18, and 16 RU, respectively. Surface a, with low ligand density offers low steric hindrance but also generates a low SPR signal (only 10 RU). Surface b, with higher ligand density is more prone to steric hindrance but actually offers the strongest SPR response (18 RU). The highly packed surface c, on the other hand, results in lower SPR response as compared to surface b, due to a stronger steric hindrance effect. In this example, surface b will be selected to carry out the binding experiment.

10.5.2.3 Mass Transport Limitation

The effect of mass transport limitation has already been mentioned in Section 10.3.2. Here, let us recall that the probability of monitoring mass transport effects increases when the immobilization level of the ligand is high. Luckily, diffusion of small molecules from the bulk solution to the sensor surface is normally fast, thus lowering the probability of mass transport effects. Still, there are cases where the binding rate of a small analyte is faster than the diffusion rate, and mass transport effects occur. Under these circumstances the initial part of the sensorgram, or even the overall association phase, is linear (corresponding to a system partially or totally mass transport limited). Here, the RU versus time linear relationship masks the genuine analyte–ligand kinetics; yet, this behaviour is advantageous

381

382

10

Analysis of Molecular Interactions by Surface Plasmon Resonance Spectroscopy

when aiming at determining the concentration of the analyte in the sample (see Section 10.4.4 of the chapter) [41].

Tip In order to minimize mass transport effects we have to perform the experiment at faster flow rates and, if necessary, introduce a parameter for mass transport limitation to the kinetic model of choice during data analysis. 10.5.2.4 Matrix Effects

Matrix effects are changes in the dimension of the polymeric matrix that supports the ligand on the sensor surface (e.g., swelling or contraction due to buffer effects such as pH changes). These changes may lead to undesired RI jumps during the SPR experiment as a consequence of a modification in mass distribution within the SPR evanescent field. Matrix effects have been attributed to modifications in the pH or ionic strength [42] and, based on our experience, they can also occur when small analytes are injected over the sensor surface at a relatively high concentration (in the millimolar range) [43]. Typically, matrix effects are less pronounced in the ligand-coated FC (target FC) in comparison to the reference FC, because the presence of the ligand protects to some extent the polymeric matrix from changes in the bulk solution. Thus, when the amount of immobilized ligand is high, differences in the matrix effect between target and reference FC become evident and yield RI changes that are different in magnitude. As a consequence, reference-subtracted sensorgrams will present an unexpected increase or drop in signal intensity that will complicate the experimental data. In this regard, special attention must be paid when working with interacting systems of low affinity (K D in the micromolar range) and fast binding kinetics, as the resulting sensorgrams often have a “block” shape (see Figure 10.5 for an example) that is highly similar to the signals typically observed for the RI change caused by the matrix effects [43]. In this case, matrix effects might remain undetected, ending up in wrong interpretation of the SPR data.

Tip Differences in the matrix effect between target and reference FC can be eliminated or minimized by immobilization of a “dummy” protein to the reference FC to mimic the ligand of the target FC, but does not interact with the analyte (Figure 10.11) [43].

10.5

SPR Applications: From Large to Small Molecules

383

Analyte injection

Matrix effect SPR response

Target FC

(a)

Time SPR response

Control FC (empty) (b)

Control FC with “dummy” protein Figure 10.11 Schematic representation of matrix effects. Reference-subtracted sensorgrams where (a) control FC is empty and (b) control FC contains a dummy protein.

10.5.2.5 Refractive Index Jumps and Baseline Drifting

Typically, when injecting an analyte solution over the sensor surface, a bulk RI jump (originated by differences in composition between the running buffer and the analyte sample) is registered, which superimposes with the SPR signal of the binding event. Owing to the small response signals, the contribution of the RI jump to the overall response is particularly important when the analyte is a small molecule and may negatively affect the quality of the processed sensorgrams. Another undesired phenomenon is the baseline drifting, which can be originated by different sources (e.g., the instrument itself ), and that takes particular relevance when the SPR response is low.

Tip In order to overcome distortions in the SPR signal originated by RI jumps, it is essential to make use of the double reference protocol during data analysis (in

Time

384

10

Analysis of Molecular Interactions by Surface Plasmon Resonance Spectroscopy

Reference subtracted

(I)

35

30

30

30

25

25

25

20

20

15

15

10

10

5

5

0

0 80

180

280

380

20

RI jump

15

Drifting

10 5 0

−5 −20

80

180

280

−5 −20

380

25

25

25

20

20

20

15

15 10

5

5

5

0

0

0

30

60

90

120 150 180

180

280

380

10

Drifting

−5

−5 0

80

15

RI jump

10

−5

(a)

Double referenced

35

−5 −20

(II)

Buffer blank injections

35

0

30

60

(b) Figure 10.12 (a–c) Sensorgrams before and after double referencing of small analytes binding to immobilized ligands. (I) Benzoylecgonine (MW = 289 g mol−1 ) and

90

120 150 180

0

30

60

90

120 150 180

(c) a monoclonal anti-benzoylecgonine antibody and (II) 4-carboxybenzenesulfonamide (MW = 201 g mol−1 ) and carbonic anhydrase II.

fact, the double referencing method is a requirement when working with small analytes). For this, it is necessary to perform injections of buffer blanks before and between analyte sample injections throughout the run. Blank subtraction from the reference-subtracted sensorgrams results in a notable increase in the signal quality and improves the sensitivity of the experiment. As an example, Figure 10.12 shows sensorgrams of the interaction between small analytes and immobilized ligands (i) before double referencing; (ii) blank injections for double referencing; and (iii) after double referencing.

10.5.2.6 Limited Solubility and Use of Organic Solvents

Small organic molecules are often hampered by poor solubility in water; in those cases, a low percentage of an organic solvent, typically 1–8% DMSO, has to be introduced in the buffered samples. As a consequence, sample injections will be accompanied by a big RI jump due to a mismatch between running buffer (devoid of DMSO) and analyte samples, which obscures the SPR analyte response. The solvent effect can usually be removed by subtracting the reference FC response from the target FC response when the solvent effect is small (∼100 RU). However,

10.5

SPR Applications: From Large to Small Molecules

in most small molecule assays where DMSO is used, the subtraction of the reference response does not eliminate the contribution of the solvent to the measured response because a higher DMSO bulk response will be obtained from the reference surface. The result is a mismatch similar to that originated by matrix effects (described in Section 10.5.2.4).

Tip An option to overcome this problem consists in minimizing the magnitude of the bulk RI, including the same amount of DMSO in the running buffer as that present in the analyte samples. The effect of the bulk RI shift can be further eliminated by using a protocol for solvent correction. For this, solvent correction solutions of running buffer containing different amounts of DMSO (less than, equal to, and greater than the DMSO concentration in the running buffer; for example, from 4.5 to 5.8% when 5% DMSO is introduced in the buffer) must be prepared and consecutively injected over the sensor surface. A calibration curve is built by plotting the signal difference between target FC and reference FC versus signal from reference FC, from which a correction factor is calculated that will permit the correction of the analyte response for the presence of DMSO in the subsequent binding experiment. Notably, this protocol has already been implemented in the last-generation software of different SPR platforms [44]. 10.5.2.7 Changes of Refractive Index Increments

In SPR technology correlation between SPR response and mass changes occurring on the sensor surface is established through the sample-dependent RI increment parameter (dn/dc). A correspondence of 1 RU = 1 pg mm−2 has been established as the standard equivalence for most SPR applications, calculated from a dn/dc value typical of proteins and nucleic acids. However, it may not be accurate when the analyte is of a substantially different nature, such as small organic molecules. This deviation does not interfere with the shape of the sensorgrams and, consequently, it does not influence kinetic analysis. However, it does affect the signal intensity leading to potential misinterpretation of results relative to the stoichiometry of the ligand–analyte complex [45].

Tip The origin of the standard non-equivalence in RU to mass correlation is in an intrinsic different value of dn/dc of the small molecule in comparison to dn/dc of proteins and nucleic acids. Therefore, it is recommended to determine the dn/dc of our small analyte with a refractometer in order to correct the RU-tomass correlation if unexpected stoichiometric results are obtained.

385

386

10

Analysis of Molecular Interactions by Surface Plasmon Resonance Spectroscopy

10.6 Beyond SPR–Orthogonal Interaction Biosensor Technologies

In addition to SPR and related technologies such as surface plasmon resonance imaging (SPRi) [46] and plasmon waveguide resonance spectroscopy (PWR)[47], alternative sensing methods for detecting biomolecular interactions are gaining attraction. Among those is biolayer interferometry (BLI; e.g., Octet platform, ForteBio), which monitors ligand–analyte binding as a measure of increasing optical thickness on biosensor tips that can be dipped into samples in standard plates. By avoiding microfluidics, BLI systems usually offer advantages in terms of flexibility and maintenance. While originally focusing on antibody analysis and protein quantitation, improvements in instrument sensitivity increasingly shift the focus on kinetic analysis of analytes including small molecules [48]. A potential limitation is that the dissociation phase is achieved by dipping the sensor tip into bufferfilled wells, thereby rendering removal of analyte molecules less efficient when compared with microfluidic-based systems. Comparative studies have shown that this limitation can be addressed using a “sink method,” in which the ligand is added to the dissociation buffer well in order to prevent analyte rebinding to the sensor tip surface [49]. Another interesting interferometric method is nanopore optical interferometry (SKi Pro, Silicon Kinetics), in which the interaction is measured on the large surface area of a porous silicon wafer that can be integrated into either a probe or an FC [50]. Optical biosensors based on refractive waveguide grating and photonic crystals (e.g., Corning Epic, SRU BIND) integrate the biosensor surface at the bottom of multi-well plates [51]. While they can be used for biomolecular analysis of binding activities and equilibrium affinities, the static nature of sample handling prevents kinetic measurement. Instead, these sensors were quickly developed into attractive platforms for measuring cell activation, in particular, in the context of GPCR stimulation, as they are capable of detecting changes in cell morphology, adhesion properties, and/or dynamic mass redistribution upon activation [51]. Together with electric impedance sensors, this optical biosensor technology thereby covers an application area that has proved challenging for SPR-based systems (though direct measurement of analyte binding to GPCR has made progress; see above) [51a,b]. Finally, label-free analysis of molecular interactions is also achieved using techniques such as nuclear magnetic resonance (NMR), quartz crystal microbalance (QCM), ITC, X-ray crystallography, or mass spectrometry, which offer unique advantages and drawbacks concerning versatility, sensitivity, extractable interaction parameters, and sample consumption when compared to SPR (see specialized reviews [52] for more on these methods). In many cases, it is the combination of SPR with orthogonal interaction methods (label-free, fluorescentbased, ELISA, etc.) that provides important cross-validation of results and reveals the most complete insight into a binding event or functional mechanism. In this respect, it is worth mentioning the increasing use of SPR and saturation transfer difference nuclear magnetic resonance spectroscopy (STD-NMR) as

References

complementary methods in the field of fragment screening to identify hit compounds for the development of novel lead bioactive compounds [53].

References 1. Liedberg, B., Nylander, C., and

2.

3.

4.

5.

6.

7.

8.

9.

Lundstrom, I. (1995) Biosensing with surface plasmon resonance–how it all started. Biosens. Bioelectron., 10, 1–9. (a) Rich, R.L. and Myszka, D.G. (2007) Higher-throughput, label-free, real-time molecular interaction analysis. Anal. Biochem., 361, 1–6; (b) Schasfoort, R.B.R.B.M. and Tudos, A.J. (2008) Handbook of Surface Plasmon Resonance, Royal Society of Chemistry, pp. 354–294. Willander, M. and Al-Hilli, S. (2009) in Micro and Nano Technologies in Bioanalysis (eds R.S. Foote and J.W. Lee), Humana Press, pp. 201–229. Homola, J. (2008) Surface plasmon resonance sensors for detection of chemical and biological species. Chem. Rev., 108, 462–493. Gedig, E.T. (2008) Surface chemistry in SPR technology, in Handbook of Surface Plasmon Resonance, Royal Society of Chemistry. Fischer, M.J. (2010) Amine coupling through EDC/NHS: a practical approach. Methods Mol. Biol., 627, 55–73. Hutsell, S.Q., Kimple, R.J., Siderovski, D.P., Willard, F.S., and Kimple, A.J. (2008) High-affinity immobilization of proteins using biotin- and GST-based coupling strategies, in Handbook of Surface Plasmon Resonance, Royal Society of Chemistry. (a) Liu, Y. and Wilson, W.D. (2010) Quantitative analysis of small moleculenucleic acid interactions with a biosensor surface and surface plasmon resonance detection. Methods Mol. Biol., 613, 1–23; (b) Zhang, F., Beaudet, J.M., Luedeke, D.M., Walker, R.G., Thompson, T.B., and Linhardt, R.J. (2012) Analysis of the interaction between heparin and follistatin and heparin and follistatin–ligand complexes using surface plasmon resonance. Biochemistry, 51, 6797–6803. (a) Rich, R.L. and Myszka, D.G. (2000) Advances in surface plasmon resonance

10.

11.

12.

13.

biosensor analysis. Curr. Opin. Biotechnol., 11, 54–61; (b) Schuck, P. and Zhao, H. (2008) The role of mass transport limitation and surface heterogeneity in the biophysical characterization of macromolecular binding processes by SPR biosensing, in Handbook of Surface Plasmon Resonance, Royal Society of Chemistry. (a) Khalifa, M.B., Choulier, L., Lortat-Jacob, H., Altschuh, D., and Vernet, T. (2001) BIACORE data processing: an evaluation of the global fitting procedure. Anal. Biochem., 293, 194–203; (b) Morton, T.A., Myszka, D.G., and Chaiken, I.M. (1995) Interpreting complex binding kinetics from optical biosensors: a comparison of analysis by linearization, the integrated rate equation, and numerical integration. Anal. Biochem., 227, 176–185; (c) O’Shannessy, D.J., Brigham-Burke, M., Soneson, K.K., Hensley, P., and Brooks, I. (1993) Determination of rate and equilibrium binding constants for macromolecular interactions using surface plasmon resonance: use of nonlinear least squares analysis methods. Anal. Biochem., 212, 457–468. (a) Karlsson, R., Katsamba, P.S., Nordin, H., Pol, E., and Myszka, D.G. (2006) Analyzing a kinetic titration series using affinity biosensors. Anal. Biochem., 349, 136–147; (b) Trutnau, H.H. (2006) New multi-step kinetics using common affinity biosensors saves time and sample at full access to kinetics and concentration. J. Biotechnol., 124, 191–195. Bravman, T., Bronner, V., Lavie, K., Notcovich, A., Papalia, G.A., and Myszka, D.G. (2006) Exploring “one-shot” kinetics and small molecule analysis using the ProteOn XPR36 array biosensor. Anal. Biochem., 358, 281–288. (a) Forneris, F., Ricklin, D., Wu, J., Tzekou, A., Wallace, R.S., Lambris, J.D., and Gros, P. (2010) Structures of

387

388

10

14.

15.

16.

17.

18.

Analysis of Molecular Interactions by Surface Plasmon Resonance Spectroscopy

C3b in complex with factors B and D give insight into complement convertase formation. Science, 330, 1816–1820; (b) Harris, C.L., Abbott, R.J., Smith, R.A., Morgan, B.P., and Lea, S.M. (2005) Molecular dissection of interactions between components of the alternative pathway of complement and decay accelerating factor (CD55). J. Biol. Chem., 280, 2569–2578; (c) Rooijakkers, S.H., Wu, J., Ruyken, M., van Domselaar, R., Planken, K.L., Tzekou, A., Ricklin, D., Lambris, J.D., Janssen, B.J., van Strijp, J.A., and Gros, P. (2009) Structural and functional implications of the alternative complement pathway C3 convertase stabilized by a staphylococcal inhibitor. Nat. Immunol., 10, 721–727. Karlsson, R. (2013) in The Immunoassay Handbook: Theory and Applications of Ligand Binding, ELISA and Related Techniques, 4 edn (ed. D.G. Wild), Newnes, pp. 209–222. Vyas, P., O’Kane, A.A., and Dowell, D. (2012) Determination of vitamin B12 in infant formula and adult nutritionals by surface plasmon resonance: First Action 2011.16 (test kit method). J. AOAC Int., 95, 329–334. (a) Pol, E. (2010) The importance of correct protein concentration for kinetics and affinity determination in structurefunction analysis. J. Vis. Exp., 17, 1746; (b) Karlsson, R., Fagerstam, L., Nilshans, H., and Persson, B. (1993) Analysis of active antibody concentration. Separation of affinity and concentration parameters. J. Immunol. Methods, 166, 75–84. (a) Roos, H., Karlsson, R., Nilshans, H., and Persson, A. (1998) Thermodynamic analysis of protein interactions with biosensor technology. J. Mol. Recognit., 11, 204–210; (b) Papalia, G.A., Giannetti, A.M., Arora, N., and Myszka, D.G. (2008) Thermodynamic characterization of pyrazole and azaindole derivatives binding to p38 mitogen-activated protein kinase using Biacore T100 technology and van’t Hoff analysis. Anal. Biochem., 383, 255–264. (a) Navratilova, I., Papalia, G.A., Rich, R.L., Bedinger, D., Brophy, S., Condon, B., Deng, T., Emerick, A.W., Guan, H.W., Hayden, T., Heutmekers, T., Hoorelbeke,

19.

20.

21.

22.

23.

24.

25.

B., McCroskey, M.C., Murphy, M.M., Nakagawa, T., Parmeggiani, F., Qin, X., Rebe, S., Tomasevic, N., Tsang, T., Waddell, M.B., Zhang, F.F., Leavitt, S., and Myszka, D.G. (2007) Thermodynamic benchmark study using Biacore technology. Anal. Biochem., 364, 67–77; (b) Myszka, D.G., Abdiche, Y.N., Arisaka, F., Byron, O., Eisenstein, E., Hensley, P., Thomson, J.A., Lombardo, C.R., Schwarz, F., Stafford, W., and Doyle, M.L. (2003) The ABRF-MIRG’02 study: assembly state, thermodynamic, and kinetic analysis of an enzyme/inhibitor interaction. J. Biomol. Tech., 14, 247–269; (c) Day, Y.S., Baird, C.L., Rich, R.L., and Myszka, D.G. (2002) Direct comparison of binding equilibrium, thermodynamic, and rate constants determined by surfaceand solution-based biophysical methods. Protein Sci., 11, 1017–1025. Ricklin, D. and Lambris, J.D. (2007) Exploring the complement interaction network using surface plasmon resonance. Adv. Exp. Med. Biol., 598, 260–278. (a) Rucker, J., Davidoff, C., and Doranz, B.J. (2010) Measuring membrane protein interactions using optical biosensors. Methods Mol. Biol., 617, 445–456; (b) Cooper, M.A. (2004) Advances in membrane receptor screening and analysis. J. Mol. Recognit., 17, 286–315. Besenicar, M.P. and Anderluh, G. (2010) Preparation of lipid membrane surfaces for molecular interaction studies by surface plasmon resonance biosensors. Methods Mol. Biol., 627, 191–200. Willis, S., Davidoff, C., Schilling, J., Wanless, A., Doranz, B.J., and Rucker, J. (2008) Virus-like particles as quantitative probes of membrane protein interactions. Biochemistry, 47, 6988–6990. Stenlund, P., Babcock, G.J., Sodroski, J., and Myszka, D.G. (2003) Capture and reconstitution of G protein-coupled receptors on a biosensor surface. Anal. Biochem., 316, 243–250. Rich, R.L., Errey, J., Marshall, F., and Myszka, D.G. (2011) Biacore analysis with stabilized G-protein-coupled receptors. Anal. Biochem., 409, 267–272. (a) Malmqvist, M. (1993) Biospecific interaction analysis using biosensor

References

26.

27.

28.

29.

technology. Nature, 361, 186–187; (b) Malmqvist, M. (1993) Surface plasmon resonance for detection and measurement of antibody-antigen affinity and kinetics. Curr. Opin. Immunol., 5, 282–286. (a) Catimel, B., Nerrie, M., Lee, F.T., Scott, A.M., Ritter, G., Welt, S., Old, L.J., Burgess, A.W., and Nice, E.C. (1997) Kinetic analysis of the interaction between the monoclonal antibody A33 and its colonic epithelial antigen by the use of an optical biosensor. A comparison of immobilisation strategies. J. Chromatogr. A, 776, 15–30; (b) Peluso, P., Wilson, D.S., Do, D., Tran, H., Venkatasubbaiah, M., Quincy, D., Heidecker, B., Poindexter, K., Tolani, N., Phelan, M., Witte, K., Jung, L.S., Wagner, P., and Nock, S. (2003) Optimizing antibody immobilization strategies for the construction of protein microarrays. Anal. Biochem., 312, 113–124; (c) Zhao, H., Gorshkova, I.I., Fu, G.L., and Schuck, P. (2012) A comparison of binding surfaces for SPR biosensing using an antibody-antigen system and affinity distribution analysis. Methods, 59, 328–335. (a) Abdiche, Y.N., Lindquist, K.C., Pinkerton, A., Pons, J., and Rajpal, A. (2011) Expanding the ProteOn XPR36 biosensor into a 36-ligand array expedites protein interaction analysis. Anal. Biochem., 411, 139–151; (b) Nahshol, O., Bronner, V., Notcovich, A., Rubrecht, L., Laune, D., and Bravman, T. (2008) Parallel kinetic analysis and affinity determination of hundreds of monoclonal antibodies using the ProteOn XPR36. Anal. Biochem., 383, 52–60. (a) Bondeson, K., Frostell-Karlsson, A., Fagerstam, L., and Magnusson, G. (1993) Lactose repressor-operator DNA interactions: kinetic analysis by a surface plasmon resonance biosensor. Anal. Biochem., 214, 245–251; (b) Nilsson, P., Persson, B., Uhlen, M., and Nygren, P.A. (1995) Real-time monitoring of DNA manipulations using biosensor technology. Anal. Biochem., 224, 400–408. Katsamba, P.S., Park, S., and Laird-Offringa, I.A. (2002) Kinetic studies

30.

31.

32.

33.

34.

35.

of RNA-protein interactions using surface plasmon resonance. Methods, 26, 95–104. Neylon, C., Brown, S.E., Kralicek, A.V., Miles, C.S., Love, C.A., and Dixon, N.E. (2000) Interaction of the Escherichia coli replication terminator protein (Tus) with DNA: a model derived from DNAbinding studies of mutant proteins by surface plasmon resonance. Biochemistry, 39, 11989–11999. Maesawa, C., Inaba, T., Sato, H., Iijima, S., Ishida, K., Terashima, M., Sato, R., Suzuki, M., Yashima, A., Ogasawara, S., Oikawa, H., Sato, N., Saito, K., and Masuda, T. (2003) A rapid biosensor chip assay for measuring of telomerase activity using surface plasmon resonance. Nucleic Acids Res., 31, E4–4. Pollet, J., Janssen, K.P., Knez, K., and Lammertyn, J. (2011) Real-time monitoring of solid-phase PCR using fiber-optic SPR. Small, 7, 1003–1006. (a) Majka, J. and Speck, C. (2007) Analysis of protein-DNA interactions using surface plasmon resonance. Adv. Biochem. Eng. Biotechnol., 104, 13–36; (b) Ritzefeld, M. and Sewald, N. (2012) Real-time analysis of specific proteinDNA interactions with surface plasmon resonance. J. Amino Acids, 2012, 816032. (a) Chang, C.C., Lin, S., Lee, C.H., Chuang, T.L., Hsueh, P.R., Lai, H.C., and Lin, C.W. (2012) Amplified surface plasmon resonance immunosensor for interferon-gamma based on a streptavidin-incorporated aptamer. Biosens. Bioelectron., 37, 68–74; (b) Lee, S.J., Youn, B.S., Park, J.W., Niazi, J.H., Kim, Y.S., and Gu, M.B. (2008) ssDNA aptamer-based surface plasmon resonance biosensor for the detection of retinol binding protein 4 for the early diagnosis of type 2 diabetes. Anal. Chem., 80, 2867–2873; (c) Murphy, M.B., Fuller, S.T., Richardson, P.M., and Doyle, S.A. (2003) An improved method for the in vitro evolution of aptamers and applications in protein detection and purification. Nucleic Acids Res., 31, e110. (a) Branden, M., Dahlin, S., and Hook, F. (2008) Label-free measurements of molecular transport across liposome

389

390

10

36.

37.

38.

39.

40.

41.

42.

Analysis of Molecular Interactions by Surface Plasmon Resonance Spectroscopy

membranes using evanescent-wave sensing. Chemphyschem, 9, 2480–2485; (b) Branden, M., Tabaei, S.R., Fischer, G., Neutze, R., and Hook, F. (2010) Refractive-index-based screening of membrane-protein-mediated transfer across biological membranes. Biophys. J., 99, 124–133. (a) Fivash, M., Towler, E.M., and Fisher, R.J. (1998) BIAcore for macromolecular interaction. Curr. Opin. Biotechnol., 9, 97–101; (b) Roden, L.D. and Myszka, D.G. (1996) Global analysis of a macromolecular interaction measured on BIAcore. Biochem. Biophys. Res. Commun., 225, 1073–1077. de Mol, N.J. (2010) Affinity constants for small molecules from SPR competition experiments. Methods Mol. Biol., 627, 101–111. (a) Mitchell, J. (2010) Small molecule immunosensing using surface plasmon resonance. Sensors, 10, 7323–7346; (b) Shankaran, D.R., Gobi, K.V., and Miura, N. (2007) Recent advancements in surface plasmon resonance immunosensors for detection of small molecules of biomedical, food and environmental interest. Sens. Actuators B, 121, 158–177. Mitchell, J.S. and Wu, Y. (2010) Surface plasmon resonance signal enhancement for immunoassay of small molecules. Methods Mol. Biol., 627, 113–129. (a) Navratilova, I. and Hopkins, A.L. (2011) Emerging role of surface plasmon resonance in fragment-based drug discovery. Future Med. Chem., 3, 1809–1820; (b) Neumann, T., Junker, H.D., Schmidt, K., and Sekul, R. (2007) SPR-based fragment screening: advantages and applications. Curr. Top. Med. Chem., 7, 1630–1642. Munoz, E.M., Lorenzo-Abalde, S., Gonzalez-Fernandez, A., Quintela, O., Lopez-Rivadulla, M., and Riguera, R. (2011) Direct surface plasmon resonance immunosensor for in situ detection of benzoylecgonine, the major cocaine metabolite. Biosens. Bioelectron., 26, 4423–4428. Karlsson, R. and Falt, A. (1997) Experimental design for kinetic analysis of

43.

44.

45.

46.

47.

48.

49.

50.

protein-protein interactions with surface plasmon resonance biosensors. J. Immunol. Methods, 200, 121–133. Guardado-Calvo, P., Munoz, E.M., Llamas-Saiz, A.L., Fox, G.C., Kahn, R., Curiel, D.T., Glasgow, J.N., and van Raaij, M.J. (2010) Crystallographic structure of porcine adenovirus type 4 fiber head and galectin domains. J. Virol., 84, 10558–10568. (a) Bio-Rad Laboratories (2011) Proteon XPR36 Protein Interaction Array System User Manual, Experiments with highly refractive cosolvents (DMSO), Bio-Rad Laboratories, pp. 83–85; (b) BIACORE (2006) Biacore® T100 Software Handbook, Solvent Correction, Biacore, pp. 103–107. Nguyen, B., Tanious, F.A., and Wilson, W.D. (2007) Biosensor-surface plasmon resonance: quantitative analysis of small molecule-nucleic acid interactions. Methods, 42, 150–161. Scarano, S., Mascini, M., Turner, A.P., and Minunni, M. (2010) Surface plasmon resonance imaging for affinity-based biosensors. Biosens. Bioelectron., 25, 957–966. Hruby, V.J. and Tollin, G. (2007) Plasmon-waveguide resonance (PWR) spectroscopy for directly viewing rates of GPCR/G-protein interactions and quantifying affinities. Curr. Opin. Pharmacol., 7, 507–514. Concepcion, J., Witte, K., Wartchow, C., Choo, S., Yao, D., Persson, H., Wei, J., Li, P., Heidecker, B., Ma, W., Varma, R., Zhao, L.S., Perillat, D., Carricato, G., Recknor, M., Du, K., Ho, H., Ellis, T., Gamez, J., Howes, M., Phi-Wilson, J., Lockard, S., Zuk, R., and Tan, H. (2009) Label-free detection of biomolecular interactions using BioLayer interferometry for kinetic characterization. Comb. Chem. High Throughput Screen., 12, 791–800. Abdiche, Y., Malashock, D., Pinkerton, A., and Pons, J. (2008) Determining kinetics and affinities of protein interactions using a parallel real-time label-free biosensor, the Octet. Anal. Biochem., 377, 209–217. Latterich, M. and Corbeil, J. (2008) Label-free detection of biomolecular

References

interactions in real time with a nano2010. J. Mol. Recognit., 25, 32–52; (c) Speight, R.E. and Cooper, M.A. (2012) porous silicon-based detection method. A survey of the 2010 quartz crystal Proteome Sci., 6, 31. microbalance literature. J. Mol. Recognit., 51. (a) Schroder, R., Janssen, N., Schmidt, 25, 451–473; (d)Velazquez-Campoy, A.; J., Kebig, A., Merten, N., Hennen, S., Ohtaka, H.; Nezami, A.; Muzammil, S. Muller, A., Blattermann, S., Mohr-Andra, and Freire, E. (2004) Isothermal titraM., Zahn, S., Wenzel, J., Smith, N.J., tion calorimetry. Curr. Protoc. Cell Gomeza, J., Drewke, C., Milligan, G., Biol., Chapter 17, Unit 17 18; (e) del Mohr, K., and Kostenis, E. (2010) DeconCarmen Fernandez-Alonso, M., Diaz, volution of complex G protein-coupled D., Berbis, M.A., Marcelo, F., Canada, J., receptor signaling in live cells using and Jimenez-Barbero, J. (2012) Proteindynamic mass redistribution measurecarbohydrate interactions studied by ments. Nat. Biotechnol., 28, 943–949; NMR: from molecular recognition to (b) Scott, C.W. and Peters, M.F. (2010) drug design. Curr. Protein Pept. Sci., 13, Label-free whole-cell assays: expanding the scope of GPCR screening. Drug Dis816–830; (f ) Palmer, R.A. and Niwa, H. covery Today, 15, 704–716; (c) Shamah, (2003) X-ray crystallographic studies of S.M. and Cunningham, B.T. (2011) Labelprotein-ligand interactions. Biochem. Soc. free cell-based assays using photonic Trans., 31, 973–979; (g) Gingras, A.-C., crystal optical biosensors. Analyst, 136, Gstaiger, M., Raught, B., and Aebersold, 1090–1102. R. (2007) Analysis of protein complexes using mass spectrometry. Nat. Rev. Mol. 52. (a) Cheng, C.I., Chang, Y.P., and Chu, Cell Biol., 8, 645–654. Y.H. (2012) Biomolecular interactions and tools for their recognition: focus on 53. Wielens, J., Headey, S.J., Rhodes, D.I., the quartz crystal microbalance and its Mulder, R.J., Dolezal, O., Deadman, J.J., diverse surface chemistries and applicaNewman, J., Chalmers, D.K., Parker, tions. Chem. Soc. Rev., 41, 1947–1971; M.W., Peat, T.S., and Scanlon, M.J. (2013) (b) Ghai, R., Falconer, R.J., and Collins, Parallel screening of low molecular B.M. (2012) Applications of isothermal weight fragment libraries: do differences titration calorimetry in pure and applied in methodology affect hit identification? research–survey of the literature from J. Biomol. Screen., 18, 147–159.

391

393

11 Determination of Absolute Configurations by Electronic CD Exciton Chirality, Vibrational CD, 1 H NMR Anisotropy, and X-ray Crystallography Methods – Principles, Practices, and Reliability Nobuyuki Harada

11.1 Introduction

It is well known that living organisms have adopted molecular chirality during their evolution, especially in the beginning of life, because the molecular reaction and/or interaction between chiral molecules provides more specific physiological functions than those between racemic molecules. Thus, molecular chirality becomes essential to life processes, and most bioactive compounds are chiral. So, to clarify the molecular mechanism of biological and pharmaceutical functions, determination of the absolute configuration (AC) becomes the first issue to be studied. Next, it is necessary to prepare enantiomerically pure compounds by asymmetric syntheses or by enantioseparation by HPLC. That is, the second issue is how efficiently the desired enantiomers can be synthesized with 100% enantiopurity or enantiomeric excess (% ee). These days 100% enantiopure drugs are required in pharmaceutical technology. Besides the life sciences mentioned above, molecular chirality is also important in material sciences. For example, the construction of molecular machines is fascinating and attractive as a future technology. We have first synthesized lightpowered chiral molecular motors, in which the direction of motor rotation was controlled by molecular chirality as described below. To determine ACs, many methods have been developed such as X-ray Bijvoet, electronic circular dichroism (ECD) exciton chirality, 1 H NMR anisotropy, X-ray internal reference, and so on. Each method has characteristic properties as reviewed below. In this chapter, the author would like to explain these methods by showing pertinent examples. The methods for determining AC are classified into two groups as shown in Figure 11.1. The first category covers the nonempirical methods, where AC can be unambiguously determined without reference to any authentic compound with known AC. This group includes (i) the X-ray Bijvoet method [1, 2], (ii) CD exciton chirality rule [3, 4], (iii) π-electron SCF-CI-DV MO method [5], and (iv) ab initio MO calculation of OR (optical rotation), ECD, and VCD (vibrational circular dichroism: CD spectrum in infrared region) [6–8]. Structure Elucidation in Organic Chemistry: The Search for the Right Tools, First Edition. Edited by María-Magdalena Cid and Jorge Bravo. © 2015 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2015 by Wiley-VCH Verlag GmbH & Co. KGaA.

394

11

Determination of Absolute Configurations

(1) Non-empirical methods (a) X-ray crystallography: Bijvoet method using the anomalous dispersion effect of heavy atoms. (b) CD exciton chirality method: applicable to non-crystalline samples. (c) MO calculation of ECD by the π-electron SCF-CI-DV method. (d) Ab initio calculation of OR, ECD, and/or VCD. (2) Empirical or relative method: reference compound or internal reference with known AC is necessary. (a) Chemical correlation, or comparison of OR or ECD. (b) 1H NMR anisotropy method: relative configuration determination by the anisotropy effect of an aromatic group contained in a chiral auxiliary with known AC. (c) X-ray crystallography: relative configuration to the internal reference => AC. Figure 11.1 Methods for determining absolute configuration (AC).

The second category includes the empirical or relative methods, where the AC of a target compound can be determined by reference to the AC of an authentic compound or to an internal reference with known AC: (i) chemical correlation to an authentic compound or by comparison of OR or ECD with those of an authentic compound; (ii) 1 H NMR anisotropy method by the use of chiral diamagnetic anisotropy reagents [9–14]; and (iii) X-ray crystallography of a compound containing an internal reference with known AC [9–11]. Each method has advantages and/or disadvantages, and AC determinations by these methods are exemplified as follows.

11.2 Reliability in the AC Determination and Selection of Method

As shown in Figure 11.1, there are several methods for determining AC. Which method is suitable for AC determination of a given chiral compound? How reliable is the AC determination carried out by the method? Of course, a proper method would depend on the molecular structure and chemical properties of the target compound. To perform unambiguous and reliable AC determination, the following issues should be considered. In general, (i) the theory and mechanism of the method have to be established. (ii) Simple theory and mechanism are much better than complex ones for AC determination in the sense of reliability. (iii) Large intensity data are essential for clear AC determination. If the observed signals are weak in intensity, it is generally difficult to judge plus or minus, and hence (R) or (S). This requirement is important even for AC determination by comparison of the observed data with the theoretically calculated ones. (iv) In the studies of AC determination, there is the possibility of misassignment due to a careless mistake and/or improper selection of a method. In the history of AC determination, there were many such cases, where the AC was later corrected. (v) If possible, it would be better to determine

11.3

Non-empirical Method: AC Determination by the X-ray Bijvoet Method

the AC of a target compound by two or more independent methods shown in Figure 11.1. As will be discussed in this chapter, CD exciton chirality, VCD, 1 H NMR anisotropy, and X-ray crystallography methods are cooperative for determining ACs. Of course, the physical phenomena of these methods are totally different from each other, but they should give the same AC for a given chiral compound. So, if the AC of a compound could be determined by two or more independent methods, AC determination would become much more reliable.

11.3 Non-empirical Method: AC Determination by the X-ray Bijvoet Method

It is well known that J. M. Bijvoet first determined the L-(2R,3R) AC of (+)-tartaric acid by using the anomalous scattering effect of heavy atoms in X-ray diffraction experiments [1]. Since then, the ACs of many chiral molecules have been determined by the Bijvoet method. In this method, AC can be more clearly determined if the following issues are considered: (i) The molecule should contain at least one heavy atom; for example, P, S, Cl, and Br atoms are mostly employed for organic compounds. (ii) In general, Cu-Kα X-ray (1.54184 Å) is better than Mo-Kα X-ray (0.71073 Å), because a stronger anomalous scattering effect is observable by CuKα X-ray. (iii) These days, the Flack parameter is used for determining ACs, where the extra measurement of Bijvoet pairs is unnecessary [2]. However, if necessary, it would be better to measure Bijvoet pairs and to compare their intensities for determining AC in a more reliable manner, as exemplified in Table 11.A.1. A pertinent example of the original Bijvoet method is shown in Figure 11.2, where the AC of 2-(1-naphthyl)propane-1,2-diol (−)-1 was determined by X-ray crystallography of its p-bromobenzoate (−)-2 [15]. p-Bromobenzoate (−)-2 was easily crystallized from ethanol giving good single crystals for X-ray OH

OH

O O

OH

Br

(S)-(–)-1

(S)-(–)-2

(S)-(–)-2

Figure 11.2 AC determination of diol (−)-1 by X-ray crystallography of p-bromobenzoate (−)-2 and ORTEP drawing. Redrawn with permission from Ref. [15].

395

396

11

Determination of Absolute Configurations

crystallography: colorless prisms; orthorhombic; space group P21 21 21 . The structure was solved by the direct method and successive Fourier syntheses. Absorption correction and full matrix least-squares refinement of parameters including anomalous scattering factors of Br, O, and C atoms led to the final convergence with R = 0.0249 and RW = 0.0342 for (S) AC. On the other hand, R and RW values for the (R)-AC were explicitly larger than those of (S)-AC: R = 0.0358 and RW = 0.0520. The AC of (−)-2 was thus clearly determined to be (S) as shown in Figure 11.2. This AC determination was confirmed by the original Bijvoet method as follows: Bijvoet pairs were measured, and their structural factors Fo(h,k,l) and Fo(h,k,−l) were compared with each other, where Fo(h,k,−l) is equivalent to Fo(−h,−k,−l) in this crystal. The ratio |Fo(h,k,l)|/|Fo(h,k,−l)| was thus compared with the calculated ratio |Fc(h,k,l)|/|Fc(h,k,−l)| as listed in Table 11.A.1, where the observed ratio agreed well with the calculated ratio in all reflections. So, the AC of ester (−)-2 was unambiguously determined to be S. Thus, the original Bijvoet method provides more reliable AC determination. The present AC assignment of (−)-2 was further confirmed by X-ray crystallography of other related compounds and chemical correlations as described in other sections.

11.4 Non-empirical Method: AC Determination by the ECD Exciton Chirality Method

The ECD exciton chirality method has successfully been applied to various natural and synthetic chiral compounds to determine their ACs. The theory and mechanism of the exciton chirality method are very simple, and the observed CD Cotton effects are very strong [3, 4]. Therefore, the AC of the exciton coupling system is easily and unambiguously determinable by applying the equations of molecular exciton theory, where any computer simulation by the use of quantum mechanical programs is unnecessary as explained below. 11.4.1 Outline of the ECD Exciton Chirality Method

Figure 11.3 exemplifies the exciton CD spectrum of a steroidal glycol bis(4dimethylaminobenzoate) 3, from which the AC of the compound could be easily determined [3]. The chromophore of 4-dimethylaminobenzoate exhibits a very strong π–π* absorption band at 𝜆max 311.0 nm (𝜀 30 400), which is polarized along the long axis of the chromophore. The UV spectrum of compound 3 shows a single band with double intensity at the corresponding region (𝜆max 309.4 nm, 𝜀 55 500), because it has two chromophores. In the corresponding region, the CD spectrum shows very intense bisignate exciton Cotton effects; the first Cotton effect at a longer wavelength is negative (𝜆ext 321.2 nm, Δ𝜀 −67.6), while the second Cotton effect at a shorter wavelength is positive (𝜆ext 295.5 nm, Δ𝜀 +24.6). The amplitude of exciton Cotton effects is

11.4

O

Δε

Non-empirical Method: AC Determination by the ECD Exciton Chirality Method

3 O

N

4 O O dma-BzO

+40 N

dma-BzO

295.5 (+24.6)

+20

0 CD

ε × 10−4

−20 p-H −40 −60

309.4 (55 500)

−80

321.2 (−67.6)

6

4

p-H UV

2

0 200

300

400

λ (nm) Figure 11.3 CD and UV spectra (solid lines) of cholest-5-ene-3α,4α-diol bis(4dimethylaminobenzoate) 3 in EtOH. The dotted lines show those of cholest-5-ene-3α,4α-diol dibenzoate 4 in EtOH. Redrawn with permission from Ref. [3].

defined as A-value, where A = Δ𝜀(first Cotton effect) − Δ𝜀(second Cotton effect), and so in this case, A = (−67.6) − (+24.6) = −92.2. On the other hand, the CD spectrum of cholest-5-ene-3α,4α-diol dibenzoate 4 (dotted line in Figure 11.3) clearly shows a negative first Cotton effect, while the corresponding positive second Cotton effect is not observed; it may be buried in the background CD. Therefore, a chromophore exhibiting an intense UV absorption at longer wavelength such as 4-dimethylaminobenzoate is much better to observe exciton split Cotton effects. Based on the observed large negative A-value of 3, the CD exciton chirality rule indicates that the electric transition dipole moments of two 4-dimethylaminobenzoate groups constitute a counterclockwise screw sense. Since this π–π* transition is polarized along the long axis of the chromophore, it can be concluded that the long axes of the chromophores constitute a

397

398

11

Determination of Absolute Configurations

H

O

4 3

HO

O

O

N Group j

Group i

wavefunction, energy, dipole strength, rotational strength,

N

a

0

β α

0

α-state: wavefunction, energy, dipole strength, rotational strength, β-state:

a

ψaα = (1/ 2)(ϕiaϕj0 – ϕi0ϕja)

E α = Ea – Vij D α = (1/2)(μi0a – μj0a)2 R α = +(1/2)πσ0 Rij • ( μi0a × μj0a) ψaβ = (1/ 2)(ϕiaϕj0 + ϕi0ϕja)

Eβ = Ea + Vij D β = (1/2)(μi0a + μj0a)2 R β = –(1/2)πσ0 Rij • ( μi0a × μj0a)

interaction energy, Vij = Rij–3{μi0a • μj0a – 3Rij–2( μi0a • Rij)(μj0a • Rij)}

0

Group i Total system Group j

If Vij > 0, the α-state is lower in energy than the β-state. α-state, longer wavelength side => 1st Cotton effect. β-state, shorter wavelength side => 2nd Cotton effect.

Figure 11.4 Theoretical summary of the CD exciton chirality rule. Redrawn with permission from Ref. [3].

counterclockwise screw sense as shown in Figure 11.3. These results enable one to determine the AC of compound 3 as shown, which agrees with the AC of steroidal skeletons assigned before by X-ray crystallography. 11.4.2 Molecular Exciton Theory of the CD Exciton Chirality Rule and Application to Steroidal Dibenzoate

As emphasized above, the theory of the CD exciton chirality rule is very simple and easily understandable, which is summarized in Figure 11.4 [3]. When two identical chromophores, for example, 4-dimethylaminobenzaote groups, interact with each other, the excited state of the whole system splits into two energy levels, 𝛼 and 𝛽, while the ground state remains as a single energy level. The parameter Vij is the interaction energy between the electric transition moments of two identical chromophores i and j. If the interaction energy Vij is positive, the 𝛼-state becomes lower in energy, while the 𝛽-state is higher. The rotational strength R, which governs the sign and intensity of CD Cotton effect, is generally formulated as R = 2.296 × 10 – 39

∫

Δ𝜀(𝜎)∕𝜎 d𝜎 cgs units

(11.1)

where Δ𝜀 is the molar CD and 𝜎 is the wavenumber. The exciton rotational strength R𝛼 of the 𝛼-state is expressed as follows: R𝛼 = +(1∕2)π𝜎0 Rij ⋅ (𝝁i0a × 𝝁j0a )

(11.2)

where 𝜎 0 is the excitation wavenumber for the π–π* transition 0 → a of the chromophore, Rij is the distance vector from chromophore i to chromophore j, 𝝁i0a is the electric transition moment of the transition 0 → a in the group i, 𝝁j0a is

11.4

Non-empirical Method: AC Determination by the ECD Exciton Chirality Method

that of group j, and symbols ⋅ and × indicate scalar and vector products, respectively (Figure 11.4). On the other hand, the rotational strength R𝛽 of the 𝛽-state is expressed as R𝛽 = –(1∕2)π𝜎0 Rij ⋅ (𝝁i0a × 𝝁j0a )

(11.3)

Thus, the rotational strengths of 𝛼- and 𝛽-states have the same absolute value, but are opposite in sign. In other words, the first Cotton effect at longer wavelength (𝛼-state) and the second Cotton effect at shorter wavelength (𝛽-state) have the same rotational strength, but are opposite in sign. In the theory of CD spectra, the summation of rotational strengths over all transitions becomes zero as shown in Equation 11.4. This is called the sum rule. ∑ Rk = 0 (11.4) From Equations 11.2 and 11.3, it is clear that the sum rule holds for the exciton transitions 0 → 𝛼 and 0 → 𝛽: ∑ Rk = R𝛼 + R𝛽 = 0 (11.5) In the theory of the CD exciton chirality rule, the electric transition moments 𝝁i0a and 𝝁j0a are key parameters. The electric transition dipole moment 𝝁i0a is defined as follows: 𝝁i0a =

∫

𝜙i0 𝝁𝜙ia d𝜏 i

(11.6)

where 𝜙i0 and 𝜙ia are ground-state and excited-state wavefunctions of chromophore i, respectively, 𝜏 i is the configuration space of chromophore i [1], and 𝝁 is the electric moment operator defined as follows: 𝝁 = er

(11.7)

where e is the elementary charge and r is the position vector of the electron. The electric transition dipole moment 𝝁0a is related to the dipole strength D of the electronic absorption band as follows: D = (𝝁0a )2 = 9.184 × 10 – 39

∫

𝜀(𝜎)∕𝜎 d𝜎

(11.8)

where 𝜀(𝜎) is the molar extinction coefficient of UV absorption band at wavenumber 𝜎. Thus, a strong absorption band gives a large electric transition dipole moment. So, Equations 11.2 and 11.3 indicate that strong exciton Cotton effects arise at an intense absorption band. In other words, to obtain strong exciton Cotton effects, it is important to select a chromophore exhibiting an intense UV band. Next, let us apply the equations in Figure 11.4 to a binary system, cholest-5ene-3α,4α-diol bis(4-dimethylaminobenzoate) 3, to determine its AC. The arrows in Figure 11.5 indicate the electric transition moments 𝝁i0a and 𝝁j0a , which are in-phase and hence the interaction energy Vij is positive in sign. Therefore, the 𝛼-state corresponds to the first Cotton effect, and the 𝛽-state to the second Cotton effect.

399

400

11

Determination of Absolute Configurations

H

O

3

HO O Group j

O

N Vector product μi0a × μj0a

Group i μi0a N

Positive 2nd Cotton

μj0a

4

Rij

λ Antiparallel

(1) Interaction energy Vij > 0. (2) Antiparallel, so (a)

Rα

Negative 1st Cotton

β

< 0, and R < 0. (b)

Figure 11.5 (a,b) Theoretical mechanism of the CD exciton chirality rule applied to cholest5-ene-3α,4α-diol bis(4-dimethylaminobenzoate) 3.

The vector product 𝝁i0a × 𝝁j0a makes a new vector, which is antiparallel to the distance vector Rij as shown in Figure 11.5a. Therefore, the triple product Rij • (𝝁i0a × 𝝁j0a ) becomes negative, and hence R𝛼 of the first Cotton effect is negative, while R𝛽 of the second one is positive as illustrated in Figure 11.5b. Thus, the sign and shape of bisignate Cotton effects of compound 3 are thus reproduced well by applying the molecular exciton theory, where any computer calculation is unnecessary. As exemplified above, the theory and mechanism of the CD exciton chirality rule are very simple, and the AC of exciton systems can be determined in a reliable manner. 11.4.3 The Most Ideal Exciton CD of (6R,15R)-(+)-6,15-Dihydro-6, 15-ethanonaphtho[2,3-c]pentaphene

The CD exciton chirality and X-ray Bijvoet methods are based on different physical phenomena, but both methods should give the same AC for a given compound. However, there were once severe controversies [3] about their AC determination, where it was claimed that ACs determined by the CD exciton method disagreed with those by the X-ray Bijvoet method. To solve this problem, we synthesized compound (+)-5, one of the most ideal compounds, proving that the CD exciton chirality rule and X-ray Bijvoet method are consistent with each other (Figure 11.6). This compound was synthesized from a precursor, whose AC was determined by X-ray Bijvoet method and chemical correlation [3, 16]. The anthracene chromophore exhibits a very strong π–π* UV absorption band around 250 nm (𝝀max 251.9 nm, 𝜀 204 000), whose electric transition moment is polarized along the long axis of the chromophore. In compound (+)-5, these two electric transition moments couple with each other to generate extremely strong exciton bisignate Cotton effects as shown in Figure 11.6: the first Cotton effect, 𝝀ext 268.0 nm, Δ𝜀 +931.3; second Cotton effect, 𝝀ext 249.7 nm, Δ𝜀 −720.8; A = +1652.1. From the positive sign of the A-value, the (6R,15R) AC could be determined, which agreed with the X-ray results.

11.4

+1000

Non-empirical Method: AC Determination by the ECD Exciton Chirality Method

+500

Δε

H

H

H

H

A = +1652.1 CD 0

ε × 10−5

268.0 (+931.3)

3 267.2 (268,000) +

−500

2

249.7 (−720.8)

1 UV

200

300

400

0

λ (nm) Figure 11.6 CD and UV spectra of (6R,15R)-(+)-6,15-dihydro-6,15-ethanonaphtho[2,3c]pentaphene 5 in EtOH. Redrawn with permission from Ref. [16].

It should be noted that (+)-5 is a cage compound, and therefore, it has no conformational flexibility. In addition, anthracene is a symmetrical chromophore. So, the CD exciton chirality rule could be exactly and unambiguously applied. As seen here, the intense CD data make AC determination more reliable. 11.4.4 Illustrative Cases: Application of the CD Exciton Chirality Rule 11.4.4.1 Acyclic 1,2-Glycols

The CD exciton chirality rule is applicable to dibenzoates of acyclic 1,2-glycols, which show typical bisignate Cotton effects as exemplified in Figure 11.7 [17]. Acyclic dibenzoates can rotate around the bond connecting two benzoates, and hence the CD sign depends on the conformational equilibrium. Based on the exciton CD and conformational analysis by 1 H NMR, the AC of acyclic 1,2-glycols can be determined. For example, (2S,3S)-2,3-butanediol bis(p-bromobenzoate) 6 adopts three rotational conformers 6A, 6B, and 6C, where conformers 6B and 6C are unstable because of three gauche relationships. Conformer 6A with only two gauche

401

11

Determination of Absolute Configurations Exciton chirality: zero

H

OBz-p-Br OBz-p-Br

p-Br-BzO

H

H3C

OBz-p-Br CH3

H3C

H

CH3

H

[6A]

[6B]

OBz-p-Br H

CH3

H

H3C

OBz-p-Br

[6C]

252.8 (+12.4)

+10 CD

Δε

A = +20.9 0 H

OBz-p-Br

Me −10

238.2 (−8.5)

Me H OBz-p-Br

4

(2S,3S)-6

244.0 (36,200)

UV in EtOH

200

ε × 10−4

402

250 λ (nm)

300

2

0

Figure 11.7 Application of the CD exciton chirality rule to (2S,3S)-2,3-butanediol bis(pbromobenzoate) 6. Redrawn with permission from Ref. [17].

relations between bulky groups dominates the equilibrium. Conformers 6A and 6B have positive and negative exciton twists between two chromophores, respectively, and conformer 6C has no exciton chirality, because two chromophores are in a trans-relationship. The preference of conformer 6A is supported by a large 1 H NMR coupling constant, J(trans) = 6.1 Hz. It should be noted that the following vicinal coupling constants are obtained for acyclic compounds: J(trans) = 6.1–8.7 Hz; J(gauche) = 2.9–4.1 Hz. The vicinal coupling constant J vic of compound 6 cannot be determined by a routine NMR measurement, because these two protons are equivalent to each other in chemical shift. In such cases, the 13 C satellite band method is useful to determine the J vic value [17, 18]. After all, the CD spectrum of dibenzoate 6 reflects a positive exciton chirality of conformer 6A. By combining exciton CD data and 1 H NMR coupling constant data, the AC of acyclic 1,2-glycol bis(p-bromobenzoate) 6 was determined to be (2S,3S) (Figure 11.7) [17].

11.5

Non-empirical Method: AC Determination by VCD Spectroscopy

11.4.4.2 Acetylene Alcohols

The CD exciton chirality rule is applicable to systems with two different chromophores, which exhibit intense π–π* UV absorption bands at similar wavelengths. For example, p-methoxyphenylacetylene chromophore (𝜆max 252 nm) can couple with p-methoxybenzoate chromophore (𝜆max 257 nm) [19]. By the use of this exciton interaction, the AC of original acetylene alcohol (+)-7 could be determined (Figure 11.8). Acetylene alcohol (+)-7 was subjected to a Sonogashira reaction yielding p-methoxyphenylacetylene alcohol (−)-8, which was esterified to give p-methoxybenzoate (−)-9 (Figure 11.8). The CD spectrum of (−)-9 showed exciton bisignate Cotton effects (Figure 11.9), the negative A-value of which led to an (R)-AC for (−)-9 as seen in the exciton chirality projection, and hence the AC of original acetylene alcohol (+)-7 was determined to be R.

11.5 Non-empirical Method: AC Determination by VCD Spectroscopy and DFT MO Simulation

The next example is the VCD of 4-ethyl-4-methyloctane (S)-(−)-10 and its AC determination by DFT MO (density functional theory/molecular orbital) simulation [20]. The VCD spectrum is generally very weak, and its S/N (signal/noise) ratio is also small. Therefore, VCD spectra are measured by FT (Fourier transformation) accumulation over 2–3 h. Furthermore, the theory and mechanism of the VCD spectrum of this compound are very complex as shown below, and in addition, the conformational flexibility of the compound makes AC determination very difficult. H OH

H OH

(R)-(+)-7

(R)-(–)-8

CH3O CH3O 252 nm

H O

CH3O

O

(R)-(–)-9

257 nm

Figure 11.8 A scheme for the AC determination of acetylene alcohol 7 by the CD exciton chirality rule. Redrawn with permission from Ref. [19].

403

11

Determination of Absolute Configurations

+20

+10

CD

(R)-(–)-9

Δε 0

−10

obsd CD 266.0 (−27.9) 246.2 (+21.0) 214.0 (−2.6)

−20

ε × 10−4

404

A = −48.9

−30

in EtOH

4

obsd UV 258.2 (41500)

UV

2

200

250

300

350

λ (nm) Figure 11.9 CD and UV spectra of 1-(4-methoxyphenyl)-1-dodecyn-3-ol 4-methoxybenzoate (R)-(−)-9 in EtOH. Redrawn with permission from Ref. [19].

(S)-(−)-4-Ethyl-4-methyloctane 10 is a cryptochiral hydrocarbon with a quaternary chirality center as shown in Figure 11.10, and its OR is very small: [𝛼]365 21 = −0.73 (neat, 𝜌 0.7565). The VCD Cotton effects observed around 1100 to 900 cm−1 are also very weak; Δ𝜀 values are of the order of 10−3 , but they are sufficiently stronger than the blank curve (Figure 11.10) [20]. It should be noted that the VCD intensity was corrected against that of a standard sample, (1R)-(+)-α-pinene. The IR spectrum shows weak absorptions in the corresponding area. To determine the AC by comparison of the experimental and theoretical VCD spectra, the VCD spectrum of 4-ethyl-4-methyloctane (R)-10 was calculated as follows: [20] (i) the stable conformers of (R)-10 were searched by the CONFLEX method using the MMFF94S force field, giving 30 conformers (total Boltzmann populations >95%); (ii) the structure–energy minimization of conformers and harmonic oscillation analysis were carried out by the DFT MO method at the B3PW91/6-31G(d,p) level [8]; (iii) the free energy of each conformer at 298.15 K was obtained by calculation of vibrational entropy, and then 24 stable conformers were selected (total Boltzmann populations >95%); and (iv) the VCD and IR

11.5

+0.004

(c)

Non-empirical Method: AC Determination by VCD Spectroscopy

VCD blank

+0.002

Δε

(b)

obsd VCD

0 −0.002

ε (S)-(–)-10

40 20

obsd IR

(a)

0 1300

1200

1100

1000

900

σ (cm−1) Figure 11.10 VCD and IR spectra of 4-ethyl-4-methyloctane (S)-(−)-[VCD(+)984]-10: (a) IR spectrum measured neat; (b) VCD spectrum measured neat; and (c) VCD blank measured neat by using racemic 4-ethyl-4-methyloctane. Redrawn with permission from Ref. [20].

spectra of each conformer were calculated by the DFT method, where the spectral band was approximated by the Lorentzian equation, and the parameter 𝛾, half the bandwidth at half peak height, was used as 𝛾 = 8 cm−1 . The total averaged VCD and IR spectra were then obtained by using Boltzmann weighting. To obtain reliable VCD spectra of 4-ethyl-4-methyloctane, we have synthesized both enantiomers with 100% ee, and their VCD spectra were measured and compared with the calculated VCD curves as shown in Figure 11.11. It is clear that the observed VCD spectrum of (−)-10 (solid line) agrees with the calculated VCD curve of (S)-10, where each observed and numbered VCD Cotton effect agrees well with the calculated Cotton effect, showing very good one-to-one correspondence. The AC of 4-ethyl-4-methyloctane was thus unambiguously determined to be (S)-(–)-[VCD(+)984], which indicates that the enantiomer showing a negative OR and a positive VCD Cotton effect at 984 cm−1 has (S)-AC. The VCD spectroscopy and DFT calculation are thus useful for determining ACs of chiral compounds. Now let us consider the next question. How reliable is the present AC determination by the VCD method? To clarify the mechanism of VCD generation, we

405

406

11

Determination of Absolute Configurations 7

+0.001 (b)

Calcd VCD 1

Δε

9

5

3

0 10 2

4

6 8

+0.004

Δε

−0.001

7

(a)

obsd VCD

9 1

3

5

0 6

2

10 8

4

−0.004 1300

1200

1100

1000

900

σ (cm−1) Figure 11.11 Observed and calculated VCD spectra of 4-ethyl-4-methyloctane enantiomers: (a) Observed VCD spectrum of (S)(−)-[VCD(+)984]-10 (solid line) and observed VCD of (R)-(+)-[VCD(−)984]-10 (dotted line). (b) Calculated VCD spectrum of (S)-10 (solid

line) and calculated VCD of (R)-10 (dotted line). The numbers on the solid lines specify VCD Cotton effects and show the one-to-one correspondence between experimental and theoretical VCD bands. Redrawn with permission from Ref. [20].

next analyzed the calculated results. Figure 11.12 shows the distribution pattern of the Boltzmann-weighted rotational strengths (R × w) calculated for 24 stable conformers of (R)-10, where R and w are the rotational strength and Boltzmann weight, respectively. At first glance, the dots distribute almost symmetrically against the zero line. In fact, the summation of (R × w) gives a value of nearly zero, ∑ (R × w) × 1044 = −0.0367, while the summation of absolute values yields a large ∑ value, |R × w| × 1044 = 264.378. Thus, the sum rule shown in Equation 11.4 holds approximately for this case. Figure 11.13 illustrates the expansion of the area between 1150 and 900 cm−1 shown in Figure 11.12 together with the calculated VCD curve. Around 1000 cm−1 , the dots generate a negative VCD Cotton effect, while around 960 cm−1 , the dots make a positive VCD Cotton effect. However, in other regions, it is difficult to judge whether they are positive or negative. Thus, VCD Cotton effects of this compound are generated by a very delicate imbalance of the distribution of Boltzmann-weighted rotational strength (R × w).

11.5

Non-empirical Method: AC Determination by VCD Spectroscopy

+3

(R × w) × 1044 cgs unit

+2

Σ (R × w) × 1044 =

(R)-10

−0.0367 cgs unit

+1

0 −1 Σ R × w × 1044 = 264.378 cgs unit

−2 −3 1600

1200

800 σ

400

0

(cm−1)

+3

+8

+2

+4

+1

Δε × 104

+12

0

0

−4

−1

−8 −12

(R)-10

1100

(R × w) × 1044 cgs unit

Figure 11.12 Boltzmann-weighted rotational strength (R × w) in cgs units calculated for all transitions in the 24 stable conformers of (R)-10 in the range 1600 to 0 cm−1 . Redrawn with permission from Ref. [20].

−2

1000

−3 900

σ (cm−1) Figure 11.13 Calculated Boltzmann-weighted rotational strength (R × w) for (R)-10 in the range 1150 to 900 cm−1 ; solid curve, the calculated VCD spectrum. Redrawn with permission from Ref. [20].

407

408

11

Determination of Absolute Configurations

To clarify the vibrational mode of these VCD Cotton effects, we have analyzed the calculation results. It became clear that these Cotton effects are based on the C–H bending motions, but it was difficult to rationalize these modes and to correlate them with the observed VCD Cotton effects in a qualitative sense. As discussed above, the generation mechanism of the VCD Cotton effects of this compound is very complex. So, let us consider again the next question at this point. Namely, how reliable is the AC determination of this cryptochiral hydrocarbon 10 by the VCD method? We are confident of this AC determination, because we have previously determined the AC of this compound by a combination of chemical correlation and X-ray crystallography or 1 H NMR anisotropy method as will be discussed below. Of course, VCD, X-ray, and 1 H NMR methods led to the same AC of hydrocarbon (S)-(−)-10, which indicates that the VCD measurement and calculation by the DFT-MO method are useful for determining the AC of such a hydrocarbon with very weak chiroptical activity.

11.6 Empirical Method: AC Determination by 1 H NMR Anisotropy Method Using M𝛂NP Acid

As indicated in Figure 11.1, the AC of chiral compounds can be determined by applying the 1 H NMR diamagnetic anisotropy method, where the relative configuration is determined by the diamagnetic anisotropy effect of an aromatic group contained in a chiral auxiliary with known AC. It is well known that the method using a Mosher acid, MTPA (α-methoxy-α-(trifluoromethyl)phenylacetic acid), is useful for determining the AC of chiral secondary alcohols [12–14]. We have developed a more powerful chiral 1 H NMR anisotropy reagent, MαNP acid {2-methoxy-2-(1-naphthyl)propionic acid 11} as shown in Figure 11.14, which has a naphthyl group exhibiting stronger diamagnetic anisotropy effects [9–11]. In general, the anisotropy effects (Δ𝛿 values) of MαNP esters are four times larger than those of MTPA esters. To determine the AC of a chiral secondary alcohol, it is esterified with (R)-(−)-MαNP acid 11 to yield ester (R,X)-12A; similarly, ester (S,X)-12B is prepared. These MαNP esters take preferred conformations as illustrated in Figure 11.14, where the Me/naphthyl plane is perpendicular to the MαNP plane; these conformations are supported by solid-state conformations determined by X-ray crystallography of many MαNP esters as will be discussed below. So, in ester (R,X)-12A, substituent R2 is located above the naphthalene plane causing the high field shift of the R2 group. On the other hand, in ester (S,X)-12B, substituent R1 exhibits a high field shift. From these results, the MαNP anisotropy method is proposed as shown in Figure 11.14, where Δ𝛿 value is defined as Δ𝛿 = 𝛿(R,X)-𝟏𝟐𝐀 − 𝛿(S,X)-𝟏𝟐𝐁

(11.9)

11.6

Empirical Method: AC Determination by 1 H NMR Anisotropy Method

CH3 COOH

OH MeO

OH

(S)-(–)-1

MαNP acid (S)-(+)-11

X-ray of p-Br-benzoate

Me/naphthyl plane

Me/naphthyl plane

High field shift (R)

Me

H Me

R2 O

O

R1

X syn

MαNP plane

O

High field shift syn

syn

syn

Me

H Me

O O syn

Two planes, perpendicular

R1

X

H (R,X)-12A

R2

(S)

O

syn

H (R,X)-12B

MαNP plane

Two planes, perpendicular Sector rule

Δδ < 0 Absolute configuration of the chiral alcohol

Δ δ = δ (R,X)-12A – δ (S,X)-12B

Δδ > 0

R2

R1 X H O-MαNP

MαNP plane

Δ δ = δ(R,X) – δ (S,X) Figure 11.14 The outline of AC determination by the MαNP acid method.

Substituent R1 having positive Δ𝛿 values is placed on the right side, while substituent R2 showing negative Δ𝛿 values is placed on the left side. From this result, the AC of chiral alcohol can be determined by NMR spectroscopy. As is well known, 1 H NMR spectroscopy itself has no ability to determine the ACs of chiral compounds; it gives only the information of relative stereochemistry. However, in the MαNP anisotropy method, the AC of MαNP acid is already determined as shown in Figure 11.14. That is, (S)-(+)-MαNP acid 11 was synthesized from (S)-(−)-2-(1-naphthyl)propane-1,2-diol 1, whose AC was determined by X-ray Bijvoet method of p-bromobenzoate derivative as discussed in Section 11.3. Thus, the ACs of chiral secondary alcohols can be determined by the MαNP anisotropy method. Another great advantage of the MαNP acid method is that diastereomeric MαNP esters can be easily separated by HPLC on silica gel, and therefore, racemic alcohols are separable into enantiopure alcohols via their MαNP esters; this is useful as an HPLC enantioresolution of alcohols in a preparative scale. By combining the HPLC separation and 1 H NMR anisotropy method, it is possible

409

410

11

Determination of Absolute Configurations

(a) O

MeO

(1) Esterification

R1

OH

(±)-13

O

R1 H

Me

R1

O

Me

R2

X

O

H Me O

–X

High field shift

Δδ Absolute configuration of the first fraction

X

O

0

R2 X

H O-MαNP MαNP plane Δδ = δ (R,X) – δ (S,X)

R1 R2

sector rule Δδ

R1

Δ δ = δ(R,X)-14 – δ (S,X)-14 = δ (S,–X)-14b – δ (S,X)-14a = δ (2nd.fr.) - δ (1st.fr.)

O

High field shift

Two planes, perpendicular

(c)

MeO

R1

syn O syn H MαNP plane

Two planes, perpendicular

(d)

R2

(S) O

syn O syn H MαNP plane

R1 H

(S,–X)-14b syn

(S)

O

R2

The second fraction (S,–X)-14b

(S,–X)-14a H Me

–X

Me/naphthyl plane

Me/naphthyl plane

syn

O

MeO

R2

The first fraction (S,X)-14a

(2) HPLC on silica gel

(b)

X

R2

HO (S)-(+)-11

O

MeO

MeO

O

–x O

R2 H

R1

Solvolysis The second fraction (S,–X)-14b

–x HO

R2 H

R1

Enantiopure alcohol (–X)-13

Figure 11.15 (a–d) The outline of enantioresolution of racemic secondary alcohols and their AC determination by the MαNP anisotropy method. Redrawn with permission from Ref. [21].

to obtain enantiopure alcohols and simultaneously determine their ACs as shown in Figure 11.15. Racemic alcohol (±)-13 is esterified with MαNP acid (S)-(+)-11 to give a diastereomeric mixture of esters, which is easily separated by HPLC on silica gel. The first-eluted ester is defined as (S,X)-14a, where S indicates the AC of the MαNP acid part, X does that of the alcohol part in the first-eluted ester, and a denotes the first-eluted ester. Similarly, the second-eluted ester is defined

11.6

Empirical Method: AC Determination by 1 H NMR Anisotropy Method

as (S,−X)-14b, where −X denotes the opposite AC of X, and b indicates the second-eluted ester. In the case of Figure 11.15, the parameter Δ𝛿 is reformulated as follows: Δ𝛿 = 𝛿(R,X)-𝟏𝟒 − 𝛿(S,X)-𝟏𝟒 = 𝛿(S,−X)-𝟏𝟒𝐛 − 𝛿(S,X)-𝟏𝟒𝐚 = 𝛿(2nd fr.) − 𝛿(1st fr.)

(11.10)

where (R,X)-14 and (S,−X)-14b are enantiomeric, and hence their chemical shift values are equal to each other. The parameter Δ𝛿 is thus expressed as Δ𝛿 = 𝛿 (2nd fraction) − 𝛿 (1st fraction). After the determination of the AC (X) of the first-eluted ester, enantiopure alcohol (X)-13 is recovered from the first-eluted ester. Similarly, alcohol (−X)-13 is obtained from the second-eluted ester (S,−X)-14b (Figure 11.15). 11.6.1 Enantioresolution of Racemic Aliphatic Alcohols Using M𝛂NP Acid and Simultaneous Determination of Their ACs

Chiral MαNP acid (S)-(+)-11 has a very strong enantioresolving power for alcohols, especially for aliphatic alcohols. As shown in Figure 11.16, diastereomeric MαNP esters (15a/15b–20a/20b) of 2-alkanols were easily separated by HPLC on silica gel, where the separation factor 𝛼 ranges from 1.15 to 1.93 [22]. This is an excellent practical method for preparing enantiopure aliphatic alcohols, to which asymmetric syntheses are hardly applicable. To determine the ACs of these MαNP esters, 1 H NMR signals were carefully assigned and Δ𝛿 values were calculated to give the ACs of the first-eluted esters as shown in Figure 11.17. The Δ𝛿 values are reasonably distributed: positive values on the right, and negative value on the left. These are the ACs of the first-eluted esters, and the second-eluted esters naturally have the opposite ACs. After AC determination, enantiopure alcohol was recovered as exemplified in Figure 11.18 [23, 24]. Enantiopure MαNP acid (S)-(+)-11 was also recovered and could be recycled. 11.6.2 Application of the M𝛂NP Acid Method to cis-2-Butyl-2-methyl-1-tetralol

The MαNP acid method was next applied to racemic cis-2-butyl-2-methyl-1tetralol (±)-22 as shown in Figure 11.19. As will be discussed later, enantiopure alcohol 22 was designed as a synthetic precursor of chiral 4-ethyl-4-methyloctane 10 [25, 26]. Racemic alcohol (±)-22 was allowed to react with MαNP acid (S)-(+)-11 to yield diastereomeric esters 23a and 23b, which were efficiently separated by HPLC on silica gel as shown in Figure 11.20. It should be emphasized that the separation factor is very large, 𝛼 = 1.81, which enabled a preparative separation of these esters.

411

412

11

Determination of Absolute Configurations

(d) 2-heptanol (S,R′)-(−)-18a (S,R′)-(–)-15a 27.1 min 39.5 min (S,S′)-(+)-15b (S,S′)-(+)-18b H α = 1.61 43.5 min α = 1.15 37.5 min Rs = 2.66 Rs = 1.18 (S,R′)-(–)-15a

(a) 2-butanol O CH3O O

0

0 (S,R′)-(–)-19a (S,R′)-(–)-16a (e) 2-octanol 26.4 min 34.2 min (S,S′)-(+)-16b (S,S′)-(+)-19b 40.5 min α = 1.69 α = 1.25 38.7 min Rs = 4.10 Rs = 2.02

(b) 2-pentanol

0

0

(f) 2-hexadecanol

(c) 2-hexanol (S,R′)-(–)-17a 28.4 min (S,S′)-(+)-17b α = 1.54 38.4 min Rs = 2.66

(S,R′)-(−)-20a 19.2 min

(S,S′)-(+)-20b 27.5 min

α = 1.93 Rs = 3.68

0

0

Figure 11.16 (a–f ) HPLC separation of diastereomeric (S)-(+)-MαNP esters of aliphatic alcohols (hexane/EtOAc = 20 : 1). Redrawn with permission from Ref. [22].

−0.19 −0.20

+0.24

−0.33

R H O-MαNP −0.03 (R)-15a

−0.12 −0.37 −0.26

(R)-16a

+0.23

R −0.32 -0.57 H O-MαNP −0.05 (R)-18a

+0.24

R −0.48 O-MαNP H −0.62 −0.05

−0.46

−0.15

−0.17 −0.21

−0.14 −0.17 −0.31 −0.24 −0.06

−0.27

+0.22

R −0.60 H O-MαNP −0.05 (R)-17a

+0.23

R –0.29 –0.60 H O-MαNP −0.05 (R)-19a

−0.17 −0.35 −0.27

CH3(CH2)13

+0.23

R H O-MαNP −0.05 (R)-20a

Figure 11.17 Determination of the ACs of first-eluted esters by the 1 H NMR anisotropy method using (S)-(+)-MαNP acid 11 and the observed Δ𝛿 values (ppm, CDCl3 ). Redrawn with permission from Ref. [22].

11.6

Empirical Method: AC Determination by 1 H NMR Anisotropy Method

O

O CH3O

CH3O

O

13

HO

2-hexadecanol (R)-(–)-21

(S,R)-(–)-20a

OH

13

(S)-(+)-11

Figure 11.18 Recovery of enantiopure alcohol and MαNP acid.

O CH3O

OH H OH (±)-cis-22

(S)-(+)-MαNP acid 11

O CH3O

H

O H

CH3O

O

(S;1S,2S)-(–)-cis-23a

O

(S;1R,2R)-(–)-cis-23b

(S;1S,2S)-(–)-cis-23a H

OH

(1S,2S)-(+)-cis-22 Figure 11.19 The preparation of enantiopure (1S,2S)-(+)-2-butyl-2-methyl-1-tetralol 22 by the MαNP acid method.

(S;1S,2S)-(–)-cis-23a 25 min

(S;1R,2R)-(–)-cis-23b 35 min

α = 1.81 Rs = 5.91

0

10

20 Time (min)

30

40

Figure 11.20 HPLC separation of diastereomeric MαNP esters 23a and 23b of cis-2-butyl-2methyl-1-tetralol: silica gel (22𝜙 × 300 mm), hexane/EtOAc = 15 : 1. Redrawn with permission from Ref. [26].

413

414

11

Determination of Absolute Configurations

MαNP plane Δδ values in ppm

eq. −0.08 ax. −0.03 −0.49 −0.38

−0.27 −0.75 −0.58

eq. +0.32 ax. +0.12 +0.27

S

+0.22 +0.39

S −0.76 +0.58 or −0.89 −0.28 H OMαNP −0.68 −0.04 or −0.81

First Fraction, (S;1S,2S)-(–)-cis-23a Figure 11.21 Distribution of Δ𝛿 values (ppm units) and AC determination of the firsteluted MαNP ester (S;1S,2S)-(−)-cis-23a. Redrawn with permission from Ref. [25].

It would be interesting to think why diastereomeric MαNP esters are largely separated by HPLC on silica gel, despite the fact that MαNP esters do not contain the so-called hetero atoms such as nitrogen. All NMR proton signals of esters 23a and 23b were assigned by using pertinent NMR techniques including 2D NMR. The calculated Δ𝛿 values {Δ𝛿 = 𝛿(2nd fr. 23b) − 𝛿(1st fr. 23a)} are illustrated in Figure 11.21. The benzene ring protons show large positive Δ𝛿 values, while the butyl and methyl groups show large negative Δ𝛿 values. Therefore, the benzene ring is placed on the right side, and the butyl and methyl groups are placed on the left side, which leads to the (1S)-AC of the first-eluted ester 23a. The cis-configuration of alcohol 22 was determined by the NOE effects, and after all, the (S;1S,2S)-AC was assigned to (−)-23a. Hydrolysis of MαNP ester (S;1S,2S)-(−)-23a with NaOMe in MeOH furnished enantiopure alcohol (1S,2S)-(+)-cis-22 in a good yield. This MαNP acid method has been successfully applied to various alcohols. 11.6.3 Verification of the AC of cis-2-Butyl-2-methyl-1-tetralol by X-ray Crystallography

As discussed above, the 1 H NMR anisotropy method is empirical, but how reliable is the AC determination by the 1 H NMR anisotropy method? We have never encountered any exception where the AC determined by the MαNP-1 H NMR anisotropy method was wrong. This fact is very important for increasing the reliability of an empirical rule. One of the advantages of the MαNP esters is that they have a high probability of affording single crystals suitable for X-ray crystallography. In the case of cis2-butyl-2-methyl-1-tetralol MαNP esters, the second-eluted ester (−)-23b gave single crystals, one of which was subjected to X-ray analysis. The ORTEP drawing of (−)-23b is shown in Figure 11.22, where MαNP group was used as an internal

Empirical Method: AC Determination by 1 H NMR Anisotropy Method

11.6

O CH3O

H O

(S;1R,2R)-(–)-cis-23b Figure 11.22 X-ray ORTEP drawing of the second-eluted MαNP ester (S;1R,2R)-(−)-cis-23b. Redrawn with permission from Ref. [25]

reference of AC. So, the (S;1R,2R)-AC of (−)-cis-23b was unambiguously determined, which confirmed the (S:1S,2S)-AC of the first-eluted ester (−)-23a including its cis relative configuration [25]. 11.6.4 Verification of the AC of (S)-(−)-[VCD(+)984]-4-Ethyl-4-methyloctane by Chemical Correlation

As discussed in Section 11.5, the AC of (+)-[VCD(–)984]-4-ethyl-4-methyloctane 10 was assigned to be R by VCD spectroscopy and DFT MO calculation. The AC was confirmed by the synthesis of chiral hydrocarbon (+)-10 starting from alcohol (+)-cis-22 as shown in Figure 11.23, where the (1S,2S)-AC of (+)-cis-22 was determined by 1 H NMR anisotropy and also by X-ray crystallography as described above [25, 26]. Enantiopure alcohol (1S,2S)-(+)-22 was reduced with NaBH4 and AlCl3 to yield hydrocarbon (S)-(+)-24, whose benzene ring was next oxidized with RuCl3 and

CH3OOC H

CH3OOC OH

(S)-(+)-24

(S)-(–)-25

(1S,2S)-(+)-cis-22 HO HO (S)-(+)-26

(R)-(+)-10

Figure 11.23 Synthesis of (R)-(+)-4-ethyl-4-methyloctane 10 from alcohol (1S,2S)-(+)-22.

415

416

11

Determination of Absolute Configurations

HIO4 . The obtained dicarboxylic acid was converted to diester (S)-(−)-25, which was reduced to glycol (S)-(+)-26. Bromination of glycol with CBr4 and PPh3 and final reduction with NaBH4 in HMPA furnished enantiopure (R)-(+)-4-ethyl-4methyloctane 10. By this chemical correlation, the AC of chiral hydrocarbon (+)10 was determined as shown in Figure 11.23, which of course agreed with the AC assigned by VCD method.

11.7 Relative Method: X-ray Crystallography Using Camphorsultam Dichlorophthalic Acid (CSDP Acid)

As discussed in Section 11.6.3, X-ray crystallography using MαNP acid as an internal reference of AC is straightforward and practical for AC determination. As such a chiral auxiliary, we have developed (1S,2R,4R)-(−)-CSDP (Camphorsultam Dichlorophthalic) acid 28, which was synthesized from camphorsulfonic acid (1S)-(+)-27 with known AC (Figure 11.24). So, CSDP acid 28 can be used as an internal reference for AC in X-ray crystallography. In addition, acid 28 contains sulfur and chlorine atoms, which are useful as heavy atoms in the X-ray Bijvoet method. Thus, AC can be doubly determined by two independent X-ray methods [9–11]. The sulfonamide group of CSDP acid 28 is important as a polar group for performing effective HPLC separation of diastereomeric isomers; that is, the polar group assists the adsorption of analytes on silica gel. In fact, CSDP acid has been successfully applied to the enantioresolution of various racemic alcohols. One of the examples is shown in Figure 11.25, where racemic cis-2-butyl-2-methyl1-tetralol (±)-22 was enantioresolved. Racemic alcohol (±)-22 was allowed to react with CSDP acid (−)-28 using DCC and DMAP yielding diastereomeric esters, which were separated by HPLC on silica gel: hexane/EtOAc = 6 : 1 (Figure 11.26). Although the separation factor (𝛼 = 1.17) is smaller than that (𝛼 = 1.81) of MαNP esters (Figure 11.20), two diastereomeric CSDP esters 29a and 29b could be baseline separated, which was sufficient for obtaining each pure ester. The second-eluted ester 29b was obtained as single crystals, one of which was subjected to X-ray analysis. The crystal structure was solved by the direct CI CI N O SO3H Camphor sulfonic acid (1S)-(+)-27

S O

O O

O

OH

CSDP acid (1S,2R,4R)-(–)-28

Figure 11.24 Synthesis of (1S,2R,4R)-(−)-CSDP acid 28.

11.7

Relative Method: X-ray Crystallography Using CSDP Acid

CI CI N S O

+ O

O

O

H

OH

OH

(+)-cis-22

CSDP acid (–)-28 CI

CI CI

CI

N S O

N O

O

O

O

S

+ H

(1S,2S)-(–)-cis-29a

O

O O

O

O

H

(1R,2R)-(+)-cis-29b

(1R,2R)-(+)-cis-29b

H

OH

(1R,2R)-(–)-cis-22 (1R,2R)-(+)-cis-29b, X-ray Figure 11.25 The preparation of enantiopure (1R,2R)-(−)-2-butyl-2-methyl-1-tetralol 22 by the CSDP acid method. Redrawn with permission from Ref. [26].

method as usual to provide the ORTEP drawing as shown in Figure 11.25: R and Rw = 0.0598 (0.0740); R and Rw for the mirror image = 0.0719 (0.0899). The (1R,2R)-AC of ester 29b was thus determined by the heavy atom effects of S and two Cl atoms. The same AC was obtained by the use of CSDP acid moiety as an internal reference. The (1R,2R)-AC of CSDP ester 29b was thus doubly determined by two independent methods. This is the advantage of the CSDP acid method. Hydrolysis of CSDP ester (+)-cis-29b with KOH/MeOH furnished enantiopure alcohol (1R,2R)-(−)-cis-22, which was employed for the synthesis of 4-ethyl-4methyloctane (S)-(−)-10. These results also supported the AC determination of cryptochiral hydrocarbon, 4-ethyl-4-methyloctane 10, discussed in Section 11.5.

417

418

11

Determination of Absolute Configurations

(1S,2S)-(–)-cis-29a 26 min

(1R,2R)-(+)-cis-29b 29 min

α = 1.17 Rs = 1.51

0

5

10

15 20 Time (min)

25

30

Figure 11.26 HPLC separation of diastereomeric CSDP esters 29a and 29b of cis-2-butyl-2methyl-1-tetralol. Redrawn with permission from Ref. [26].

11.7.1 Application of the CSDP Acid Method to Other Racemic Alcohols

The CSDP acid method has been successfully applied to various alcohols to obtain enantiopure alcohols and to determine their ACs by X-ray crystallography. Their chemical structures and ORTEP drawings are illustrated in Figure 11.27 and followings. The chiral diphenylmethanol moiety is contained in many chiral synthetic drugs, and so the CSDP acid method was first applied to this group. Figure 11.27 exemplifies the application of this method to methoxy-substituted diphenylmethanols, where diastereomeric CSDP esters were baseline separated by HPLC on silica gel (separation factor 𝛼 = 1.12 (o-OCH3 ), 𝛼 = 1.15 (m-OCH3 ), 𝛼 = 1.20 (pOCH3 )). HPLC separation is thus affected by the polarity and position of methoxy group. In all cases, the first-eluted CSDP esters gave single crystals, which were subjected to X-ray crystallography to provide ORTEP drawings as shown [27–29]. The ACs of alcohol parts were unambiguously determined using the CSDP group as an internal reference of AC. It was also easy to recover enantiopure chiral alcohols with established ACs from the corresponding CSDP esters. Similarly, the CSDP acid method has been applied to diphenylmethanols with electron-withdrawing groups (Figure 11.28); diastereomeric CSDP esters were more efficiently separated by HPLC on silica gel (separation factor 𝛼 = 1.16 (m-CF3 ), 𝛼 = 1.26 (p-NO2 ), 𝛼 = 1.34 (p-CF3 )) than the methoxy-substituted diphenylmethanol CSDP esters [29, 30]. It should be noted that p-substituted alcohol CSDP esters were more effectively separated by HPLC. Again the first-eluted esters 34a, 35a, 36a, and 37a gave single crystals, whose crystal structures were determined by X-ray crystallography. In the case of mCF3 -diphenylmethanol, the second-eluted ester 36b also afforded single crystals, and its ORTEP drawing is shown in Figure 11.28 instead of 36a. Interestingly, the trifluoromethyl group takes a disordered structure in 36b and 37a, but their ACs were unambiguously determined and the corresponding enantiopure alcohols were easily recovered. Next, we attempted to apply the CSDP acid method to racemic diphenylmethanols with a less polar substituent. For example, (4-methylphenyl)

11.7

Relative Method: X-ray Crystallography Using CSDP Acid

CI CI N S

O

O

O

O

O H OCH3

(S)-(–)-30a, X-ray CI CI N S

O O O CH3O

O

O

H

(S)-(–)-31a, X-ray

N S O

O O

O

O H

CH3O (S)-32a, X-ray CI CI N S O

O O O CH3O

O

H

OCH3 (S)-(–)-33a, X-ray Figure 11.27 X-ray ORTEP drawings of methoxy-substituted diphenylmethanol CSDP and related esters. Redrawn with permission from Refs. [27–29].

419

420

11

Determination of Absolute Configurations

N S

O O

O

O

O H NO2

(R)-34a, X-ray CI CI N S

O O

O

O O F

H

F (S)-(–)-35a, X-ray

CI CI N S O

O

OO

O H CF3

(S)-(–)-36b, X-ray

CI CI N S O

O O

O

O

H

CF3 (R)-(–)-37a, X-ray

Figure 11.28 X-ray ORTEP drawings of electron-withdrawing diphenylmethanol CSDP and related esters. Redrawn with permission from Ref. [29, 30].

11.7

HO H

HO H

H3C (a)

Br (R)-(–)-38 HO

H

Relative Method: X-ray Crystallography Using CSDP Acid

H3C

Br (S)-(–)-39

OH

HO H CH 3

HO

(b)

40 HO

H CH3

H CH3

H3C (c)

(R)-(+)-41

(R)-(–)-42

(d)

(R)-(+)-43

Figure 11.29 (a–d) The strategy to determine the ACs of less polar diphenylmethanols by the CSDP acid method.

phenylmethanol (±)-39 was esterified with CSDP acid giving a diastereomeric mixture of CSDP esters. However, the mixture could not be separated by HPLC on silica gel, because of the nonpolarity of substituent. So we have adopted an indirect route as shown in Figure 11.29a. If a diastereomeric mixture of CSDP esters of (4-bromophenyl)-4′ methylphenylmethanol (±)-38 can be separated by HPLC, it is easy to synthesize the target alcohol 39 from the CSDP esters. In fact, CSDP esters 44a and 44b were baseline separated by HPLC on silica gel (𝛼 = 1.18), and the first-eluted ester 44a was obtained as single crystals. From the ORTEP drawing of 44a, the AC of the alcohol part was determined to be R (Figure 11.30). The recovered alcohol (R)-(−)-38 was converted to the target alcohol (S)-(−)-39 (Figure 11.29a) [29]. The AC of (2-methylphenyl)phenylmethanol 42 had been in much confusion; once the AC of (R)-(−) was assigned based on asymmetric reductions, but later the opposite AC (R)-(+) was reported based upon catalytic asymmetric syntheses. Thus, AC determination by the analysis of reaction mechanism is not unambiguous, and therefore, another more reliable determination is necessary. To apply the CSDP acid method, we adopted a method similar to the case of p-methyl diphenylmethanol shown in Figure 11.29a. That is, racemic (4-bromophenyl)-2′ -methylphenylmethanol (±)-40 was esterified with CSDP acid (Figure 11.29b). However, the obtained diastereomers could not be separated by HPLC, and so, we took an alternative route as shown in Figure 11.29c. Racemic (2-(hydroxymethyl)phenyl)phenylmethanol 41 was selected as a synthetic precursor, which was reacted with CSDP acid giving a mixture of esters 45a and 45b. The mixture was baseline separated by HPLC on silica gel (𝛼 = 1.14), and the second-eluted ester 45b was recrystallized affording single crystals, one of which was analyzed by X-ray crystallography. From the ORTEP drawing, the AC of 45b was determined to be (S)-(−) [31]. From the first-eluted ester 45a, enantiopure alcohol (R)-(+)-41 was recovered, and it was not difficult to convert it into (2-methylphenyl)phenylmethanol (R)-(−)-42. Thus, the AC of (2-methylphenyl)phenylmethanol was unambiguously determined by X-ray

421

422

11

Determination of Absolute Configurations

CI CI N S O

O O

O

O H

H3C

Br

(R)-44a, X-ray

CI CI N S O

O O

O

O

H OH

(S)-(–)-45b, X-ray

CI CI N S O

O O

O

O

H OTBDPS

(R)-(–)-46a, X-ray

CI CI N S O O

O

O

O H

(R)-(–)-47a, X-ray

Figure 11.30 X-ray ORTEP drawings of CSDP esters used for the preparation of methylsubstituted diphenylmethanol. Redrawn with permission from Refs. [27, 29, 31, 32].

11.7

Relative Method: X-ray Crystallography Using CSDP Acid

crystallography of the CSDP ester [31]. It should be noted that the AC of alcohol 42 that was previously determined by 1 H NMR anisotropy method was confirmed by this X-ray analysis. TBDPS (t-butyldiphenylsilyl) ethers 46a and 46b were more efficiently separated by HPLC on silica gel (𝛼 = 1.26), and the first-eluted ether 46a was obtained as single crystals, one of which was subjected to X-ray crystallography. The ORTEP drawing of ester (−)-46a indicates that the AC of the alcohol part is R (Figure 11.30), and ether 46a was converted to alcohol (R)-(−)-42; this result also confirmed the above AC determination [27]. The OR of alcohol (R)-(−)-42 is relatively small as [𝛼]D 23 −7.64 (c 1.51, CHCl3 ) and [𝛼]D 24 −12.9 (c 0.570, EtOH). In such a case, a CD spectrum is useful for designation of the enantiomer, because CD measurement generally needs a much smaller amount of sample than [𝛼]D measurement. Figure 11.31 illustrates the CD spectrum of alcohol (R)-(−)-42, which shows a positive Cotton effect at +8 CD HO

X 10

H

CH3

+4 (R)-(–)-42

Δε ε × 10−4

in EtOH 0

obsd CD 271.2 (+0.55) 264.4 (+0.54) 257.8 (+0.33) 225.4 (+5.82)

UV −4

X 75

4 obsd UV 263.8 (500) 258.6 (500)

200

6

250

300

2

0 350

λ (nm) Figure 11.31 CD and UV spectra of (2-methylphenyl)phenylmethanol (R)-[CD(+)225.4]-(−)42. Redrawn with permission from Ref. [31].

423

11

Determination of Absolute Configurations

225.4 nm together with a weak positive Cotton effect with vibrational structure in the 1 La transition region at 240–280 nm. So, the alcohol is designated as (R)-[CD(+)225.4]-42, which indicates that the enantiomer showing positive CD at 225.4 nm has (R)-AC [31]. The next is a very interesting example, where the comparison of CD spectra leads to erroneous ACs. Racemic (2,6-dimethylphenyl)phenylmethanol 43 (Figure 11.29d) was reacted with CSDP acid yielding esters 47a and 47b, which could be efficiently separated by HPLC on silica gel (𝛼 = 1.25) despite the nonpolar substituents. From the first-eluted ester (−)-47a, enantiopure alcohol (+)-43 was obtained: [𝛼]D 27 + 139.0 (c 1.10, CHCl3 ). To determine the AC, the CD spectrum was measured as shown in Figure 11.32, which was compared with that of (2-methylphenyl)phenylmethanol (R)-[CD(+)225.4]-(−)-42 [32]. The CD spectral curve of (+)-43 is similar in shape but opposite in sign to that of (2-methylphenyl)phenylmethanol (R)-[CD(+)225.4]-(−)-42, and hence we had

HO

H

+5

CH3 (R)-(+)-43

H3C in EtOH 0 obsd CD 276.2 (−0.35) 270.4 (+0.08) 267.2 (−0.38) 260.8 (−0.26) 227.0 (−7.58)

CD

Δε

X 10

ε × 10−4

424

6

−5

UV

X 75

4 obsd UV 275.6 (300) 265.4 (500) 259.4 (500)

−10

2

0 200

250

300

350

λ (nm) Figure 11.32 CD and UV spectra of (2,6-dimethylphenyl)phenylmethanol (R)-[CD(−)227.0](+)-43. Redrawn with permission from Ref. [32].

11.7

Relative Method: X-ray Crystallography Using CSDP Acid

naturally thought that alcohol (+)-43 would have the opposite (S)-AC; however, this was incorrect, as detailed below. Later, we found that the first-eluted CSDP ester (−)-47a could be recrystallized, giving single crystals suitable for X-ray crystallography. The ORTEP drawing of ester (−)-47a clearly indicates that the alcohol part has (R)-AC as seen in Figure 11.30 [32]. These results thus indicate that comparison of CD spectra sometimes leads to erroneous ACs. The CSDP acid method was applied to 1-(2,6-dimethoxy-4-methylphenyl)-3butenol 52 to yield the first-eluted ester (−)-48a, the ORTEP drawing of which is illustrated in Figure 11.33. The AC of (−)-52 was thus unambiguously determined to be S. Similarly, the AC of 1-(4-fluorophenyl)-3-butenol (+)-53 was determined to be R, where the X-ray ORTEP drawing of CSDP ester (−)-49a was used for AC determination (Figure 11.33) [33]. We have applied the CSDP acid method to the preparation of a light-powered chiral molecular motor (2S,2′ S)-(M,M)-(E)-(−)-55A, which was synthesized from alcohol (1S,2S)-(+)-54 as shown in Figure 11.34a [34, 36]. That is, racemic alcohol 54 was esterified with CSDP acid to give a diastereomeric mixture of esters, which was separated by HPLC on silica gel (𝛼 = 1.17). The second-eluted ester (−)50b was recrystallized giving single crystals, one of which was analyzed by X-ray crystallography. The ORTEP drawing clearly indicates the AC of the alcohol part to be (1S,2S) (Figure 11.33) [34]. Starting from enantiopure alcohol (1S,2S)-(+)-54, motor molecule (2S,2′ S)(M,M)-(E)-(−)-55A was synthesized, where chiral keto-derivative was dimerized by the McMurry coupling. The chirality of the methyl group was retained during the reactions, because the final product 55A was obtained as chiral. Interestingly, motor molecules 55A–55D take twisted structures, where the helicity between naphthalene and the central double bond is designated P- or M-AC. How can we determine these helical absolute stereostructures? To determine the AC of motor molecule (−)-55A, we adopted the X-ray internal reference method, because the chirality of the methyl group is already known as shown in Figure 11.34a [34]. Recrystallization of chiral olefin (−)-55A was attempted from various solvents, but single crystals could not be obtained. However, the crystallinity of the racemate is generally different from that of the enantiomer, and hence we next attempted the recrystallization of racemic olefin (±)-55A. It was fortunate that single crystals of (±)-55A suitable for X-ray crystallography could be obtained. The obtained ORTEP drawing clearly indicates the relative stereochemistry to be (2S*,2′ S*)-(M*,M*)-(E), where the asterisk * indicates the relative stereochemistry (Figure 11.34b). From these results, the absolute stereochemistry of (−)-55A was unambiguously determined to be (2S,2′ S)-(M,M)-(E) [34]. Thus, X-ray crystallography of racemate is also useful for AC determination. The motor molecule (−)-55A undergoes photochemical and thermal reactions as shown in Figure 11.34c, where the photochemical reaction steps are reversible, but the thermal reaction steps are non-reversible [36]. Therefore, the total reaction proceeds one way, 55A → 55B → 55C → 55D → 55A, during which one of the

425

426

11

Determination of Absolute Configurations

CI CI N S O O O O

O

H OCH 3

CH3O

CH3

(S)-(–)-48a, X-ray

CI CI N S

O O

O

O

O

H

F

(R)-(–)-49a, X-ray

CI CI N S

O O

O

O

CH3

O

(1S,2S)-(–)-50b, X-ray CI CI N S O

O O

O

O

CH3

(3S,4S)-(–)-51b, X-ray HO

H OCH 3

CH3O

(S)-(–)-52

HO

H

F

CH3

(R)-(+)-53

Figure 11.33 X-ray ORTEP drawing of some CSDP esters. Redrawn with permission from Refs. [33–35].

11.7

H

HO

Relative Method: X-ray Crystallography Using CSDP Acid

CH3

CH3 H

CH3

(1S,2S)-(+)-54 X-ray

[CD(–)257.8]-(2S,2′S)(M,M)-(E)-(–)-55A

(a)

(b)

(2S*,2′S*)-(M*,M*)-(E)-(±)-55A

Δ hν H 1

CH3 H

CH3

6

CH3

8 5

hν [CD(+)279.2]-(2S,2’S)(P,P)-(Z)-55B

3

2

H

4 1 2

4

CH3 H

5 8 6

H

Δ

CH3

hν

[CD(–)257.8]-(2S,2′S)(M,M)-(E)-(−)-55A CH3

(c)

CH3 H

H

3

CH3

[CD(–)270.0]-(2S,2′S)hν (M,M)-(Z)-(−)-55C

H

[CD(+)269.0]-(2S,2′S)(P,P)-(E)-55D

Figure 11.34 (a–c) Light-powered molecular motor, rotation mechanism, and ACs. Redrawn with permission from Ref. [34].

two naphthalene moieties rotates 360∘ clockwise around the central double bond against the other naphthalene moiety. It is obvious that the rotational direction is governed by the chirality of the motor molecule. It should be emphasized that chiral molecular motor (−)-55A rotates successively clockwise by the use of light energy. In the case of molecular motor (−)-55A, the opposite AC was once assigned by another research group by comparing the CD spectrum of motor rotation isomer (−)-cis-55C with that of a related compound with known AC. However, it was incorrect, and thus the comparison of CD spectra sometimes leads to erroneous ACs here too [34]. The original light-powered molecular motor was a chiral olefin with sixmembered rings. The motor molecule was synthesized in a similar manner, where the enantiopure starting material was prepared by the CSDP acid method. The AC of CSDP ester (−)-51b was determined to be (3S,4S) by X-ray crystallography

427

428

11

Determination of Absolute Configurations

O

CI O

CI

S N

CH2O

O

CH2O

O

O

O

O O

S N

CI CI (M,M)-(+)-57b, X-ray Figure 11.35 X-ray ORTEP drawing of 1,1′ :4′ ,1′′ -ternaphthalene-2,2′′ -dimethanol bis(CSDP ester) (M,M)-(+)-57b. Redrawn with permission from Ref. [37].

as shown in Figure 11.33 [35]. The CSDP acid method is thus useful for the syntheses of enantiopure light-powered molecular motors. The preparation of enantiopure 1,1′ :4′ ,1′′ -ternaphthalene-2,2′′ -dimethanol 56 and its AC determination were carried out by using the CSDP acid method as follows (Figures 11.35 and 11.36) [37, 38]. Diastereomeric diesters 57a and 57b were baseline separated by HPLC on silica gel (𝛼 = 1.2); the second-eluted ester (+)-57b was obtained as single crystals, and the (M,M)-AC was assigned on the basis of the ORTEP drawing as shown in Figure 11.35. Reduction of diester (+)-57b with LiAlH4 furnished enantiopure diol (M,M)(+)-56, whose CD and UV spectra are shown in Figure 11.36 [38]. Ternaphthalene compound (+)-56 shows intense exciton Cotton effects in the 1 Bb transition region: 𝜆ext 231.7 nm, Δ𝜀 −333.9, and 𝜆ext 223.4 nm, Δ𝜀 +225.4; A = −559.3. The 1 B transition of naphthalene is polarized along the long axis of the chromophore, b and the dihedral angle between two naphthalene planes is about 90∘ . From these results, the (M,M)-AC with counterclockwise screw sense between the three naphthalene planes is unambiguously determined. Thus, AC determinations by X-ray crystallography and CD exciton chirality rule are naturally consistent with each other. Another important application of the CSDP acid method is the preparation of enantiopure 2-(1-naphthyl)propane-1,2-diol 1, which was isolated as a chiral metabolite of 1-isopropylnaphthalene in rabbits. To determine the AC, racemic diol (±)-1 was allowed to react with CSDP acid giving esters (−)-58a and (−)58b, which were easily separated by HPLC on silica gel (𝛼 = 1.27) (Figure 11.37) [15]. Despite many attempts at recrystallization, both CSDP esters 58a and 58b were obtained as amorphous solids, and hence X-ray crystallography could not be applied. So, the first-eluted ester (−)-58a was converted to diol (−)-1, whose AC was determined to be S by X-ray Bijvoet measurements of its 4-bromobenzoate as described in Section 11.3.

11.7

Relative Method: X-ray Crystallography Using CSDP Acid

obsd CD 285.4 (+21.9) 231.7 (–333.9) 223.4 (+225.4)

+200 CD

A = –559.3 0 Δε

ε × 10−4

CH2OH −200 CH2OH 20

−400

(M,M)-(+)-56 UV

200

obsd UV 292.8 (24000) 224.0 (186500)

250

300

λ (nm)

10

0 350

Figure 11.36 CD and UV spectra of 1,1′ :4′ ,1′′ -ternaphthalene-2,2′′ -dimethanol (M,M)-(+)-56 in 95% aqueous EtOH. Redrawn with permission from Ref. [38].

CI CI H3C

OH

OH N OH

S O

(±)-1

H3C O

O

O

(S)-(–)-58a

O

OH

OH CH3 (S)-(–)-1

Figure 11.37 Preparation of enantiopure 2-(1-naphthyl)propane-1,2-diol (S)-(−)-1.

429

430

11

Determination of Absolute Configurations

11.7.2 Application of the CSDP Acid Method to Asymmetric Reaction Products

Asymmetric reactions are very useful for the preparation of chiral compounds, but it is difficult to assign the ACs of products on the basis of reaction mechanisms. So, it is desired to determine the AC by an independent method such as X-ray crystallography of CSDP esters. In fact, the CSDP acid method has been applied to various asymmetric reaction products by other research groups (Figure 11.38). In addition, asymmetric reaction products are not always enantiopure, and hence the CSDP acid method is also useful for preparing enantiopure products. Chiral alcohol (1S,2R)-59 (90–94% ee) was synthesized by an asymmetric reaction, and its AC was determined as follows. The esterification of alcohol (1S,2R)-59 with (−)-CSDP acid yielded ester (1S,2R)-(−)-60, which was obtained as single crystals suitable for X-ray crystallography; the ACs of (−)-60 and 59 were unambiguously determined as shown from the X-ray results [39]. Alcohol (2R,3R)-(+)-61 was prepared for determining the ACs of synthetic intermediates of benzastatin E and virantmycin. A single crystal of CSDP ester (−)-62 was subjected to X-ray crystallography, which led to the (2R,3R)-AC [40]. The fluorination reaction of β-ketophosphonates catalyzed by chiral palladium complexes yielded chiral fluoro compounds. To determine the AC of a keto-product, the product was reduced to alcohol (1R,2S)-63 (94% ee), which was esterified with CSDP acid giving ester (−)-64. The (1R,2S)-AC of (−)-64 was unambiguously determined by X-ray crystallography [41]. Alcohol (2S,3R)-65 is a product of the asymmetric aldol reaction catalyzed by a chiral rhodium complex. To determine its AC, it was converted to CSDP ester (−)-66, X-ray analysis of which led to the (2S,3R)-AC [42]. Alcohol (S)-(−)-67 is a derivative of the product obtained by the chirality transfer from epoxide to carbanion. To determine its AC, the following experiments were carried out; racemic alcohol (±)-67 was esterified with (−)-CSDP acid yielding a diastereomeric mixture of esters, which was separated by chiral HPLC. However, the CSDP esters could not be obtained as single crystals. So the second-eluted CSDP ester (−)-68b was hydrolyzed to give alcohol (−)-67, from which 4-bromobenzoate (+)-69 was obtained as single crystals. The AC of (+)-69 could be determined to be S by X-ray Bijvoet method [43]. The catalytic asymmetric aldol reaction of β-ketoesters with acetals yielded chiral keto-acetal esters. Alcohol (+)-70 was obtained from the asymmetric reaction, and converted to CSDP ester (−)-71, the AC of which was determined to be (2R,3S,4S) by X-ray crystallography [44]. Alcohol (2R,3R,4S)-72 is a product of the stereoselective reductive aldol reaction catalyzed by a chiral rhodium complex. To determine its AC, it was converted to CSDP ester (−)-73, the X-ray analysis of which led to the (2R,3R,4S)-AC [45]. Chiral glycol 74 was derived from the product of an asymmetric reaction, and its (R)-AC was determined by X-ray crystallography of bis(CSDP) ester 75 [46]. Similarly, to determine the AC of chiral compound 76, it was converted to alcohol 77, CSDP ester of which was obtained as single crystals. The (R) AC of ester 78

11.7

OR

Relative Method: X-ray Crystallography Using CSDP Acid

H N

OR

CI (1S,2R)-59, R = H (2R,3R)-(+)-61, R = H (1S,2R)-(–)-60, R = CSDP (2R,3R)-(–)-62, R = CSDP O H OR

O

RO

P(OEt)2 F

NO2

(1R,2S)-63, R = H (1R,2S)-(–)-64, R = CSDP

(2S,3R)-65, R = H (2S,3R)-(–)-66, R = CSDP

HO RO

OCH2Ph

RO N(i-Pr)2

HN

O (S)-(–)-67, R = H (S)-(–)-68b, R = CSDP (S)-(+)-69, R = 4-Br-Bz

COO-t-Bu (2R,3S,4S)-(+)-70, R = H (2R,3S,4S)-(–)-71, R = CSDP

OR COO-t-Bu

OR

OR (2R,3R,4S)-72, R = H (2R,3R,4S)-(–)-73, R = CSDP

O

(R)-74, R = H (R)-75, R = CSDP OR

O

O

O (R)-77, R = H (R)-78, R = CSDP

(R)-76

H N N

OCH3

3

2 R O H 79, R = COOCH3 (2S,3S)-80, R = CH2O-CSDP

Figure 11.38 Applications of the CSDP acid method to AC determination of asymmetric reaction products by X-ray crystallography.

431

432

11

Determination of Absolute Configurations

was unambiguously determined by X-ray crystallography. Therefore, the AC of 76 was assigned to be S [46]. Methyl ester 79 is a product of the chiral-acid-catalyzed addition reaction. To determine its AC, ester 79 was reduced to a primary alcohol, which was esterified with CSDP acid yielding ester 80 as single crystals. X-ray crystallographic analysis led to the relative and absolute configurations of compounds 79 and 80 as shown [47]. 11.8 Relative Method: X-ray Crystallography Using of M𝛂NP Group as Internal Reference

MαNP esters have a great advantage that they have a high probability of affording single crystals suitable for X-ray crystallography. MαNP esters contain no heavy atoms, but their ACs can be unambiguously determined from the X-ray ORTEP drawings, because the MαNP acid part can be used as an internal reference for AC. Therefore, the MαNP acid method leads to straightforward and unambiguous AC determination. So, the remaining problem is how to get single crystals. It should be noted that although the 1 H NMR diamagnetic anisotropy method using MαNP esters is an empirical rule, their ACs can be confirmed by X-ray crystallography. Both methods are based on totally different physical phenomena, but they should give the same conclusions. Interestingly, we have never encountered any exceptional case, where 1 H NMR and X-ray methods disagreed with each other. This is a very important fact to validate the empirical 1 H NMR anisotropy method. 11.8.1 Alternative Preparation of Enantiopure M𝛂NP Acid

Enantiopure MαNP acid (S)-(+)-11 was previously synthesized via diol (S)-(−)-1 as summarized in Figures 11.14 and 11.37. However, to use as a chiral auxiliary, a more efficient method had to be developed. So, we decided to enantioresolve racemic MαNP acid (±)-11 by HPLC. In general, for enantioresolution of carboxylic acids, chiral synthetic amines or alkaloids have been used. However, we adopted the following unique strategy to use chiral alcohols as a chiral auxiliary (Figure 11.39). O CH3O

(±)-11

OH

CH3O

O

O O

(S;1R,3R,4S)-(–)-81a

CH3O

(S)-(+)-11

Figure 11.39 Preparation of enantiopure MαNP acid (S)-(+)-11 [24].

OH

11.8

Relative Method: X-ray Crystallography Using MαNP Acid

O CH3O O

(R;1R,3R,4S)-(–)-81b, X-ray

Figure 11.40 The X-ray ORTEP drawing of (R;1R,3R,4S)-(−)-81b. Redrawn with permission from Ref. [48].

As a chiral alcohol, natural (1R,3R,4S)-(−)-menthol was selected and esterified with racemic acid (±)-11. It was splendid that diastereomeric esters 81a and 81b were largely separated by HPLC on silica gel (hexane/EtOAc = 10 : 1), (𝛼 = 1.83). Such a large separation enabled a preparative scale HPLC: esters 81a/81b (1.0–1.8 g) could be separated in one run using a glass column of silica gel (25𝜙 × 400 mm) [24]. The first-eluted ester (−)-81a was subjected to hydrolysis to yield chiral acid (S)-(+)-11, while the second-eluted ester (−)-81b gave acid (R)-(−)-11. Their ACs were confirmed by comparison of the CD spectra of methyl ester with that of the authentic sample prepared by the procedure summarized in Figures 11.14 and 11.37. Both esters 81a and 81b were obtained as amorphous solids. However, later we succeeded in obtaining single crystals of MαNP ester (−)-81b, one of which was analyzed by X-ray crystallography to give the ORTEP drawing as shown in Figure 11.40, where the menthol moiety was used as an internal reference for AC [48]. Thus, the ACs of MαNP acid (S)-(+)-11 was confirmed, and the result is naturally consistent with the previous AC assignment of 4-bromobenzoate (S)(−)-2 carried out by the Bijvoet method (Figure 11.2). 11.8.2 AC Determination of Other M𝛂NP Esters by X-ray Crystallography

As described above, X-ray method using MαNP ester is very useful for AC determination, and we have been able to determine the ACs of various chiral compounds by X-ray crystallography of MαNP esters as shown in Figures 11.41–11.44. Acyclic alcohol MαNP ester (+)-82b was obtained as single crystals from the second-eluted diastereomer by HPLC. From the X-ray ORTEP drawing, the AC of the alcohol part was clearly determined to be R. Acetylene alcohol MαNP ester (+)-83a was similarly obtained as single crystals, one of which was subjected to X-ray crystallography. The ORTEP drawing clearly indicates the (S;S)-AC, where the first S indicates the AC of the MαNP acid part and the second S does that of the alcohol part [48].

433

434

11

Determination of Absolute Configurations

O

O CH3O

O

H

(S;R)-(+)-82b

O CH3O

O

H

(S;S)-(+)-83a

O CH3O

O H

(S;1R,2R)-(–)-84a

O CH3O

O H

(S;1R,2R)-(–)-85a

Figure 11.41 AC determination of acyclic and cyclic aliphatic alcohol MαNP esters by X-ray crystallography. Redrawn with permission from Ref. [48].

11.8

O CH3O

Relative Method: X-ray Crystallography Using MαNP Acid

H O O

(S;1R,8aS)-(+)-86a

CH3O

O H O OSi

(S;1R,6R,8aR)-(–)-87a

Figure 11.42 AC determination of Wieland–Mischer ketone derivative/MαNP esters by X-ray crystallography. Redrawn with permission from Ref. [48].

Cyclic aliphatic alcohol MαNP ester (−)-84a was obtained as single crystals, whose X-ray ORTEP drawing indicated the (S;1R,2R)-AC, which agreed with that previously assigned by the 1 H NMR anisotropy method. The AC of MαNP ester (−)-85a was similarly determined to be (S;1R,2S) [48]. It should be noted that relative configurations are also directly confirmed by X-ray crystallographic analyses. The Wieland–Mischer ketone has been used as a chiral starting material for the syntheses of various natural products, and therefore, the practical preparation of enantiopure derivative was desired. As one of such preparations, we have applied the MαNP acid method to its derivatives. For example, MαNP ester 86a was obtained as single crystals. The X-ray ORTEP drawing clearly indicated (S;1S,8aS)-AC of (+)-86a, which confirmed the AC previously assigned by 1 H NMR anisotropy method (Figure 11.42) [48]. It should be emphasized that t-butyldimethylsilyl (TBDM) ether MαNP esters 87a and 87b were very efficiently separated by HPLC on silica gel (𝛼 = 1.80), and hence this large separation is useful for the preparation of enantiopure Wieland–Mischer ketone on a large scale. The first-eluted ester (−)-87a was

435

436

11

Determination of Absolute Configurations

H

O CH3O

O F

(R;R)-(+)-88

O CH3O

O

OH

(S;R)-(+)-89b

O H CH3O

O

(S;S)-(+)-90a

O CH3O

O

H H3C

(S;R)-(–)-91a

Figure 11.43 AC determination of aromatic alcohol MαNP esters by X-ray crystallography. Redrawn with permission from Ref. [48, 49].

11.8

O CH3O

Relative Method: X-ray Crystallography Using MαNP Acid

H O

19

17

(S;19R)-(–)-93b

H HO (S;19S)-(–)-93a

(S)-(–)-92 Figure 11.44 X-ray ORTEP drawing of 17-octatriacontyn-19-ol MαNP ester (S;19R)-(−)-93b and preparation of enantiopure alcohol (S)-(−)-92. Redrawn with permission from Ref. [50].

recrystallized giving single crystals, one of which was subjected to X-ray crystallography. From the ORTEP drawing in Figure 11.42, the (S;1R,6R,8aR)-AC of ester (−)-87a was unambiguously determined, which was consistent with the results obtained by the 1 H NMR anisotropy method. Although the TBDM group takes a disordered structure as shown, unambiguous AC determination was possible, because the relative configuration was clearly obtained [48]. Chiral benzene-methanol derivative MαNP ester (R;R)-(+)-88 was recrystallized giving single crystals, and its X-ray ORTEP drawing is illustrated in Figure 11.43. It should be noted that in this ester, (R)-MαNP was used and hence the AC of the alcohol part was determined as shown [48]. In the case of chiral benzene-ethanol derivative MαNP ester (S;R)-(+)-89b, the X-ray ORTEP drawing clearly shows the difference between methyl and hydroxyl groups. So, the AC of the alcohol part was determined as shown in Figure 11.43 [48]. The AC of 1,2,3,4-tetrahydro-4-phenanthrenol MαNP ester (S;S)-(+)-90a was determined by X-ray crystallography as shown in Figure 11.43 [49]. Interestingly, this X-ray analysis was the first example to show that the crystalline state conformation of MαNP ester takes a similar conformation in solution, which was used for the 1 H NMR anisotropy method as shown in Figures 11.14 and 11.15. The next example shows how the MαNP acid method is powerful for enantioresolving racemic alcohols by HPLC separation of diastereomeric esters and also for determining their ACs by X-ray crystallography. The mixture of (2-methylphenyl)phenylmethanol MαNP esters (S;R)-(−)-91a and (S;S)-(−)-91b

437

438

11

Determination of Absolute Configurations

was baseline separated by HPLC on silica gel (𝛼 = 1.12). Remember that the corresponding CSDP esters could not be separated, and therefore, an indirect method was adopted as shown in Figure 11.29. In addition, both diastereomeric MαNP esters 91a and 91b gave single crystals suitable for X-ray crystallography. From their ORTEP drawings, ACs were unambiguously determined as exemplified in Figure 11.43, and of course, these results were consistent with the previous AC determinations by 1 H NMR anisotropy method and by X-ray crystallography (Figures 11.29 and 11.30) [48]. Surprisingly, the MαNP acid method could be applied to long-chain acetylene alcohols such as 17-octatriacontyn-19-ol 92, whose diastereomeric MαNP esters (S;19S)-(−)-93a and (S;19R)-(−)-93b were largely separated by HPLC on silica gel (𝛼 = 1.78). To determine the ACs of these MαNP esters by X-ray crystallography, we attempted recrystallizations from various solvents, and finally got thin-plate single crystals of (−)-93b from iso-PrOH. However, they are extremely thin with 5 μm thickness, and so the X-ray diffraction experiment was carried out by using the strong X-ray of synchrotron radiation at SPring-8, Japan. The (S;19R)-AC of (−)-93b was determined from the ORTEP drawing (Figure 11.44), which was consistent with the results obtained by 1 H NMR anisotropy method. From the firsteluted ester (S;19S)-(−)-93a, enantiopure 17-octatriacontyn-19-ol (S)-(−)-92 was prepared [50].

11.9 Conclusion

In this chapter, the principles, practices, and reliability of various methods for determining ACs of chiral compounds are discussed using mostly our own data, where the X-ray crystallographic Bijvoet method, ECD exciton chirality rule, VCD with DFT MO calculation, 1 H NMR diamagnetic anisotropy, and X-ray crystallography using an internal reference for AC are highlighted. In the history of AC determination, there were many cases where ACs were erroneously assigned and later revised by other methods. Therefore, it is important to select a suitable method and to carry out reliable AC determination by understanding the principle and mechanism of the methods. Chiral auxiliaries, MαNP and CSDP acids, are very powerful for AC determination by 1 H NMR anisotropy method and/or X-ray crystallography, where the chirality of these acids is used as an internal reference. X-ray crystallography using an internal reference is straightforward and hence the AC can be unambiguously determined. In addition, MαNP and CSDP acid methods are very useful for the preparation of enantiopure compounds. Chiral reagents, (1S,2R,4R)-(−)-CSDP, (R)-(−)-MαNP, and (S)-(+)-MαNP acids, are commercially available from TCI (http://www.tciamerica.com/ or http://www.tcieurope.eu/). It would be a great pleasure for the author if this review is helpful for the readers’ research.

References

11.A.1 Appendix Table 11.A.1 Bijvoet pairs of (S)-(−)-2-(1-naphthyl)propane-1,2-diol 1-p-bromobenzoate (2): observed and calculated absolute values of the structural factors for (h,k,l) and (h,k,−l) reflections, and their ratios.a),b) h

k

l

|Fo(h,k,l)| [|Fc(h,k,l)|]

|Fo(h,k,–l)| [|Fc(h,k,–l)|]

|Fo(h,k,l)|/|Fo(h,k,–l)| [|Fc(h,k,l)|/|Fc(h,k,–l)|]

1 1 2 4 5 2 4 5 1 2 2 2 3 5 2 2 7 4

4 5 8 1 5 1 4 6 3 1 3 5 7 4 1 10 5 4

1 1 1 1 1 2 2 2 3 3 3 3 3 3 4 3 3 4

39.4 [35.4] 39.3 [37.7] 78.4 [74.1] 102.6 [91.1] 10.1 [11.3] 162.2 [154.3] 83.0 [81.0] 71.0 [68.1] 76.0 [74.9] 75.8 [72.8] 89.7 [86.5] 80.9 [77.3] 66.8 [63.6] 40.0 [40.1] 104.6 [99.5] 49.4 [49.7] 42.2 [40.9] 80.9 [75.5]

32.1 [27.9] 46.2 [42.2] 73.8 [68.4] 92.8 [84.6] 20.2 [19.0] 149.3 [143.6] 90.7 [87.6] 66.4 [62.6] 83.6 [79.6] 69.5 [66.6] 99.6 [94.5] 73.8 [69.4] 73.2 [69.1] 46.4 [45.6] 98.0 [92.6] 45.0 [43.7] 36.3 [35.3] 87.0 [80.7]

1.23 [1.26] 0.85 [0.89] 1.06 [1.08] 1.11 [1.08] 0.50 [0.59] 1.09 [1.07] 0.92 [0.92] 1.07 [1.09] 0.91 [0.94] 1.09 [1.09] 0.90 [0.90] 1.10 [1.11] 0.91 [0.92] 0.86 [0.88] 1.07 [1.07] 1.10 [1.07] 1.16 [1.16] 0.93 [0.94]

Reflections satisfying ||Fo(h,k,l)| − |Fo(h,k,nl)|| > 10 𝜎(Fo) were selected, where 𝜎(Fo) = [𝜎(count)2 + (0.007 |Fo|)2 ]0.5 . b) Cu-Kα X-ray was used. Reprinted with permission from Ref. [15]. a)

Acknowledgments

The author thanks all the coworkers for their efforts and cooperation, whose names are listed in the references cited. He also thanks Dr George A. Ellestad, Department of Chemistry, Columbia University, for valuable suggestions. Our research work described here was supported by grants from the Ministry of Education, Science, Sports, Culture, and Technology, Japan and/or the Japan Society for the Promotion of Science. References 1. Bijvoet, J.M., Peerdeman, A.F., and van

Bommel, A.J. (1951) Determination of the absolute configuration of optically active compounds by means of X-rays. Nature, 168, 271–272.

2. Flack, H.D. (1983) On enantiomorph-

polarity estimation. Acta Crystallogr., A39, 876–881. 3. Harada, N. and Nakanishi, K. (1983) Circular Dichroic Spectroscopy – Exciton

439

440

11

4.

5.

6.

7.

8.

Determination of Absolute Configurations

Coupling in Organic Stereochemistry, University Science Books, Mill Valley, CA, and Oxford University Press, Oxford. Harada, N., Nakanishi, K., and Berova, N. (2012) in Comprehensive Chiroptical Spectroscopy, vol. 2, Chapter 4 (eds N. Berova, P. Polavarapu, K. Nakanishi, and R.W. Woody), John Wiley & Sons, Inc., pp. 115–166. Harada, N. and Kuwahara, S. (2012) in Comprehensive Chiroptical Spectroscopy, vol. 2, Chapter 5 (eds N. Berova, P. Polavarapu, K. Nakanishi, and R.W. Woody), John Wiley & Sons, Inc, pp. 167–215. Goerigk, L., Kruse, H., and Grimme, S. (2012) in Comprehensive Chiroptical Spectroscopy, vol. 1, Chapter 22 (eds N. Berova, P. Polavarapu, K. Nakanishi, and R.W. Woody), John Wiley & Sons, Inc., pp. 643–673. Polavarapu, P. (2012) in Comprehensive Chiroptical Spectroscopy, vol. 2, Chapter 11 (eds N. Berova, P. Polavarapu, K. Nakanishi, and R.W. Woody), John Wiley & Sons, Inc., pp. 387–420. Frisch, M.J., Trucks, G.W., Schlegel, H.B., Scuseria, G.E., Robb, M.A., Cheeseman, J.R., Montgomery, J.A., Vreven, T., Kudin, K.N., Burant, J.C., Millam, J.M., Iyengar, S.S., Tomasi, J., Barone, V., Mennucci, B., Cossi, M., Scalmani, G., Rega, N., Petersson, G.A., Nakatsuji, H., Hada, M., Ehara, M., Toyota, K., Fukuda, R., Hasegawa, J., Ishida, M., Nakajima, T., Honda, Y., Kitao, O., Nakai, H., Klene, M., Li, X., Knox, J.E., Hratchian, H.P., Cross, J.B., Adamo, C., Jaramillo, J., Gomperts, R., Stratmann, R.E., Yazyev, O., Austin, A.J., Cammi, R., Pomelli, C., Ochterski, J.W., Ayala, P.Y., Morokuma, K., Voth, G.A., Salvador, P., Dannenberg, J.J., Zakrzewski, V.G., Dapprich, S., Daniels, A.D., Strain, M.C., Farkas, O., Malick, D.K., Rabuck, A.D., Raghavachari, K., Foresman, J.B., Ortiz, J.V., Cui, Q., Baboul, A.G., Clifford, S., Cioslowski, J., Stefanov, B.B., Liu, G., Liashenko, A., Piskorz, P., Komaromi, I., Martin, R.L., Fox, D.J., Keith, T., Al-Laham, M.A., Peng, C.Y., Nanayakkara, A., Challacombe, M., Gill, P.M.W., Johnson, B., Chen, W.,

9.

10.

11.

12.

13.

14.

15.

16.

17.

Wong, M.W., Gonzalez, C., and Pople, J.A. (2004) Gaussian 03, Revision C.02, Gaussian, Inc., Wallingford, CT. Harada, N. (2008) Determination of absolute configurations by X-ray crystallography and 1 H NMR anisotropy. Chirality, 20, 691–723. Harada, N. (2006) in Chirality in Drug Research, Chapter 9 (eds E. Francotte and W. Lindner), Wiley-VCH Verlag GmbH, Weinheim, pp. 283–321. Harada, N., Watanabe, M., and Kuwahara, S. (2006) in Chiral Analysis, Chapter 18 (eds K.W. Busch and M.A. Busch), Elsevier Science Publishers, Amsterdam, pp. 661–691. Dale, J.A. and Mosher, H.S. (1973) Nuclear magnetic resonance enantiomer reagents. Configurational correlations via nuclear magnetic resonance chemical shifts of diastereomeric mandelate, O-methylmandelate, and α-methoxy-αtrifluoromethylphenylacetate (MTPA) esters. J. Am. Chem. Soc., 95, 512–519. Ohtani, I., Kusumi, T., Kashman, Y., and Kakisawa, H. (1991) High-field FT NMR application of Mosher’s method. The absolute configurations of marine terpenoids. J. Am. Chem. Soc., 113, 4092–4096. Seco, J.M., Quinoa, E., and Riguera, R. (2004) The assignment of absolute configuration by NMR. Chem. Rev., 104, 17–117. Kuwahara, S., Fujita, K., Watanabe, M., Harada, N., and Ishida, T. (1999) Enantioresolution and absolute stereochemistry of 2-(1-naphthyl)propane-1,2-diol and related compounds. Enantiomer, 4, 141–145. Harada, N., Takuma, Y., and Uda, H. (1976) The absolute stereochemistries of 6,l5-dihydro-6,l5-ethanonaphtho[2,3c]pentaphene and related homologues as determined by both exciton chirality and X-ray Bijvoet methods. J. Am. Chem. Soc., 98, 5408–5409. Harada, N., Saito, A., Ono, H., Murai, S., Li, H.-Y., Gawronski, J., Gawronska, K., Sugioka, T., and Uda, H. (1996) A CD method for determination of the absolute stereochemistry of acyclic glycols.

References

18.

19.

20.

21.

22.

23.

24.

2. application of the CD exciton chirality method to acyclic 1,2-dibenzoates systems. Enantiomer, 1, 119–138. Harada, N., Li, H.Y., Koumura, N., Abe, T., Watanabe, M., and Hagiwara, M. (1997) NMR 13 C satellite signals useful for the first-order analysis of complex spin systems. Enantiomer, 2, 349–352. Naito, J., Yamamoto, Y., Akagi, M., Sekiguchi, S., Watanabe, M., and Harada, N. (2005) Unambiguous determination of the absolute configurations of acetylene alcohols by combination of the Sonogashira reaction and the CD exciton chirality method – exciton coupling between phenylacetylene and benzoate chromophores. Monatsh. Chem., 136, 411–445. Kuwahara, S., Obata, K., Fujita, T., Miura, N., Nakahashi, A., Monde, K., and Harada, N. (2010) (R)-(+)[VCD(–)984]-4-Ethyl-4-methyloctane, a cryptochiral hydrocarbon with a quaternary chirality center. (2) vibrational CD spectra of both enantiomers and absolute configurational assignment. Eur. J. Org. Chem., 2010, 6385–6392. Kasai, Y., Sugio, A., Sekiguchi, S., Kuwahara, S., Matsumoto, T., Watanabe, M., Ichikawa, A., and Harada, N. (2007) Conformational analysis of MαNP esters, powerful chiral resolution and 1 H NMR anisotropy tools – aromatic geometry and solvent effects on 𝛥𝛿 values. Eur. J. Org. Chem., 2007, 1811–1826. Taji, H., Kasai, Y., Sugio, A., Kuwahara, S., Watanabe, M., Harada, N., and Ichikawa, A. (2002) Practical enantioresolution of alcohols with 2-methoxy2-(1-naphthyl)propionic acid and determination of their absolute configurations by the 1 H NMR anisotropy method. Chirality, 14, 81–84. Taji, H., Watanabe, M., Harada, N., Naoki, H., and Ueda, Y. (2002) Diastereomer method for determining % ee by 1 H NMR and/or MS spectrometry with complete removal of the kinetic resolution effect. Org. Lett., 4, 2699–2702. Kasai, Y., Taji, H., Fujita, T., Yamamoto, Y., Akagi, M., Sugio, A., Kuwahara, S., Watanabe, M., Harada, N., Ichikawa, A., and Schurig, V. (2004) MαNP acid, a powerful chiral molecular tool for

25.

26.

27.

28.

29.

30.

31.

preparation of enantiopure alcohols by resolution and determination of their absolute configurations by the 1 H NMR anisotropy method. Chirality, 16, 569–585. Fujita, T., Obata, K., Kuwahara, S., Miura, M., Nakahashi, A., Monde, K., Decatur, J., and Harada, N. (2007) (R)-(+)-[VCD(+)945]-4-Ethyl-4methyloctane, the simplest chiral saturated hydrocarbon with a quaternary stereogenic center. Tetrahedron Lett., 48, 4219–4222. Fujita, T., Obata, K., Kuwahara, S., Nakahashi, A., Monde, K., Decatur, J., and Harada, N. (2010) (R)-(+)[VCD(–)984]-4-Ethyl-4-methyloctane, a cryptochiral hydrocarbon with a quaternary chirality center. (1) synthesis of enantiopure compound and unambiguous determination of absolute configuration. Eur. J. Org. Chem., 2010, 6372–6384. Kuwahara, S., Watanabe, M., Harada, N., Koizumi, M., and Ohkuma, T. (2000) Enantioresolution and absolute stereochemistry of o-substituted diphenylmethanols. Enantiomer, 5, 109–114. Kosaka, M., Sugito, T., Kasai, Y., Kuwahara, S., Watanabe, M., Harada, N., Job, G.E., Shvet, A., and Pirkle, W.H. (2003) Enantioresolution and absolute configurations of chiral meta-substituted diphenylmethanols as determined by the X-ray crystallographic and 1 H NMR anisotropy methods. Chirality, 15, 324–328. Harada, N., Fujita, K., and Watanabe, M. (1997) Enantioresolution and absolute stereochemistry of diarylmethanols. Enantiomer, 2, 359–366. Naito, J., Kosaka, M., Sugito, T., Watanabe, M., Harada, N., and Pirkle, W.H. (2004) Enantioresolution of fluorinated diphenylmethanols and determination of their absolute configurations by X-ray crystallographic and 1 H NMR anisotropy methods. Chirality, 16, 22–35. Watanabe, M., Kuwahara, S., Harada, N., Koizumi, M., and Ohkuma, T. (1999) Enantioresolution by the chiral phthalic acid method: absolute configurations

441

442

11

32.

33.

34.

35.

36.

37.

38.

39.

Determination of Absolute Configurations

of (2-methylphenyl)phenylmethanol and related compounds. Tetrahedron: Asymmetry, 10, 2075–2078. Kosaka, M., Kuwahara, S., Watanabe, M., Harada, N., Job, G.E., and Pirkle, W.H. (2002) Comparison of CD spectra of (2-methylphenyl)- and (2,6dimethylphenyl)-phenylmethanols leads to erroneous absolute configurations. Enantiomer, 7, 213–218. Kosaka, M., Watanabe, M., and Harada, N. (2000) Enantioresolution by the chiral phthalic acid method: absolute configurations of substituted benzylic alcohols. Chirality, 12, 362–365. Fujita, T., Kuwahara, S., and Harada, N. (2005) A new model of light powered chiral molecular motor with higher speed of rotation (1). Synthesis and absolute stereostructure. Eur. J. Org. Chem., 2005, 4533–4543. Harada, N., Koumura, N., and Feringa, B.L. (1997) Chemistry of unique chiral olefins. 3. Synthesis and absolute stereochemistry of trans- and cis-1,1′ ,2,2′ ,3,3′ ,4,4′ -octahydro-3,3′ dimethyl-4,4′ -biphenanthrylidenes. J. Am. Chem. Soc., 119, 7256–7264. Kuwahara, S., Fujita, T., and Harada, N. (2005) A new model of light powered chiral molecular motor with higher speed of rotation (2). Dynamics of motor rotation. Eur. J. Org. Chem., 2005, 4544–4556. Harada, N., Vassilev, V.P., and Hiyoshi, N. (1997) Absolute configuration and conformation of 1,1′ :4′ ,1′′ ternaphthalene compounds as determined by X-ray crystallography. Enantiomer, 2, 123–126. Harada, N., Hiyoshi, N., Vassilev, V.P., and Hayashi, T. (1997) Synthesis, circular dichroism, and absolute stereochemistry of 1,1′ :4′ ,1′′ -ternaphthalene compounds. Chirality, 9, 623–625. Bertozzi, F., Pineschi, M., Macchia, F., Arnold, L.A., Minnaard, A.J., and Feringa, B.L. (2002) Copper phosphoramidite catalyzed enantioselective ring-opening of oxabicyclic alkenes: remarkable reversal of stereocontrol. Org. Lett., 4, 2703–2705.

40. Ori, M., Toda, N., Takami, K., Tago,

41.

42.

43.

44.

45.

46.

47.

48.

K., and Kogen, H. (2005) Stereospecific synthesis of 2,2,3-trisubstituted tetrahydroquinolines: application to the total syntheses of benzastatin E and natural virantmycin. Tetrahedron, 61, 2075–2104. Hamashima, Y., Suzuki, T., Takano, H., Shimura, Y., Tsuchiya, Y., Moriya, K., Goto, T., and Sodeoka, M. (2006) Highly enantioselective fluorination reactions of β-ketoesters and β-ketophosphonates catalyzed by chiral palladium complexes. Tetrahedron, 62, 7168–7179. Inoue, H., Kikuchi, M., Ito, J., and Nishiyama, H. (2008) Chiral Phebox–rhodium complexes as catalysts for asymmetric direct aldol reaction. Tetrahedron, 64, 493–499. Sasaki, M., Kawanishi, E., Shirakawa, Y., Kawahata, M., Masu, H., Yamaguchi, K., and Takeda, K. (2008) Chirality transfer from epoxide to carbanion: base-induced alkylation of O-carbamoyl cyanohydrins of β-silyl-α,β-epoxy aldehyde. Eur. J. Org. Chem., 2008, 3061–3064. Umebayashi, N., Hamashima, Y., Hashizume, D., and Sodeoka, M. (2008) Catalytic enantioselective aldol-type reaction of β-ketosters with acetals. Angew. Chem. Int. Ed., 47, 4196–4199. Hashimoto, T., Ito, J., and Nishiyama, H. (2008) Felkin–Anh selectivity in Rh(bisoxazolinylphenyl)-catalyzed reductive aldol coupling reaction: asymmetric synthesis of stereotriads. Tetrahedron, 64, 9408–9412. Miyata, K., Kutsuna, H., Kawakami, S., and Kitamura, M. (2011) A chiral bidentate sp2 -N ligand, naph-diPIM: application to cpRu-catalyzed asymmetric dehydrative C-, N-, and O-allylation. Angew. Chem. Int. Ed., 50, 4649–4653. Terada, M., Moriya, K., Kanomata, K., and Sorimachi, K. (2011) Chiral Brønsted acid catalyzed stereoselective addition of azlactones to 3-vinylindoles for facile access to enantioenriched tryptophan derivatives. Angew. Chem. Int. Ed., 50, 12586–12590. Kuwahara, S., Naito, J., Yamamoto, Y., Kasai, Y., Fujita, T., Noro, K., Shimanuki, K., Akagi, M., Watanabe, M., Matsumoto, T., Watanabe, M., Ichikawa,

References

A., and Harada, N. (2007) Crystalline state conformational analysis of MαNP esters, powerful resolution and chiral 1 H NMR anisotropy tools. Eur. J. Org. Chem., 2007, 1827–1840. 49. Fujita, T., Kuwahara, S., Watanabe, M., and Harada, N. (2002) Crystalline state conformation of 2-methoxy2-(1-naphthyl)propionic acid ester. Enantiomer, 7, 219–223.

50. Sekiguchi, S., Akagi, M., Naito, J.,

Yamamoto, Y., Taji, H., Kuwahara, S., Watanabe, M., Ozawa, Y., Toriumi, K., and Harada, N. (2008) Synthesis of enantiopure aliphatic acetylene alcohols and determination of their absolute configurations by 1 H NMR anisotropy and/or X-ray crystallography. Eur. J. Org. Chem., 2008, 2313–2324.

443

445

12 An Integrated Approach to Structure Verification Using Automated Procedures Juan Carlos Cobas Gómez, Michael Bernstein, and Stanislav S´ykora

12.1 Introduction 12.1.1 Setting the Scene: The Need for an Automatic Structure Verification (ASV) Platform

Since the first measurement of nuclear magnetic moments by Rabi in 1938 [1] and the subsequent first experimental evidences of NMR in bulk matter observed independently and nearly simultaneously by Purcell [2] and Bloch [3] in late 1945, followed by the prompt discovery that the measured frequencies were sensitive to their chemical environments [4, 5], NMR has experienced immense advances, both in instrumentation and methodology in such a way that it is now considered one of the most powerful analytical tools with a wide range of applications in chemistry, physics, and medicine. Long gone are the days when molecular structure determination was effectively considered an art based mostly on the power of painstaking chemical transformations (i.e., degradation or derivatization processes or total chemical synthesis). Spectroscopic methods – of which NMR is one of the most vital players – now have almost entirely replaced those old “wet chemistry”-based approaches and the art has become a science. However, it remains the case that the vast majority of full NMR assignments are still performed by a skilled, human operator. However, despite outstanding improvements in the analytical techniques to isolate and characterize molecules, mistakes are still a relatively common occurrence as pointed out by Nicolaou and Snyder in 2005 [6]. They concluded that well over 1000 articles containing incorrectly assigned structures were published overall for the period of January 1990 to March 2004. A somewhat astonishing recent example of incorrect structure determination was the case in which the structure of a reported natural product isolate was incorrectly assigned to a binaphthalenetetrol derivative (1) [7] instead of the correct tetrabrominated diphenyl ether (2) [8] (Scheme 12.1). Another example is the infamous bosutinib fiasco [9]. Bosutinib is a tyrosine kinase inhibitor undergoing research for use in the treatment of chronic myeloid Structure Elucidation in Organic Chemistry: The Search for the Right Tools, First Edition. Edited by María-Magdalena Cid and Jorge Bravo. © 2015 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2015 by Wiley-VCH Verlag GmbH & Co. KGaA.

446

12

An Integrated Approach to Structure Verification Using Automated Procedures

OH HO

OH O

OMe OMe

Br

Br

Br Br

HO OH 1

2

Scheme 12.1 (1) Original reported natural product and (2) revised structure.

leukemia and is also being used as a research tool in a number of academic groups. However, it turned out that these groups were not working with the molecule they thought they were using. Instead of being a 2,4-dichloro-5-methoxy derivative, many commercial samples appear to be 3,5-dichloro-4-methoxy derivatives, as first noticed by inspection of an X-ray structure deposited in the Protein Data Bank by Stefan Knapp, Frank von Delft, and coworkers at England’s Oxford University. The differences between these two isomers are, from a spectroscopist standpoint, more subtle than in the previous example: both compounds would produce the same mass ion, but even though the 1 H-NMR spectra of both compounds would be expected to be very similar, the C 2 symmetry of the aniline ring in the bosutinib isomer should be a clear giveaway that something is wrong with the purported structure (Scheme 12.2). N

N N

N

N

O Cl

N

N

O O

NH

Cl

O O

N

NH

O

Cl

Cl (a)

Bosutinib

(b)

Bosutinib isomer

Scheme 12.2 The incorrect structure of bosutinib (a) would be expected to have significant differences from the correct structural isomer (b) because of the symmetry of the aniline ring.

On the other hand, tremendous advancements on both technological and methodological fronts have made possible the acquisition of enormous volumes of data. Presently, open access NMR laboratories probably outnumber traditional NMR laboratory measurements by the synthetic chemist both in industry and in academic service laboratories. This enormous information growth in

12.1

Introduction

collected data has the potential to outpace our capabilities to process and analyze them, thereby hindering the fundamental ability to translate information into knowledge. IBM has estimated that 2.5 quintibillion bytes of data are being generated each day, more than 90% of which has been created in the last 2 years. It is difficult to scale this level of information into analytical data, but it is quite likely that they also follow a similar growth. This enormous increase in analytical data has followed an opposite path to analytical human resources and this poses new challenges, such as the consequences of deducing incorrect structural integrity from the data. In this sense, a large pharmaceutical company may acquire in the order of >105 1 H-NMR spectra per year. Considering current skilled human analytical resources, a manual validation analysis of all these spectra would be virtually impossible and some compromises must therefore ensue. Time pressures and a trend toward basic analytical services that are not run by trained experts are increasingly the norm. A certain level of responsibility for structural proof can be placed on the synthetic chemist, but there are cases of high-throughput chemistry and automated synthesis that make this impractical. So the analytical question becomes, “out of all these automatically generated spectra, is there a way to restrict the analysis to a sensible number that then is amenable to manual analysis by experts in spectrum assignment?” Ultimately, we would like to have a fully automatic structure verification system ASV, which, given a molecule and its corresponding analytical data (i.e., NMR spectra), will tell us correctly 100% of the time whether a molecule is consistent with the experimental evidence. Even so, one would have to bear in mind that, taking into account the unavoidable experimental noise and other artifacts, the same spectrum might be compatible with different molecules and, considering the specific conditions in which the spectra are taken, the same molecule might give somewhat different spectra. A 100% “certain” ASV system is therefore an idealization, and in real life any such test will produce false positives (FPs) and false negatives (FNs). If we consider a hypothetical ASV system, we could reasonably assume for the sake of this argument that if a molecule is actually correct, this test will incorrectly claim that it is wrong only about 10% of the time (i.e., 10% of FNs). On the other hand, if the molecule is actually incorrect, this test will detect it about 80% of the time (i.e., 20% of FPs). Now suppose we apply this test to a molecule and it tells us that it is correct; what is the probability that this molecule is actually correct? If we consider just the statistics we have used so far, the answer could be 80%. However, in this analysis we are not exploiting the prior probability that we have available. In this case, it would be very reasonable to assume that the vast majority of the samples are synthesized correctly (otherwise, something would be very wrong with commercial providers or company synthetic chemists). Based on prior success, a 95% level of correctness could be a sensible estimate. Assuming that ASV will result in a positive score if the molecule is compatible with the data and negative otherwise, what would be the posterior probability that the molecule is correct when ASV gives a positive result (a true positive (TP))?

447

448

12

An Integrated Approach to Structure Verification Using Automated Procedures

Table 12.1 Baye’s theorem applied to the ASV example. Prior probability Initial estimate of how likely it is that a molecule is correct A new event occurs: ASV > 0 Probability of ASV giving positive conditional on the molecule being correct Probability of ASV giving positive conditional on the molecule being wrong Posterior probability Revised probability of how likely it is that the molecule is wrong, given that the test is negative

x

95%

y

90%

z

20%

xy xy + z(1−x)

98.8%

This can be calculated using Bayes’ theorem. Briefly, Bayes’ theorem is concerned with conditional probability: that is, it tells us the probability that a theory or hypothesis is true if some event has happened. While the philosophical underpinnings are surprisingly rich, its mathematics is stunningly simple and can lead to enormous predictive insights. In this particular example, the calculation (and the simple algebraic expression that yields it) is shown in Table 12.1. As it turns out, this probability of nearly 99% is significantly higher than the initially expected value of 80%. This very high probability may seem counterintuitive, but it stems from the fact that we have assigned a high prior probability to the molecule being correct. In other words, when our priors are strong, they can be surprisingly resilient in the face of new evidence. As a result, the probability that the molecule will be incorrect conditional, on the ASV test giving a positive result (FP), will be as low as 1.2%. This low number of FPs dominates the equation because very few molecules are incorrect to begin with. This Bayesian analysis helps answer the initial question about the utility of an ASV system to identify the bad samples whose structures are incorrect (true negatives (TNs)) and ensure they are not screened when the number of samples is too large to be analyzed manually. Assuming that the ASV system performs as in the example above, if we have an initial set of 10 000 samples, they first can be divided into two groups (Figure 12.1) – (i) 9500 correct molecules and (ii) 500 wrong molecules. If we consider the first group of correct molecules, after they have been passed through the ASV test, we find that 9025 (95%) will give a positive ASV result and consequently, they will correspond to TPs. These are molecules whose spectra will not require any additional inspection. On the other hand, ASV will give about 475 negative scores (5%). The molecules falling in this group are FNs and will be referred by the system for further analysis to determine whether they are actually correct structures. Considering the second group of 500 incorrect structures, we predict that ASV will yield 400 TNs and 100 FPs. The TNs can be added to the FN group giving rise to a total of 875 molecules that would be referred by the system for manual review. In our example, therefore, the use of an ASV system with the performance described above would result in an increase in our compound integrity from 95 to

12.1

95%

9025

True positive

475

False negative

9500

10 000

5%

Introduction

Manual analysis 400

True negative

100

False positive

500

Figure 12.1 The decision tree explained in the text. Starting with 10 000 compounds only 875 could be negative and a manual analysis of these should rescue the false negatives and identify true negatives with certainty.

99%, in exchange for the reasonable amount of effort needed to review 875 samples for every 10 000 submitted. 12.1.2 Automatic Structure Verification: What It Is and What It Is Not

We define ASV as the computer algorithms attempting to assess the degree of compatibility between a proposed molecular structure and one or more sets of spectral data. It does not, however, address the question of whether other molecules might also match the data, and neither does it prove that molecular structure is definitely correct. Furthermore, an automatic verification system can be classified as a fuzzy logic problem in which many aspects cannot be described in an exact way using deterministic rules. The fact that any ASV system just measures the degree of compatibility between a proposed molecular structure and the available spectroscopic data is of fundamental importance. Obviously, this property will depend upon the amount and type of available analytical data. For example, if the verification process of a putative molecule is carried out using only a mass spectrum (MS), the analysis will result in a positive (i.e., the experimental isotopic cluster is compatible with the calculated one from the molecule) or in a negative. In the latter case, the relevance of this analysis will be very significant, whereas a positive result, due to the lack of structural information of the technique, will not guarantee that the molecule is correct. Many structural isomers may have the same molecular formula and molecular mass, and will therefore be perfectly compatible with the LC/MS (liquid chromatography/mass spectrometry) data. Adding more spectroscopic information may raise the degree of (or conversely, the lack of ) compatibility between the molecule and the experimental evidence. For compounds in liquid state, NMR is beyond doubt the richest structural information analytical tool, yet the principle that it will not unequivocally prove that molecule is correct still applies. For example, (isobaric) regioisomers shown in Figure 12.2 will both pass any LC/MS test. On the other hand, considering

449

450

12

An Integrated Approach to Structure Verification Using Automated Procedures

O 8 7

(a) 3 5 O− 6 12 N+ 11 O 13

1

(b) CH3 O 10 9

O− 13

N+ O 12 5 14

2 4

3 1

O 9

CH3 10

2

6

Br 14

O 8 7

4

Br 11

0.07 ppm 0.03 ppm 0.05 ppm

8.70 8.65 8.60 8.55 8.50 8.45 8.40 8.35 8.30 8.25 8.20 8.15 8.10 8.05 8.00 7.95 7.90 4.00 3.95 3.90 3.85 f1 (ppm) Figure 12.2 Experimental 1 H spectra of the two regioisomers (a) and (b) displayed overlapped to show the very small chemical shift differences.

the 1 H-NMR spectra of these molecules, they have the same spin system and therefore, our ability to distinguish their 1 H-NMR profiles rests exclusively on the recognition of chemical shift differences [10]. The accuracy of measured chemical shift values depends upon the digital resolution, which in turn is given by the smallest possible distance – called the Rayleigh limit or bound 𝜔min = 2𝜋/T – between any two adjacent regularly spaced Fourier frequencies for the chosen total acquisition time T. It is this Rayleigh bound, 𝜔min, which inherently limits the resolution in the FFT (fast Fourier transform) [11]. Apart from this inherent limit to the accuracy of the chemical shift, these are influenced to a much greater extend by a number of experimental variables, including pH, solvent, and analyte concentration, salt content, and temperature. If these factors are also combined with the uncertainty in the theoretical prediction of chemical shifts, the ability to uniquely validate one structure and discard a similar one by NMR can be challenging or impossible. As can be seen in Figure 12.2, the largest chemical shift difference for any multiplet type amounts to only 0.07 ppm, which is within experimental error, considering both the actual experimental fluctuations by the factors described before and the prediction errors: it would be very hard, if not impossible to discard one of the structures unless they are compared side by side, that is, rank one structure higher than the other.

12.1

Introduction

In summary, an ASV system attempts to answer the question of whether a structure could be possibly compatible with an NMR spectrum. However, in a similar context, one could devise other similar queries, such as the following: – “Given this spectrum–structure pair, can this structure be ruled out?” This query is similar to ASV, but not the same: the focus is different and can be termed a “structure exclusion query.” Rigorously speaking, unlike exclusion, a full confirmation is impossible. For example, when ASV gives a positive result, it is basically saying “I can’t rule this out,” and not “the structure is correct.” – “Given this spectrum and these n structures, which structure is the best match; and is the difference significant?” This is structure discrimination or ranking and is very different from ASV, although it can be based on the same tools. – “Could this structure be present in this spectrum?” This is structure detection in a mixture of compounds. 12.1.3 Background and Existing ASV System

In this section, we present a very brief survey of existing computer-based verification systems. A comprehensive discussion of such methods is beyond the scope of this chapter and therefore we refer the interested readers to the bibliographic references. The ASV software for which the authors have contributed to the development will be covered in more detail in Section 12.3. The efforts toward automating the analysis of NMR spectra have a long history and find their origins in the iterative analysis exemplified by the programs NMREN/NMRIT of Swalen and Reilly [12], and the program LAOCOON of Castellano and Bothner-By [13]. These methods required a significant amount of manual work, so that a sufficient number of transitions in a synthetic spectrum were assigned to their experimental counterparts. An important breakthrough into automatic analysis was achieved by Diehl, S´ykora, and Vogt who exploited the fact that the information contained in a spectrum could be concentrated into a small number of regions by means of an integral transform (IT) [14]. This approach has the advantage of avoiding the assignment step altogether and furthermore opens the possibility of allowing a solution starting from initial parameters far from their correct values. Obviously, it is advantageous to use as good estimates of trial parameters as possible in order to avoid local minima, especially with large spin systems. This procedure was subsequently extended by the work of Laatikainen et al. [15, 16]. Briefly, the IT procedure is used to find the correct solution with a minimum knowledge of the spectral parameters. In order to get more accurate values, it may be necessary to refine the result using standard assignment iteration [17]. A related approach was suggested by Binsch [18]. It uses a generalization of the least-squares formalism to “flatten” the error function and thereby avoid local minima. Once a solution has been found, the flattening is decreased in stages, allowing progressively more accurate determination of the parameters while

451

452

12

An Integrated Approach to Structure Verification Using Automated Procedures

staying near the global minimum function. This approach was implemented in the computer program DAVINS and its sequels, DAVSYM, DAVCYM, and DAISY [19]. However, while these computer tools are useful for the analysis of complex spin systems, alone they cannot be considered to be ASV systems: they are, at best, an elementary component of them. Perhaps some of the earlier attempts toward structure verification by NMR were the visually guided approaches developed by Hamper et al. [20] and Keifer et al. [21], in which all the NMR spectra corresponding to each molecule were displayed in a stacked plot or as a pseudo-2D map so that the presence or absence of any expected peak was evident [22]. A significant step toward a new automatic verification paradigm came from the work of Griffiths and Bright [23], who addressed the problem of assessing the consistency between the structure and spectrum pairs by comparing the experimental spectrum with the predicted spectrum of the proposed structure. The underlying concept is a mismatch methodology in which a matrix having the experimental and predicted chemical shifts distributed along columns and rows respectively is created, followed by an optimization procedure aimed atminimizing the sum of the diagonal. This measures the mismatch between predicted and experimental chemical shifts, and a correct match should not exceed a predefined threshold. Additional filters, such as the number of coupling constants and total protons in the molecule, could also be used. This method, however, did not provide assignments, that is, which protons in the molecule are paired with which experimental NMR multiplets. Following similar principles, Golotvin et al. [24] proposed an objective function, which accounts for all of the measured differences in the multiplet properties (including chemical shifts, number of protons, and multiplicities) in such a way that the minimum of this function would correspond to the best possible assignment. This value is then used as a measure of spectrum-to-structure correspondence. The same authors further extended this mismatch methodology with the ability to incorporate HSQC (heteronuclear single quantum coherence) spectral data [25, 26]. An alternative validation procedure, exploiting chemical shift correlations in 2D NMR spectra (HSQC, COSY, and HMBC), optionally supported by chemical shift prediction, was recently proposed [27]. This software, named CCASA, takes advantage of several internal parts of the LSD (Logic for Structure Determination) computer system [28], which proposes molecular structures that fit with 2D NMR data sets, which are the same as those required by CCASA. A hybrid approach between the quantum mechanical spin system and the prediction of spectra from the molecular structure is the so-called ACA system (Automated Consistency Analysis) [29]. This software performs a complete NMR spectral analysis by predicting the chemical shifts and scalar couplings and optimizing them to match the experimental data using the IT approach described above. In this chapter, a novel fuzzy logic verification program, Mnova Verify, will be described. It is a complex expert system that automates all the steps involved in

12.2

Practical Aspects of NMR Automatic Verification

molecular confirmation procedure, ranging from the processing of analytical data and molecular structures to prediction and advanced analysis of the same data.

12.2 Practical Aspects of NMR Automatic Verification

Even though an automatic verification system should be as robust as possible to potential deficiencies in the acquired NMR data, optimal results will only be achieved if the spectra are acquired and processed in a sensible way. With 1 H spectra, the best algorithmic performance will be possible only when the spectral multiplets are correctly identified, and their relative integrations come close to the theoretical values for the number of nuclides (NN) that each represents. In this section, we review the rudiments of NMR data acquisition and processing. We start by presenting the well-known theory on signal processing to lay the basis required to ensure a minimum level of data quality. We show some practical examples as well as some general recommendations that could be followed in the conditions commonly used in the context of verification by NMR. 12.2.1 Digital Resolution

Resolution refers to the ability to distinguish components of the signal that are close in frequency. In the context of FT (Fourier transform), which is the most commonly applied time-domain processing method for NMR data, resolution is limited by the Fourier uncertainty principle, which states that the resolution is determined exclusively by the total acquisition time T = N𝜏 , where 𝜏 is the dwell time and N is the total number of sampled complex digital points. Consequently, the FT converges linearly with respect to the signal length according to 𝛿𝜔 ∼ 1/N𝜏. However, other signal processing methods have been described, but not widely adopted, such as the maximum entropy method [30] or the fast Padé transform [31], which can bypass this limitation, providing a higher resolution power. These more advanced techniques are not covered in this chapter and only the most widely used FT is assumed throughout this text. The free induction decay (FID) coming from the sample in the spectrometer is an analog signal in the radio frequency range, which is then converted into the audio frequency range by mixing it with the receiver reference frequency signal usually placed at the center of the spectral width. This analog signal must be digitized, typically at regular time intervals using an analog-to-digital converter (ADC). With the newest spectrometers, the analog RF FID is sampled directly without the need for the analog mixing, so that the conversion to audio frequencies is done by digital multiplication of the sampled signal. In order to digitize this signal, it is necessary to define how many points should be sampled. Obviously, it is possible that the ADC will not be fast enough if we acquire too many digital points per period. On the other hand, if we sample

453

454

12

An Integrated Approach to Structure Verification Using Automated Procedures

(a) 195 points

(b) 24 points

(c)

6 points

Figure 12.3 A quadruplet digitized with different resolution. Note the gradual loss of detail from (a–c), as fewer data points are used.

too few points, then we will run into the danger of losing some information in the signal. The answer to this question is given by the Nyquist sampling criterion, which says that in order to be certain that a signal position is correctly represented, it is necessary to record at least two points per period of the fastest oscillation in the FID. For example, correct digitization of an NMR spectrum located between −7 and 20 kHz requires at least 40 kHz sampling rate. Clearly, the higher the number of acquired data points, the better the resolution of the spectrum. This is illustrated in Figure 12.3, in which three “synthetic” FIDs were generated using a different number of digital points and then Fourier transformed to yield the corresponding three-frequency domain spectra. As can be noticed, as the number of points decreases, the quartet becomes less smooth until a point where the finer structure of the quadruplet is no longer recognized. For a given spectral width, the number of points can be increased by acquiring the FID for a longer period of time. This is because the three acquisition parameters, acquisition time, number of points, and spectral width, are wedded by Equation 12.1, so that modifying any of the three will require changing another to maintain the equality: Acquisition time = Number of complex points∕Spectral Width

(12.1)

However, attempting to improve the spectral resolution by increasing the acquisition time may lead to poorer signal-to-noise ratio (SNR), since at longer times compared with the T 2 relaxation time of the sample, mainly noise will be collected. In practice, the sampling rate is set by choosing the spectral width of the spectrum. With some spectrometers (i.e., Bruker), changing the spectral width will result in the acquisition time being modified according to Equation 12.1 whereas in other instruments (i.e., Agilent) the acquisition time is kept constant and the number of points is adjusted to satisfy Equation 12.1. There is a simple way to improve the digital resolution that costs nothing in terms of acquisition time. This technique is known as zero filling (ZF) and is discussed next. 12.2.1.1 Zero Filling

If we consider an FID acquired during t seconds where the signal has already decayed near to zero, we could acquire more points in order to achieve higher resolution. However, as stated above, what we will be recording during this extra

12.2

Practical Aspects of NMR Automatic Verification

period of time will be mostly noise, which will get reflected into the FT spectrum and consequently reduce the SNR. However, since we know anyway that there is no signal in this extra time, we can expand the end of the FID with zeroes, which offers the benefit of not having any noise so the SNR will not be compromised. Mathematically, this can be justified as follows. Each point in the original spectrum, before ZF, can be described as the discrete FT of the FID: ∑

N−1

Fn =

2πikn

dk e

N

(12.2)

k=0

where dk are the points in the FID. If the original number of points in the FID, N, is doubled by adding an equal amount of zeroes, then Equation 12.2 becomes ∑

2N−1

Fn =

2πikn

dk e

2N

(12.3)

k=0

Because dk has zeroes after N, the sum in Equation 12.3 can be reduced to N instead of 2N so Equation 12.3 becomes: ∑

N−1

Fn =

2πikn

dk e

2N

(12.4)

k=0

The main difference between Equations 12.2 and 12.4 is that the frequency step becomes smaller by a factor of 2, which is another way of saying that the number of points accurately describing a peak in the frequency spectrum has doubled. It would seem possible that by padding the FID with more and more zeroes, the digital resolution could be boosted indefinitely. As is shown below, doubling the FID will enhance the actual digital resolution while subsequent zero-fills will improve the apparent digital resolution, but will not increase the spectral information content. These findings can be understood on the basis of the complex nature of the acquired data. The digitized FID consists of a total of N real values, usually acquired in simultaneous N/2 pairs by digitizing the outputs of two RF phase detectors, whose reference RF signals have the same frequency, but 90∘ shifted phases. Traditionally, the two outputs are referred to as the U and V “channels” or, improperly, as the “real” and “imaginary” parts of the signal. In modern “digital” RF receivers, all this signal-processing complexity is hard-wired inside FPGAs (field programmable gate arrays), but the result is the same, namely, N/2 complex points, each with a “real” and an “imaginary” component. The U and V channels, despite being statistically uncorrelated because of the reference channels’ orthogonality,1) are not independent. In fact, the two components of the signal are related by the Kronig–Kramers relations. They are, in fact, the Hilbert transform of each other, including most of the noise. 1) Just as sin(x) and cos(x) functions are orthogonal “uncorrelated,” but not independent (sin2 (x) = 1 − cos2 (x)).

455

456

12

An Integrated Approach to Structure Verification Using Automated Procedures

However, there definitely is an increase in information associated with the doubling of data points. As shown by Bartholdi and Ernst [32], the new extra points in the FT spectrum obtained after one level of ZF contain “fresh information”; they are not just an interpolation between the adjacent “old” points (that happens to a progressively increasing extent only when ZF is pushed beyond the factor of 2). Getting new information from 2 equiv. sets of data may sound a contradiction until one understands that discrete Fourier transform (DFT), as opposed to functional transform (FT) does not extract all the information available in an FID. Doubling the number of points helps to get the most out of the acquired data. In other words, it is not that ZF somehow creates new information, but rather that, without ZF, the discrete FT is not good enough at extracting it. Consequently, one level of ZF should always be performed; otherwise, there will be a strong penalty in the spectral content after FT. However, if the FID is truncated, and only in that case, zero filling leads to the additional and independent problem of creating sincwiggle artifacts, but these can be suppressed either by a proper apodization or by linear prediction (LP) (Section 12.2.3). Going beyond one level of ZF before transformation would result in a more finely digitized spectrum, which may be easier to interpret. In this case, the additional points are practically just interpolated between the ones obtained after one ZF level, and so little new information is added. Even so, however, the finer digital resolution can substantially improve the performance of many subsequent dataprocessing algorithms. O 11 6

(a)

2

4 N 3

13

10 5

1

H3C 15

7 O 8

O 12 O 9

CH3 14

CH3 18

16

(b)

CH3 17

Figure 12.4 High factors of zero filling may result in better analysis of the spectrum. In (a) one level of zero filling was applied and the peak picking algorithm was only capable of recognizing one peak. In (b), the FID

was extended fourfold by zero filling, making possible that the peak picking algorithm can detect the underlying two peaks corresponding to C-13 and C-16. See the text for more details.

12.2

Practical Aspects of NMR Automatic Verification

For example, in Figure 12.4 an expansion of the 13 C spectrum of a pyridine derivative is shown. The FID was acquired with 32 Kb of complex points and a spectral width of 18 832.4 Hz. In (a), the FID was zero filled to 64 Kb of points yielding an apparent spectral digital resolution of 0.29 Hz/point. Under these conditions, the peak-picking algorithm was only able to identify one signal, which is displayed as a darker line superimposed over the experimental peak (lighter line). On the other hand, if the FID is padded with zeroes up to 128 Kb, it can be seen that the peak becomes more asymmetric and the peak-picking algorithm detects two overlapped peaks that are consistent with the molecular structure and can be assigned to carbons 13 and 16. The bottom line is that even though multiple ZF does not add any inherent information beyond that available from a singly zero filled spectrum, it can render that information more visually obvious and thereby facilitate the computer analysis of the signals via, for example, peak picking, peak fitting, integration, and so on. Ideally, one should aim at having at least five digital points per peak above half height for correct peak description [33]. Furthermore, as Bourg and Nuzillard have shown [34], even though ZF does not result in an improvement√in the spectral SNR, it may increase the integral precision by a factor of up to 2 when the time domain noise is not correlated. 12.2.2 Window Functions

For 1 H-NMR, the best practice is to acquire the signal in such a way that it has been allowed to decay smoothly to zero. Under these conditions, ZF will give good results and no artifacts will be obtained. However, in other spectra, including 13 C NMR and most importantly in the indirect dimension of multidimensional spectra, the signals are usually heavily truncated. When this happens, there is a discontinuity in the FID that results in artifacts (sinc-wiggles or side-lobe artifacts) in the spectrum. This can be easily understood by considering the convolution theorem (Equation 12.5), which states that convolution in one domain is equivalent to multiplication in the corresponding Fourier domain. FT(g ∗ h) = FT(g) ⋅ FT(h)

(12.5)

Truncation can be considered as the multiplication in the time domain of an ideal untruncated FID (Figure 12.5a) by a step function (Figure 12.5c), which has unit value up to the truncation point and zero from there on. The FT of a step function is a sinc function, sinc(x) = sin(x)/x (Figure 12.5d), and so truncation is equivalent to convolution with a sinc function. This results in line broadening and wiggles around the lines as depicted in Figure 12.5d,f. These side-lobe artifacts can be removed by multiplying the FID by a decaying exponential function of the form exp(−π Lb t) (where Lb is the line broadening or decay rate of the exponential function) prior to FT, so the acquired signal appears as if it has been allowed to decay to about zero before further zeros are added. This effectively weakens the discontinuity, and consequently reduces the

457

458

12

An Integrated Approach to Structure Verification Using Automated Procedures

(a)

(b)

X (c)

(d)

(e)

(f) =

Figure 12.5 Demonstration of truncation effects. Multiplying (a) and (c) gives (e), while (f ) is the convolution of (b) and (d); (b), (d), and (f ) are the Fourier transforms of (a), (c), and (e) respectively.

side rings. Considering again the convolution theorem, multiplication by a decaying exponential function is equivalent to convolving with a Lorentzian broadening function in the frequency domain, and therefore the wiggles are smoothed out. This occurs at the expense of widening the lines and therefore, decreasing the resolution. This process of reducing the strength of these side lobes or side rings is known as apodization, a word that is from the Greek and literally means “to remove the feet,” where the “feet” are the side lobes. While the term apodization originally meant bringing the interferogram or FID smoothly down to zero to suppress the side lobes, over time it has come to describe any function applied in the time domain to optimize the SNR or to change lineshapes and improve resolution to reveal hidden fine structures. This process is generally known as weighting or windowing, and the basic idea lies in the fact that in the FID the signal intensity drops throughout the acquisition period, whereas the noise remains constant. Therefore, decreasing the tail of the FID will help to reduce the noise amplitude in the corresponding frequency domain spectrum, thereby increasing the sensitivity. Conversely, increasing the intensity of points in the middle and latter part of the FID is equivalent to retarding the decay of the signal, thus narrowing the peaks and enhancing resolution [35]. 12.2.2.1 Sensitivity Enhancement

As stated above, multiplication by an exponential decaying function reduces the contribution from noise in the tail of the FID, and therefore can improve the SNR. However, as it also increases the apparent decay rate of the FID, it can lead to a

12.2

Practical Aspects of NMR Automatic Verification

decrease in SNR in the resulting spectrum, because the broadening of the lines causes a reduction of their peak heights. The optimum occurs when the decaying function exactly matches the decay of the FID (matched filter) [36]. This results in a doubling of the resonance linewidth. Even though this will give the optimal SNR, this extra line broadening may not be acceptable because of the loss of resolution it causes. An additional problem of the matched filter is that theoretically, the matched condition can only be met when all the lines have the same shape and width in the spectrum, and this is seldom the case in practice. From a practical point of view, if we consider routine 1 H-NMR spectra, it is usually enough to apply a very mild exponential function to attenuate the excess noise at the tail but with only a minimal increase in linewidth. Alternatively, a very convenient weighting function is the so-called Hanning function [37]. In the case of 13 C-NMR spectra in which the signal is always weak, the line broadening side effect of the exponential apodization is usually a lesser concern and the increase in SNR is usually worth the price. Here, as well, signals are usually spread over a wide frequency range and signal overlap is less common than in the 1 H spectral case. The Hanning or a Cosine Bell functions can also be good options. 12.2.2.2 Resolution Enhancement

The linewidths of the spectrum can be narrowed by multiplying the FID by a rising function. However, this has the effect of accentuating the noise in the latter time points in the FID, and so decreasing the SNR. Furthermore, if the original FID is obviously truncated and zero filled to increase digital resolution, the process will also boost the side ringing. A simple way to minimize these difficulties or at least to keep the noise and sinc artifacts under control while enhancing the resolution consists in multiplying the FID by a function that first rises and then falls. One of the most popular weighting functions that follows the above principles is the so-called Lorentz-to-Gauss transformation. This can be considered as a composite weighting function W (t) = exp(−πLb t) ⋅ exp(−𝛼t 2 )

(12.6)

where Lb is the line broadening factor and 𝛼 is the Gaussian parameter. This equation is best understood if it is split into two parts. The first term, exp(−π Lb t), is the same as the standard apodization function discussed above. If Lb is positive, we will have a decaying exponential function that will result in a broadening of the peaks. In contrast, if Lb is negative, we will have a raising exponential function that will enhance the latter part of the FID and so increase the decay time, which will result in narrower lines. The second part of Equation 12.6, exp(−𝛼t 2 ), is then used to control the noise and artifacts that were created by the first part of the equation. This can be recognized as a Gaussian function and has the benefits of decaying smoothly to zero over a significant part of the FID and then more rapidly at the end. This also changes the lineshape from the natural Lorentzian to a Gaussian, which can be useful in its own right, since Gaussian lines are narrower at the base than Lorentzian lines with the same half-height linewidth.

459

460

12

An Integrated Approach to Structure Verification Using Automated Procedures

In addition to this Lorentz-to-Gauss transformation function, there are many other resolution enhancement functions such as TRAF [38] and the Sine Bell function. The latter is frequently used in 2D NMR spectroscopy. 12.2.2.3 Weighting Functions and Integration

There has been some debate about the influence of the weighting function on the accuracy of the integrals in an NMR spectrum. While it is very evident that any weighting function that decreases the SNR would undermine the quality of the computed integrals, the main point under discussion is whether an apodization function that modifies the first point in the FID would change the ratios of peak integrals in the corresponding spectrum. As it turns out, as long as the first point of the weighting function is not zero, the ratios of the peak integrals will not change, regardless of the weighting function. This can be proved by exploiting two properties of the Fourier theory: (i) the FT is a linear operation and (ii) the amplitude of the first point in the FID is proportional to the sum of all points in the frequency-domain spectrum. This is easy to show: ∑

N−1

dn = c

∑

N−1

2πikn

fk e

⇒ d0 = c

N

k=0

∑

N−1

fk e0 = c

k=0

fk

(12.7)

k=0

where d and f correspond to the points in the FID and in the spectrum, respectively, and c is the FT normalization coefficient. So let us suppose that we have a spectrum comprised by only two peaks, P1 and P2 . The linearity of the FT implies that if we consider the spectrum as the sum of P1 and P2 , then the FID, F(t), must be the sum of the individual FIDs of P1 and P2 , F 1 (t) and F 2 (t). It follows that, no matter how dissimilar may be the shapes of the peaks, their total integrals I 1 and I 2 are proportional to F 1 (0) and F 2 (0), respectively: r=

I1 F (0) = 1 I2 F2 (0)

(12.8)

Let us now multiply the FID by an apodization function W (t), creating a new one, F ′ (t), as indicated in Equation 12.9: F ′ (t) = W (t)F(t)

(12.9)

The multiplication by W (t) is again a linear operation and therefore all components present in the FID get multiplied by the same function W (t) as shown in Equation 12.10. F1′ (t) = W (t)F1 (t) F2′ (t) = W (t)F2 (t)

(12.10)

It follows that though the integrals I 1 and I 2 get scaled by W (0) the apodization does not change their ratio r Equation 12.11. r′ =

I1′ I2′

=

F1′ (0) F2′ (0)

=

W (0)F1 (0) I1 = =r W (0)F2 (0) I2

(12.11)

12.2

Practical Aspects of NMR Automatic Verification

(c)

(d)

3.60

3.55

3.50

3.45

3.40

3.35

1.55

1.50

Figure 12.6 (a) Synthetic FID of CH3 CH2 Cl with a Sine Bell function superimposed on top of it, (b) resulting FID after the weighting function has been applied, (c) spectrum

1.45

1.40 3.60

3.55

3.50

3.45

0.00

0.00

3.00

(b)

2.00

(a)

461

3.40

3.35

1.55

1.50

corresponding to the unweighted FID, and (d) spectrum of the Sine Bell weighted FID. Notice that the integrals are zero.

There is, however, one exception: If W (0) = 0, the two integrals I 1 and I 2 become simultaneously zero and their ratio becomes indefinite. After any such apodization, the peaks always exhibit negative lobes that compensate the positive parts of the peaks and null the integrals. A typical example is the Sine Bell weighting function, and this is illustrated in Figure 12.6. As can be appreciated, multiplication of the original FID by a Sine Bell function leads to a spectrum (Figure 12.6d) in which the area of the peaks must necessarily be zero, because the first point in the weighted FID is zero. This is reflected by side lobes with negative parts on each side of the peaks. As a result, whenever the relative integrals are important, as it is in the case in the scope of structure verification, weighting functions for which the first point is zero should be avoided. This applies, of course, to 1 H-NMR spectra and not, for example, to 2D HSQC spectra, where the relative integrals are not relevant. On the other hand, weighting functions in which the first point is very close to zero should also be avoided due to the influence of the noise. From a practical point of view, all the apodization functions typically used in those NMR experiments in which the relative integrals are important (i.e., 1 H-NMR spectra) can be used with no concern, as none of them impose values close to zero under standard conditions.

1.45

1.40

462

12

An Integrated Approach to Structure Verification Using Automated Procedures

12.2.3 Linear Prediction

We have seen that ZF is a simple yet effective procedure for increasing the digital resolution of a spectrum without having to acquire the signal for a longer period of time. We also described the problems associated with this technique when the signal is severally truncated, leading to the appearance of the truncation artifacts. There is a very popular alternative to ZF, which is known as Linear Prediction (LP). This is fundamentally quite simple, although the mathematical details are more convolved and an elaborate discussion of this method is beyond the scope of this text. Conceptually, it exploits the fact that an NMR FID signal can be represented, to a good extent, as a linear combination of damped sinusoids. One can therefore make the key assumption that the future values (dm ) of an FID may be obtained approximately as a linear combination of the past values (dm−p ). Mathematically, the LP equation can be expressed as dm =

P ∑

ap dm−p ,

m = p, … , N − 1,

(12.12)

p=1

where N is the number of experimental points used in the LP problem. The number of coefficients p determines prediction accuracy in such a way that the higher this number, the better (although the computational cost will also increase). Generally, a reasonable value for p is set according to the expected number of distinct resonances in the spectrum. Once the coefficients are determined, it is then straightforward to apply the LP equation to either predict points in the signal beyond the acquired data points, as an improved ZF method, or even to predict any points in the FID that were corrupted for some reasons. The first application of LP is known as forward LP. In theory, in the light of the definition of LP, consideration could be given to use it in all kind of spectra. However, it is important to take into account a few aspects. First of all, it must be highlighted that LP does not add any new information from the acquired data points, but simply extracts the most out of the available data. If one considers, for example, high resolution 1 H-NMR, usually the signal has already decayed very close to zero or at least, this is the recommended way in which a 1 H spectrum should be recorded. In this case, ZF and LP would yield virtually the same results, but the former is computationally faster and more robust. On the other hand, when the time-domain signal is truncated, we get the sinc-wiggles artifacts which, as discussed in the previous section, can be suppressed by multiplying the FID by a weighting function that forces the signal to decay smoothly at zero. However, this results in significant line broadening, compromising the resolution. In this case, forward LP becomes a useful procedure. The most common scenario where the signal is usually severally truncated is in the case of the indirect dimension of two dimensional spectra (or multidimensional more generally) to minimize the total experiment time. For instance, HSQC spectra represent a good example where forward LP along the t 1

12.2

H2N 21 18

Practical Aspects of NMR Automatic Verification

463

52.0

52.0

52.5

52.5

53.0

53.0

53.5

53.5

54.0

54.0

54.5

54.5

55.0

55.0

55.5

55.5

56.0

56.0

19

17 16

20 15

S O 12 13 O 14

NH 11 5 4

N 6 7 O 9

3 N 8

10

O 2 1

56.5

56.5 3.88 (a)

3.84

3.80

3.76

3.72

3.68

3.88 (b)

3.84

3.80

3.76

3.72

Figure 12.7 Illustration of the difference in resolution achieved when linear prediction (a) or zero filling (b) is used to extend the data points along the indirect dimension of a phase sensitive HSQC experiment.

dimension is very useful because each column or interferogram at a particular f 2 frequency contains only a small number of peaks. The LP can therefore be very efficient because the requirement that the number of LP coefficients be larger than the number of signals constituting the FID/interferogram will be easily fulfilled. An example of the power of forward LP is shown in Figure 12.7. This shows a portion of a HSQC spectrum acquired with 256 t 1 increments (i.e., 128 complex points). The expanded region corresponds to the frequency range of the two –OCH3 groups (H-10 and H-11 in the structure). In (b), the spectrum is shown after ZF from 128 to 1024 data points, after a Sine Bell apodization function was applied. As can be noticed, the two methyl groups are indistinguishable, and only one wide cross-peak is observed. In (a), LP was used instead of ZF: now the two methyl groups are clearly resolved. LP can also be used to predict missing or distorted points in the early part of the FID, immediately after the observe pulse. This is known as Backward LP and the most common application is the reconstruction of the first few data points of the FID, where these points have been corrupted by pulse breakthrough or by electronic filtering. These corrupted data points may cause severe baseline distortion, as illustrated in Figure 12.8c. A potential solution could be a simple deletion of these corrupted early points (Figure 12.8a), but this would create a new problem, namely, a significant first-order phase distortion of the spectrum. A better approach would be, as shown in Figure 12.8b,d, a reconstruction of the first data points from the succeeding ones using the LP principle, resulting in a spectrum showing a straight baseline.

3.68

464

12

An Integrated Approach to Structure Verification Using Automated Procedures

(a) 5 10 15 20 25 30 35 40

(c)

(b) 5 10 15 20 25 30 35 40

(d)

Figure 12.8 Expansion of an experimental FID showing its first 45 points (a). Notice that approximately the first seven points are corrupted, which gives rise to the distorted baseline in its corresponding frequency

domain spectrum (c). These first seven points were deleted and recalculated using backward LP (b). The FT spectrum of the repaired FID (d).

12.2.4 Relaxation Times and Delays

In order to obtain reliable quantitative results when working with 1 H-NMR spectra, it is very important to wait for the spins to fully relax between pulses, demanding recycle times (defined as the total time between the start of the acquisition of the first FID and the start of the next period of radio-frequency excitation) of least 5T 1 times of the slowest relaxing nuclides, in which case 99.3% of the equilibrium magnetization is measured. This allows the application of a 90∘ pulse, which results in the creation of maximum signal intensity in the resultant spectrum. To acquire good quantitative 1H-NMR data in a reasonable period of time, however, a tradeoff in the pulse width is employed. In practice, pulse widths of 5 (high significances). While the score is the result of comparison between a hypotheses and some experimental data using a certain algorithm (test), significance is a statistical property of the algorithm itself and it can be assessed (tuned) only empirically on the basis of statistically meaningful experience. 12.3.2.3 Quality

Quality (Q) is simply a combination of the score and the significance to arrive at a single value. This parameter should be zero whenever either score (s) or significance (𝜎) is zero (i.e., if a test with negligible significance results in a high score, close to +1, the quality of that test is nevertheless zero). Its absolute value should increase when the absolute value of any of the two factors increases (assuming the other factor is nonzero), while its sign should match that of score. However, when the significance reaches high levels, minor differences should be of little importance. A formula that satisfies all these criteria is Q = s [𝜎∕(1 + 𝜎)] When comparing, in a mathematical sense, “elementary or composite tests” (score–significance pairs), the Quality should be used. One should not use, for instance, high scores if their significance is very low. A useful analogy could be a review panel. Imagine such a panel with three people and that they are presented with the same problem as the software, that is, a structure confirmation problem to be resolved by using some analytical data. The three panelists are the following: 1) An analytical expert with 30 years’ experience who has shown near infallibility when making these types of evaluations in the past 2) An analytical chemist with 3 years’ experience and a propensity to be too optimistic when passing structures in verification problems

473

474

12

An Integrated Approach to Structure Verification Using Automated Procedures

3) A first year undergraduate student who has taken a 4 h course in analytical chemistry and is evaluating his/her first real case. Evidently, we will assign a lot more significance (say 10) to the first panelist than to the second one (3) who, in turn, will be assigned a lot more significance than the third (1). Now, each of these panelists will give a score to the data, and it is quite possible that the absolute values of the respective scores may be quite high, say 0.8, meaning that they all have a strong opinion about whether the data are correct (+0.8) or incorrect (−0.8). If they all agree, or if at least panelists 1 and 2 agree, the final score for this dataset is bound to be something like 0.85 (the extra boost is for the concord) and the significance will be substantially higher than 10. The potential disagreement of the least significant vote is of little consequence. If only panelist 2 disagrees with the expert, however, the final score and significance are bound to be both lower than the expert’s, though still aligned with him. Finally, if both panelists 2 and 3 oppose the expert, we get a fairly neutral result, which might still tend toward the expert’s opinion, but with a very low significance. Actually, given the propensity of the second reviewer to be overoptimistic, we might want to assign higher significance to his negative scores than to his positive scores, which would lead to a further differentiation of the final votes. 12.3.3 NMR Prediction and Spectral Synthesis 1

H and 13 C NMR predictions are carried out using NMRPredict software by Modgraph Consultants [47], which is seamlessly integrated within Mnova Verify. A short overview of these methods follows.

12.3.3.1

13 C-NMR Prediction

Prediction of 13 C NMR chemical shifts is carried out using two different procedures, which are then combined by means of the so-called “Best” prediction. This algorithm is used, in the light of a number of heuristic rules, to decide the final unified predicted chemical shift for every individual carbon atom. First, a database-oriented chemical shift prediction is carried out [48]. This is done with an extended HOSE code method [49] (hierarchically ordered spherical of environment), which consists of a one-dimensional coding of the chemical environment of each carbon atom. Starting from the atom of interest, all atoms bonded directly to this atom (first sphere), over two bonds (second sphere) – and so on – are coded using characters that define atom types, bond types, ring closures, and spheres. The number of described spheres depends on the length of the code (Figure 12.10). The HOSE code approach works very well for query structures that are well represented in the reference collection. If atoms can be predicted to three spheres or more, the prediction can be considered to be very reliable. However, if the query structure is not well represented in the database and the atom can only be predicted to one or two spheres, the prediction cannot be relied

12.3

The Architecture of the Automatic Verification Expert System

CH3

I

II III

O Figure 12.10 The HOSE code is built spherewise around the reference atom (focus). The HOSE starts at the carbon atom whose shift is to be predicted, looks one bond away from the carbon, and tries to find this environment in its database. If it

is successful, it moves two bonds away and tries again and so on, until it either comes across something not represented in the database or it reaches the boundary of the molecule, or reaches a specified limit.

upon at all. Also the HOSE code approach exactly reproduces the contents of the reference database, including every error within that reference database. In order to cope with these issues, NMRPredict 13 C prediction also uses a neural network algorithm [50], which is more error tolerant than the HOSE code approach, giving more accurate results when the query atom is not represented in the database. Overall, if a carbon can be predicted at high spheres (i.e., number of shells ≥4), then the Best prediction method takes the value from the HOSE code procedure. However, if the predicted carbon is not well represented in the HOSE database, the chemical shift from the Neural Network algorithm will be used. 12.3.3.2

1 H-NMR Prediction

Prediction of 1 H-NMR spectra follows a similar approach to the case of 13 C spectra. First, a prediction algorithm that is based on tabulated chemical shifts for classes of structures, corrected with additive contributions from neighboring functional groups or substructures, is carried out. For a given molecule, the appropriate substructures are automatically assigned following a hierarchical list. These substructures provide the base value of a final predicted chemical shift [51, 52]. Furthermore, a complementary prediction approach based upon partial atomic charges and steric interactions is also performed [53]. This algorithm, named CHARGE, is a composite program made up of a neural network based approach for the one-, two-, and three-bond substituent effects plus a theoretical calculation of the long range effects of substituents. This method requires first the generation of 3D conformers from a 2D structure so the individual spectra of all conformers are predicted. Finally, an average predicted spectrum is calculated (employing a Boltzmann weighted average of the shifts calculated for all low-energy conformers). 1 H-NMR Best prediction analyzes the individual chemical shifts from the two complementary methods and gives a single, unified predicted chemical shift.

475

476

12

An Integrated Approach to Structure Verification Using Automated Procedures

12.3.3.3

1 H Spectral Synthesis

Once the 1 H-NMR chemical shifts and coupling constants have been predicted, the corresponding 1 H spectrum must be synthesized. There are several ways to accomplish this task, ranging from the more traditional Hilbert space of spin states to the more dense Liouville space of spin-operators approach. While the former only handles static problems rigorously, it is the one that best fits our needs, since a thorough treatment of dynamic problems and relaxation is not usually needed in the scope of spectral verification. The Hilbert-space approach consists in setting up the static, isotropic NMR Hamiltonian (H) followed by its diagonalization to get the eigenvectors and eigenvalues that will be used to compute transition frequencies and intensities. H=

∑ i

𝛿i Iiz +

∑ ij

∑ Jij (Iiz Ijz )+ Jij (Ii+ Ij− + Ij+ Ii− ) i1 peak, which is an experimental anomaly, probably caused by insufficient time allowed for temperature equilibration.

12.3.6 ASV Tests

All the procedures described so far are the preparatory steps required before the actual structure verification tests can be applied. Presently, the ASV scoring system is formed by three major tests as follows. 12.3.6.1 Number of Nuclides Test (NN)

The list of signals that have been classified as compound peaks in the previous stages is used to construct multiplets that are normalized to the total area equal to the expected NN (obtained from the proposed molecular structure). Then, each multiplet is tested against the requirement that its area should be an integer number. A Bayesian-like approach is used to make a probability estimate for the overall quantitative pattern of all multiplets and converted into the [+1, −1] scoring scale. It is efficient to detect failures provided there are not too many nuclides and a sufficient number of multiplets (NMs). Clearly, if there were just one multiplet (all peaks overlapping), the outcome would be meaningless (a pass, regardless of NN), while if each multiplet corresponded to just one nuclide, that would have a very high significance. Likewise, if the NN is very high (say, >20), then quantitation errors may again cause the test’s significance to drop. For these reasons, this test uses a Bayesian-based formula for the significance of this test as a function of NM and NN. This is actually a composite test made up, in addition to the actual NN calculation, of two other subtests that compare, in a similar way, the number of experimental or effective versus the expected peaks, and the number of experimental multiplet intervals with the expected ones. 12.3.6.2

1 H Prediction Bounds Metrics

In this test, the experimental peaks list is compared to the array of predicted shifts (Section 12.3.5) and their error bounds. The comparison is based on the calculation of the distance between the experimental spectrum and the set of 2) Handling of labile protons in 1 H-NMR is a very complex process, which involves many different tests: absence of 13 C satellites, linewidth, analysis of coupling correlations, solvent specific characteristics, chemical shift distributions according to different functional groups, and so on.

483

484

12

An Integrated Approach to Structure Verification Using Automated Procedures

all possible spectra compatible with the predicted values, including their error bounds. This test provides more discriminating power than the NN test. In particular, the test will detect all situations where even a single nuclide should be present (or absent) in a certain local region. On the other hand, similarly to the NN test, it also becomes less meaningful when the spectrum becomes more complex, but the tendency is less pronounced than in the NN test. This test goes as far as possible to exploit predicted chemical shift values (taking account of the error bounds) without attempting any actual assignment between multiplets and nuclides. Note: Even though predicted shifts of labile protons have large error bounds, these protons are fully compatible with this test and therefore do not need to be excluded. Indeed, the test operates more safely when labiles are included. Problems arise only if some of the labile protons signals are missing (two broad and/or merged with solvent water) while others are still present; such cases can be still handled, but they decrease the significance of this particular test. 12.3.6.3 Automatic Assignments Test

The aim of this test is to look for reasonable, complete atom-to-multiplet assignments, and assign a score to them. Algorithmically, automatic assignments of protons in the molecule to the different multiplets in the experimental 1 H-NMR spectrum is performed by first constructing a matrix whose rows and columns correspond to the predicted and the experimental multiplets, respectively, while the individual values assess the degree of compatibility between a given experimental multiplet and the predicted ones that have been assigned to it. Their values are also obtained by means of the scoring system applied to each predicted/experimental multiplet pair. The individual tests within each such system include primarily the chemical shifts, the number of nuclei, and the multiplet shapes.3) Next, the matrix is used to enumerate all the most likely assignments. To do so, an additional scoring is applied to each assignment based on how well the pattern of multiplets matches the expected one. This includes, for example, the intra-multiplet coupling constants. Not infrequently, thousands of likely assignments result from such an enumeration. If HSQC data is available this is also used, particularly for diastereotopic proton identification and 13 C shift compatibility. Finally, the best-scoring assignment is selected and proposed as the final “solution” of the problem. Because all the indications on assignments are scored, there is a global assignment score so that the best-scoring assignment is compared with 3) Multiplet shape is evaluated by calculating its high order spectral moments such as the kurtosis. This avoids having to determine the actual multiplicity (i.e., doublet, triplet, and quadruplet), but instead represents the so-called pure-shape characteristic of a multiplet, meaning that its value does not change when the multiplet is stretched either vertically or horizontally. In addition, as this pure shape property is calculated using only principal peaks, it is quite insensitive to outlying peaks. This makes the system more robust to potential artifacts in the spectrum as well as introduces some level of fuzziness in the scoring system.

12.4

Performance of the Automated Structure Verification Systems

Table 12.4 Number of correct vs incorrect assignments.

With DB No DB

Correct

Wrong

%

639 616

34 57

94 92

a soft threshold. Actually, in the context of ASV, it does not really matter whether there are different assignment possibilities of similar likelihood. As long as some reasonable assignment is possible, ASV will succeed. In order to assess the performance of the algorithm we have selected a test set of 90 molecules and their corresponding 1 H-NMR spectra recorded at 500.13 MHz. All FIDs were acquired with 64 Kb of complex data points, apodized using a Hanning apodization function, and zero filled to 128 Kb data points before the FT was applied. The phase was corrected automatically and no baseline correction was required. The whole process was conducted in full automation. An ad hoc script was implemented to calculate the number of correct and incorrect assignments achieved by comparison of the results obtained by the automatic algorithm with the manual assignments done by two experienced spectroscopists working independently followed by a cross-validation in order to detect and correct any potential misassignment. In a first test, the assigned molecules were added to the NMR Prediction engine internal data base (DB) so as to minimize the effect that predicted chemical shifts with large deviations could have in the performance of the algorithm. As a result of this process, the prediction errors are typically bounded within ±0.2 ppm. Under these conditions, the automatic assignment algorithm achieved an excellent success ratio of correct assignments of 94% (Table 12.4). Interestingly, when the assigned molecules were excluded from the NMR Prediction database, the drop in performance was very small – only 2% – proving that the algorithm is not overly sensitive to the quality of the predicted chemical shifts. An example of the auto assignments is shown in Figure 12.17. The circles drawn over the atoms in the molecule and on the labels in the spectrum depict graphically the quality of the elementary assignments. In the actual software, they are color coded, from best to worst using green, yellow, red, and gray colors respectively (not shown in the figure because of the lack of color).

12.4 Performance of the Automated Structure Verification Systems 12.4.1 Basic Definitions

An automatic verification system can be considered as a binary classifier – that is, a system that classifies the spectra–structure pairs into two groups on the basis of

485

486

H3C 7

12

An Integrated Approach to Structure Verification Using Automated Procedures O 32 24

5 6

N 4 3 1

S 9

O 10

23

HN 25

O 8

N 2

11 12

22

21 13

N 20 18

14

16

O 19

15

CH3 33 N 26 N 27 28 30

29

CH3 17

CH3 31

33 (s) 4.16 30 (t) 2.78 J (7.47)

33

25 (s) 12.19

11,16 (m) 7.83

15 (d) 7.37 J (8.73)

18 (q) 4.22 J (6.95)

7 (s) 2.14 3,5 (t) 2.36 J (4.85)

1,6 (t) 2.91 J (4.65)

7

29 (h) 1.74 J (7.41)

17 (t) 1.33 J (6.93)

31 (t) 0.94 J (7.36) 31

17

12.2

8.0

7.8

7.4

4.4

4.2

3.0

2.8 ppm

2.6

2.4

2.2

1.8

1.6

1.4

3.0

3.1

2.1

29

3.0

3.8 3.4

3,5

30

3.9

1,6

2.1 2.9

1.0

2.1

0.8 12.4

18 15

2.1

11,16 25

1.2

1.0

0.8

0.0

Figure 12.17 Assignments yielded by the algorithm presented in this work for the molecule sildenafil. All the discs are colored green in this case, indicating reliable assignments.

whether they are consistent or not. This type of classification is a well-developed area of statistical analysis used in many fields including quality control, machine learning, signal detection theory, and clinical trials, to name a few. We can use many different metrics from the binary classification theory, but in the most basic form, the performance of the structural verification system can be analyzed by controlling two types of errors: 1) False Negatives (FNs): the spectrum–structure pair is consistent, but the system judges that they are inconsistent. 2) False Positives (FPs): the spectrum–structure pair is inconsistent, but the system judges that they are consistent. Obviously, optimal performance of the system means minimizing both types of false results. These values have an inverse relationship: minimizing one of these two errors – for example, FNs – might result in an increase in the number of instances of the other, for example, more FPs. This is similar to what normally happens with weighting functions: adjusting the parameters of a given weighting function to improve resolution usually results in a decrease of the SNR, and vice versa. Some of the most commonly used metrics to control both types of errors are summarized in Table 12.5 [60]. We add the classes “True Positives” (TPs)

12.4

Performance of the Automated Structure Verification Systems

Table 12.5 Binary classification metrics. Metric

Formula

Description

Sensitivity

TP/(TP + FN)

Specificity

TN/(FP + TN)

Accuracy

(TP + TN)/(TP + TN + FP + FN)

Positive likelihood

Sensitivity/(1 − specificity)

Negative likelihood

Specificity/(1 − sensitivity)

Positive predicted value (PPV)

TP/(TP + FP)

Negative predicted value (NPV)

TN/(TN + FN)

Proportion of actual positives which are predicted positive. It is also known as true positive rate (TPR) Proportion of actual negatives which are predicted negative. It is also known as true negative rate (TNR) Proportion of true results (both true positives and true negatives) in the full data set Likelihood that a predicted positive is an actual positive Likelihood that a predicted negative is an actual negative Proportion of true positives with respect to total number of positives Proportion of true negatives with respect to total number of negatives

and “True Negatives” (TNs), which represent successful classification by the algorithm. Calculation of FNs and TPs is trivial in a controlled environment in which the consistency between the spectra and the structures is known beforehand. However, estimation of FPs and TNs is a subjective process, which will depend upon how different the negative control structures (NCS) and their corresponding correct ones (PCS, positive control structure) are. If NCS and PCS are too similar, it is possible that the consistence of the NCS cannot be shown to be TNs using the available NMR data, leading to FPs. On the other hand, if they are too different, it would be expected that any ASV system would be able to discard the NCS, but this would add little value to the ASV performance evaluation test. In order to measure the challenge (e.g., degree of difficulty of the particular ASV experiment) applied to the verification system and thus probe its robustness and selectivity to small molecular changes, a new molecular similarity coefficient, MolSimNMR [61] (molecular similarity for NMR), has been proposed. This is a computational method for the calculation of the expected NMR data similarity based solely on structural information. It is a fingerprint-based similarity calculation method, comparable to the Tanimoto coefficient, but specific for NMR data. From each PCS, this algorithm calculates the corresponding NCS, which are retained if they are sufficiently similar (or dissimilar) to the PCS.

487

488

12

An Integrated Approach to Structure Verification Using Automated Procedures

12.4.2 Tests of Performance

As was discussed in the beginning of this chapter using the Baye’s theorem, an ASV system must be very robust with PCSs, that is, should give a minimum amount of FNs, regardless of whether this may compromise in some extent the performance against false structures. It is also worth mentioning that the performance of an ASV strongly depends upon how similar the NCSs are, and this makes ASV different from traditional binary classification problems. ASV results are given in the form of continuous values in the interval of [−1, +1] (Section 12.3.1) and it is necessary to reduce them into three categories by defining empirically two cutoff values (Table 12.6): if the ASV result is lower than the negative threshold (NT), the structure–spectrum pair will be classified as inconsistent (dark gray in Table 12.6). If the ASV result is above the positive threshold (PT), the structure–spectrum pair will be designated as consistent (positive, light gray in the table). In these two cases, there will be no need for the user to take any action. ASV results outside of these two actions can be understood as cases in which the system does not have enough evidence to confirm or reject one structure in the light of the available NMR data and thus, human intervention would be needed. This is shown as uncertain in Table 12.6. Optimization of the FP and FN parameters is a critical element in ASV. Obviously, the aim is to accept or reject compounds with an almost 100% certainty of success, while the rest must be analyzed by an expert because the automated system could not classify them unambiguously. The expert only looks at the uncertain band (Table 12.6), trusting the system for positives and negatives. The uncertain band can be determined by looking at the threshold at which the negative predictive value (NPV, Table 12.5) becomes 1, meaning 100% accurate classification (no FNs). The same can be done for the upper limit by looking at the threshold at which the PPV = 1 (positive predictive value), that is, there are no FPs. However, such a perfect classification would result in too wide a yellow band and

Table 12.6 A negative threshold (NT) and positive threshold (PT) are used to categorize the ASV results.

ASV result

*1 to NT

NT to PT

PT to+1.0

Classification

Inconsistent

Uncertain

Consistent

Result scenario

True negative False negative

Uncertain

True positive False positive

User action

None

Manual evaluation

None

They are important to minimizing the number of false negatives and false positives while also keeping the number of ambiguous structures low.

12.4

Performance of the Automated Structure Verification Systems

consequently the number of spectra needed to be evaluated manually will be unacceptably high. In practice, it is therefore more reasonable to assume some level of risk. We have found that our ASV system gives optimal results with NT = −0.3, which corresponds to 95% accurate negative prediction and with PT = +0.3 with an 80% accurate positive prediction. Of course, this latter value is subjective and largely depends on the similarity of the NCSs. We have tested the performance of ASV with a sample set consisting of 220 1 HNMR spectra recorded in DMSO and their corresponding structures obtained from different sources. Some of these structures are publicly available, while others have been obtained from several pharmaceutical companies: all are commercial compounds. Overall, this data set represents a wide chemical space. Assuming the thresholds NT = −0.3 and PT = +0.3, when ASV was run using only 1 H-NMR data, only seven FNs were found, which is equivalent to a false negative rate (FNR) of 4.3% (FNR = 100 − Sensitivity). When ASV was run against 220 NCSs generated automatically with MolSimNMR using an average similarity score of 0.80, the system produced 40 FPs, corresponding to a false positive rate (FPR) of 31.7% (FPR = 100 − Specificity) when ASV is run using 1 H-NMR spectra only (Table 12.7). When HSQC data are added, we see a significant improvement, especially in the performance with respect to FP. As it can be seen in Table 12.7, the number of FPs reduces from 40 to 20, as is also reflected in the specificity and FPR metrics. This is a consequence of better assignments of diastereotopic protons and labile proton detection as well as the addition of the 13 C chemical shift information into structure evaluation. For example, in the case of O alkyl and N alkyl groups in a molecule, the 1 H data alone are not usually adequate to distinguish them, and FPs or FNs can easily ensue. The 13 C-NMR data, however, are beautifully discriminating, representing a case where HSQC data will usually add significantly to the analysis. With the ASV system now working, we can assess our initial assumptions that we used for the Bayesian analysis in Table 12.1. The assumption of >95% correct identification of TPs is shown to be valid for this test set of 220 structures and 1 H-NMR data alone. When 1 H and HSQC data are used, the basic assumptions of Table 12.1 are also supported.

Table 12.7 Summary results for ASV using 220 spectra and positive and negative control structures. Experiment 1H 1 H + HSQC

False negatives Sensitivity (%) FNR (%) False positives Specificity (%) FPR (%)

7 4

95.7 97.5

4.3 2.5

40 20

68.3 84.1

FNR = False negative rate (100 − sensitivity) and FPR = false positive rate (100 − specificity).

31.7 15.9

489

490

12

An Integrated Approach to Structure Verification Using Automated Procedures

12.5 Conclusions

We have described a collection of sophisticated algorithms that can be applied to various forms of the question of whether the NMR data for a molecule supports its purported structure. This artificial intelligence can be analogous to the product of a specialized and experienced analytical NMR spectroscopist. We describe a scenario where the technology is applicable and useful. The algorithm must be given the best chance of success by adjusting the processes of data collection and basic processing, and these are discussed in detail. Failure to adhere to these will seriously affect the performance. We have described the major elements of an ASV functionality by focusing on each critical component in turn. While testing is possibly more of an art than a science, we describe this in general terms and how the system devised by Mestrelab Research fares in this regard. It seems reasonable to conclude that this system is at a stage in early 2013 where it can very reasonably be put to good use under the advised conditions. This is, however, still an area of intense development and significant improvements will be realized. The addition of other spectroscopic data can play a significant, special role in some circumstances: this will be the topic of future discussion. It is clear that there is no single ASV functionality to meet all needs, and users should think of expectation under carefully prescribed conditions. Matching performance with this expectation is then, to some degree, a question of choosing the input data wisely, and adjusting pass/fail thresholds. Finally, while the system described here uses only 1 H and HSQC data, it has been designed in a way that can easily incorporate other NMR information (i.e., HMBC) as well as MS data.

Acknowledgments

The authors thank John Hollerton and Gary Sharman who inspired the Bayesian analysis and the workflow of Figure 12.1.

References 1. Rabi, I.I., Zacharias, J.R., Millman, S.,

5. Arnold, J.T., Dharmatti, S.S., and

and Kusch, P. (1938) Phys. Rev., 53, 318–318. 2. Purcell, E.M., Torrey, H., and Pound, V.R. (1946) Phys. Rev., 69, 37–38. 3. Bloch, F., Hansen, W., and Packard, M.E. (1946) Phys. Rev., 70, 474–485. 4. Proctor, W.G. and Yu, F.C. (1950) Phys. Rev., 77, 717–717.

Packard, M.E. (1951) J. Chem. Phys., 19, 507–507. 6. Nicolaou, K.C. and Snyder, S.A. (2005) Angew. Chem. Int. Ed., 44, 1012–1044. 7. Dai, J., Liu, Y., Zhou, Y.-D., and Nagle, D.G. (2007) J. Nat. Prod., 70, 1824–1826. 8. Podlesny, E.E. and Kozlowski, M.C. (2012) J. Nat. Prod., 75, 1125–1129.

References 9. Chemical and Engineering News

10.

11.

12. 13. 14. 15. 16.

17. 18.

19.

20.

21.

22.

23. 24.

25.

http://cen.acs.org/articles/90/web/2012/ 05/Bosutinib-Buyer-Beware.html (accessed 21 May 2013). Napolitano, J.G., Lankin, D.C., Graf, T.N., Friesen, J.B., Chen, S.N., McAlpine, J.B., Oberlies, N.H., and Pauli, G.F. (2013) J. Org. Chem., 78, 2827–2839. Belkic, D. (2005) Quantum Mechanical Signal Processing and Spectral Analysis, Taylor & Francis Group, London. Swalen, J.D. and Reilly, C.A. (1962) J. Chem. Phys., 37, 21–29. Castellano, S. and Bothner-By, A.A. (1964) J. Chem. Phys., 41, 3863–3869. Diehl, P., Sykora, S., and Vogt, J. (1975) J. Magn. Reson., 19, 67–82. Laatikainen, R. (1991) J. Magn. Reson., 92, 1–9. Laatikainen, R., Niemitz, M., Weber, U., Sundelin, J., Hassinen, T., and Vepsäläinen, J. (1996) J. Magn. Reson., A120, 1–10. Laatikainen, R. (1988) J. Magn. Reson., 78, 127–132. Stephenson, D.S. and Binsch, G. (1978) J. Magn. Reson., 32, 145–152, and references cited therein. Stephenson, D.S. (1995) Analysis of spectra: automatic methods, in Encyclopedia of NMR (eds D.M. Grant and R.K. Harris), John Wiley & Sons, Ltd, Chichester. Hamper, B.C., Snyderman, D.M., Owen, T.J., Scates, A.M., Owsley, D.C., Kesselring, A.S., and Chott, R.C. (1999) J. Comb. Chem., 2, 140–150. Keifer, P.A., Smallcombe, S.H., Williams, E.H., Salomon, K.E., Mendez, G., Belletire, J.L., and Moore, C.D. (2000) J. Comb. Chem., 2, 151–171. Bernstein, M.A. and Stoddart, S. (2006) Magn. Reson. Chem., 44 (12), 1102–1108. Griffiths, L. and Bright, J.D. (2002) Magn. Reson. Chem., 40, 623–634. Golotvin, S.S., Vodopianov, E., Lefebvre, B.A., Williams, A.J., and Spitzer, T.D. (2006) Magn. Reson. Chem., 44, 524–538. Griffiths, L., Beeley, H.H., and Horton, R. (2008) Magn. Reson. Chem., 46, 818–828.

26. Golotvin, S.S., Vodopianov, E., Pol,

27. 28. 29. 30. 31.

32. 33. 34. 35.

36. 37.

38. 39. 40.

41. 42.

43. 44. 45.

R., Lefebvre, B.A., Williams, A.J., Rutkowske, R.D., and Spitzer, T.D. (2007) Magn. Reson. Chem., 45, 803–814. Plainchont, B. and Nuzillard, J. (2013) Magn. Reson. Chem., 51, 54–59. Nuzillard, J. (2003) Chin. J. Chem., 21, 1263–1267. PERCH Solutions www.perchsolutions. com (accessed 18 March 2013). Hoch, J.C. and Stern, A.S. (1996) NMR Data Processing, Wiley-Liss, New York. Belkic, D. and Belkic, K. (eds) (2010) Signal Processing in Magnetic Resonance Spectroscopy with Biomedical Applications, Taylor & Francis Publishers, London. Bartholdi, E. and Ernst, R.R. (1973) J. Magn. Reson., 11, 9–19. Malz, F. and Jancke, H. (2005) J. Pharm. Biomed., 38, 813–823. Bourg, S. and Nuzillard, J. (1988) J. Magn. Reson., 134, 184–188. Claridge, T.D. (2008) High Resolution NMR Techniques in Organic Chemistry, Tetrahedron Organic Chemistry, Elsevier. Ernst, R.R. (1966) Adv. Magn. Reson., 2, 1–135. Ernst, R.R., Bodenhausen, G., and Wokaun, A. (eds) (1987) Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Oxford University Press, Oxford. Traficante, D.D. and Ziessow, D. (1986) J. Magn. Reson., 66, 182–186. Ernst, R.R. and Anderson, W.A. (1966) Rev. Sci. Instrum., 37 (1), 93–102. Harris, R.K., Becker, E.D., Cabral de Menezes, S.M., Goodfellow, R., and Granger, P. (2001) Pure Appl. Chem., 73, 1795–1818. Pauli, G.F., Jaki, B., and Lankin, D. (2007) J. Nat. Prod., 70 (4), 589–595. Keyes, P., Hernandez, G., Cianchetta, G., Robinson, J., and Lefebvre, B. (2009) Magn. Reson. Chem., 47 (1), 38–52. Plainchont, B. and Nuzillard, J. (2012) Magn. Reson. Chem., 51, 54–59. Reynolds, W.F. and Enríquez, R.G. (2002) J. Nat. Prod., 65, 221–244. Kay, L.E., Keifer, P., and Saarinen, T. (1992) J. Am. Chem. Soc., 114, 10663–10665.

491

492

12

An Integrated Approach to Structure Verification Using Automated Procedures

46. Mestrelab Research Mnova Verify

47. 48. 49. 50. 51. 52.

53.

54.

www.mestrelab.com (accessed 23 July 2014). Modgraph www.modgraph.co.uk (accessed 21 May 2013). Robien, W. (1998) Nachr. Chem. Technol. Lab., 46, 74–77. Bremser, W. (1978) Anal. Chim. Acta, 103, 355–365. Chen, L. and Robien, W. (1993) Anal. Chem., 65, 2282–2287. Fürst, A. and Pretsch, E. (1990) Anal. Chim. Acta, 229, 17–25. Bürgin Schaller, R., Munk, M.E., and Pretsch, E. (1996) J. Chem. Inf. Comput. Sci., 36, 239–243. Abraham, R.J. and Mobli, M. (2004) Spectrosc. Eur., 6, 16–22, and references cited therein. Sykora, S. (1968) Collect. Czech. Chem. Commun., 33, 3073–3080.

55. States, D.J., Haberkorn, R.A., and Ruben,

D.J. (1982) J. Magn. Reson., 48, 286–292. 56. Marion, D. and Wüthrich, K. (1983)

57.

58. 59.

60. 61.

Biochem. Biophys. Res. Commun., 113 (3), 967–974. Cobas, C., Seoane, F., Domínguez, S., and Sykora, S. (2010) Spectrosc. Eur., 23 (1), 26–30. Savitzky, A. and Golay, M.J.E. (1964) Anal. Chem., 36, 1627–1639. Hugo, E., Gottlieb, H.E., Kotlyar, V., and Nudelman, A. (1997) J. Org. Chem., 62, 7512–7515. Sokolova, M. and Lapalme, G. (2009) Inf. Process. Manage., 45 (4), 427–437. Hernández, G., Cianchetta, G., and Keyes, P. eds (2011) MolSimNMR: a molecular similarity method predictive of NMR data similarity. Proceedings of the 52nd ENC Conference, April 10–15, 2011, Monterey, CA.

493

13 On the Search for the Appropriate Techniques for Structural Elucidation of Small Molecules María Magdalena Cid and Jorge Bravo

13.1 Introduction

Nature has provided us with a vast complexity of and boundless abundance of structural motifs whose variability is based on biological and geographical diversity. Molecules constitute the language of chemistry and the structure of a molecule contains specific pieces of information that are not always easy to elucidate. A classical review on structure misassignments was published in 2005 by Nicolaou and Snyder [1] in which they state that imaginative detective work and chemical synthesis have important roles to play in the process of solving Nature’s most intriguing molecular puzzles. There is a long way to go before natural product characterization can be considered a process devoid of adventure, discovery, and even unavoidable pitfalls. Maier in 2009 [2] presented a review covering the time period between 2005 and 2009 in which the importance of total synthesis in structural revisions of natural products was highlighted. Unless relevant synthetic work is carried out, errors in structural assignments are sometimes not detected. As McPhail and coworkers [3] mentioned in 2011 in a review focused on structural revisions of marine natural products that appeared within the 2005–2010 period, considerable “detective work” remains to be done in structure elucidation, in spite of the spectacular advances in spectroscopic techniques. Even under these circumstances, there are examples that have needed repeated revisions to arrive at the correct structural assignment. In this context, we have recently performed a search in the SciFinder data base using the term “structure revision” and more than 300 examples of structure revisions were found in the last 4 years. From these data, it is evident that the number of publications in which the structures of new natural products are incorrectly determined is quite large, and reducing this stream of errors is clearly an important challenge. Several errors, in regard to the structural elucidation of natural products, could be avoided if the plausible biosynthetic [4] or phylogenetic [5] origin of the target had been taken into account. Structure Elucidation in Organic Chemistry: The Search for the Right Tools, First Edition. Edited by María-Magdalena Cid and Jorge Bravo. © 2015 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2015 by Wiley-VCH Verlag GmbH & Co. KGaA.

494

13

On the Search for the Appropriate Techniques for Structural Elucidation of Small Molecules

H

OH B

1

Figure 13.1 Concerted ring closure and deprotonation proposed for the formation of edaxadiene (1).

Thus, the unlikeliness of the enzymatic process, which would insert an allylic cation into an allylic C–H bond followed by the loss of a proton to explain the formation of edaxadiene (1) (Figure 13.1), a diterpene isolated from Mycobacterium tuberculosis, led to its structural revision from a tricyclic structure [6] to a [4.4.0]bicyclodecane [7]. This molecular structure proved to be that of nosyberkol (2) [8], as later confirmed by total synthesis. The authors of the revised structure pointed out that “the 13 C NMR spectrum of edaxadiene showed a peak at 72.9 ppm which suggested the presence of a tertiary alcohol, which could readily lose H2 O to give the high mass peak corresponding to C20 H32 .” Noticeably, the authors that firstly reported the edaxadiene structure described a heteronuclear multiple-bond coherence (HMBC) contact between positions 7 and 15 that is obviously impossible in the final structure. 11 12 9

8 7

OH

13

14 15

2

It is then apparent that determining the structure of complex naturally occurring molecules involves a multifaceted investigation that exploits several resources and expertise, and often results in a long and winding path to the final target. Given such complexity, it is desirable to devise novel ways that help to sort out candidate structures, especially at the spectroscopic stage [9]. Modern computational chemistry methods, especially density functional theory (DFT), have proved to be excellent tools for determining molecular structures of natural or synthetic origin [10]. High-level DFT calculations have helped the structure determination of several compounds and the structural revision of others. In fact, the combination of synthetic, spectroscopic, and computational prediction of 13 C NMR spectra led the group of Tong and Lin to conclude that three structures reported as different are in fact the same, cephalosporolide C (3) [11].

13.2

OH

HO

O

The Challenge of Structural Determination

N H

HO O N

Me

CF3

CF3

O 3

4

Herein, we give an overview of the tools that play a major role in structure elucidation, highlighting those that are not commonly used or have not been treated as such in the preceding chapters. Examples are solid-state NMR, which correlates with experiments in anisotropic media, and ROA (Raman optical activity), which is the equivalent to optical rotation in the vibrational spectral region. We present these using some representative examples, arbitrarily chosen; it is not our aim to be comprehensive. Many examples show that until the compound is synthesized, the molecular structure cannot be taken as definitive. For instance, nearly 40 years passed before the correct structure of mefloquine (4) was established unambiguously [12]. Mefloquine is a chiral molecule whose racemate is used in malaria prophylaxis. However, it is believed that the (−)-mefloquine stereoisomer is the agent responsible for some of the adverse side effects. The exact knowledge of the absolute configuration (AC) is, obviously, a critical aspect in pharmaceutical sciences [13].

13.2 The Challenge of Structural Determination

Structural determination of chemical compounds is commonly a difficult task and frequently entails the combined use of several tools rooted in different physical principles. Many of these tools are spectroscopies because they involve interactions between molecules and electromagnetic radiation (Chapter 1), as opposed to mass spectrometry (MS) (Chapter 4). Before the explosion of spectroscopies, such processes relied on chemical degradation or derivatization followed by partial or total synthesis. The development of quantum theory and its application to molecular structure has provided an important additional tool for structure determination. In the same sense, the structure elucidation process has also benefited from the evolution of computer-assisted structure elucidation (CASE), which proposes a plausible structure based on correlations between spectral and structural features (Chapter 12). Nuclear magnetic resonance (NMR) and X-ray crystallography are the two techniques of choice for structure determination of compounds of natural or synthetic origin, NMR being the most important and widely used method in solution (Chapters 7, 8, and 11). The combination of MS data with the presence or absence of diagnostic NMR resonances constitutes a concise way to distinguish between

495

496

13

On the Search for the Appropriate Techniques for Structural Elucidation of Small Molecules

known and new molecular structures. In some cases, however, these techniques do not succeed in the unambiguous determination of the chemical structure of unknown compounds. Special caution must be taken in cases in which the ratio of protons to other elements is very low (see below) and single crystals are not available. Help to ensure an unambiguous structure determination by these more conventional techniques may come from atomic resolution scanning probe microscopy (SPM) [14], which maps the atoms and the electron density of a molecule. The usefulness of this technique combined with quantum-chemical calculations has been demonstrated in the structure determination of the natural product cephalandole A (5), a structure that had already been revised and proved challenging to NMR techniques [15]. O O N NH

5

Cephalandole A is a suitable compound to be studied by SPM because it is planar and, therefore, can lie flat on an adsorbing surface. Currently, these are the requirements for this technique to be successful. Because SPM maps the atoms and the electron density of a single molecule, it may not present a structure representative of the bulk solid or solution. This technique cannot be considered of routine use, but should be taken into account in those cases where the traditional ones fail [16]. Single crystal X-ray diffraction, as well as total synthesis, often gives definitive support to a particular molecular structure. However, the need for a single crystal of suitable size and quality imposes a limitation on the scope of X-ray diffraction (limitation that can be minimized if there is access to other X-ray sources, such as synchrotron facilities or free-electron lasers). In such a case, powder X-ray diffraction data, although more difficult to analyze than single crystal X-ray diffraction, due mainly to overlapping peaks, has offered new opportunities [17]. The limiting step in the structure determination process from powder diffraction data is quite often to find a reliable unit cell at the indexing stage, which can be hindered by the presence of different polymorphs. Another limitation when trying to determine the structure of a powder sample is the presence of preferred orientations, although experimental approaches have been developed to alleviate the effects of the anisotropy of the sample [18]. The diffraction pattern of a crystalline solid, whether obtained from a single crystal or a powder, gives the dimensions of the unit cell from the positions of the diffraction maxima. They are characterized by the Miller indices (h, k, l) and the position of atoms from the relative intensities of those maxima because they are

13.3

Tools: Mass Spectrometry (MS)

dependent on the distribution of scattering points within the periodic unit. In the case of X-ray diffraction, the structure factor, which is obtained from the diffraction maximum, is related to the electron density within the unit cell and hence to the crystal structure. Although single crystal diffraction gives more precise data, a properly refined crystal structure from powder diffraction data provides reliable information on the arrangement of atoms and molecules in the crystal structure. The applicability to structure determination of powder X-ray has expanded considerably due to improvements in measuring the individual peak intensities over the last two decades. 13.3 Tools: Mass Spectrometry (MS)

Because MS measures the relative molecular mass of molecules, it provides important information not available through spectroscopic methods. It requires very little sample due to its high sensitivity, and the fragmentation of the species produced by ionization of the subject molecule frequently gives very important clues to its composition (see also Chapter 4). There are different ionization methods available depending on the type of information sought. Electron impact ionization (EI) and chemical ionization (CI) usually produce a high fragmentation of the sample molecule providing important structural information. EI employs an electron beam as a source of fragmentation, and CI uses a reagent gas (NH3 , CH4 ). Softer ionization methods can be employed when it is important to detect molecular ions. Among them, fast atom bombardment (FAB), liquid secondary ion mass spectrometry (LSIMS), electrospray ionization (ESI), and matrix-assisted laser desorption ionization (MALDI) are the most widely used. In the case of FAB and LSIMS, beams of Xe or Cs+ , respectively, are employed as a source of sample ionization. In ESI, an aerosol of charged droplets is obtained by applying a high voltage to a sprayed sample solution. Eventually, sample ions are produced by solvent evaporation from the droplets. In MALDI, the sample molecules, dissolved in an absorbing matrix, are irradiated with a laser. The matrix transfers the laser energy to the sample resulting in its ionization. Once the ions have been obtained, they are transferred to the mass analyzer (Section 4.2.2) to be separated according to their mass-to-charge ratio. Commonly used mass analyzers employ electric and/or magnetic fields to accomplish this task. Measurement of mass to charge ratios (m/z) permit the masses of each charged species to be ascertained if the charge is known. In such an arrangement the highest m/z will correspond to the singly charged intact molecule whose exact detected mass will depend on the ionization method. In MS, individual ionized molecules are measured, in contrast to UV, IR, or NMR spectroscopies in which the bulk sample is analyzed. Consequently, it is possible to distinguish molecules containing different isotopes such as 79 Br and 81 Br. The intensity ratio of peaks in the region of the molecular ion provides information on the composition of the sample since there are several atoms that are not monoisotopic (such as H, C, Br, Cl, Si, and S). In addition to producing an intact

497

498

13

On the Search for the Appropriate Techniques for Structural Elucidation of Small Molecules

ion, in some cases, depending on the ionization technique, sufficient energy is transferred to vibrational modes of the molecule so that it undergoes bond ruptures, giving rise to ionic and neutral fragments. Those fragments that retain the charge will also be deflected in the magnetic field but to a greater extent than the molecular ions due to their lower mass. The signal generated at the detector is linearly dependent upon the number of ions of any particular mass arriving at the analyzer. It is worth mentioning that compounds containing heteroatoms may lose smaller molecules. In this regard, the liability of the functional group is a critical parameter. These cleavages end up leading, in many cases, to proposed incorrect structures, as in the case of Malhamensilipin A (6), a bisulfate bioactive chlorosulfolipid metabolite isolated from the freshwater alga Poterioochromonas malhamensis, which was initially thought to be the monosulfate analog (7) [19]. SO3– Cl O

Cl

Cl

Cl

C7H15

OH Cl

Cl

C7H15 7

Cl

Cl

Cl

OSO3–

Cl

Cl

Cl

7

OSO3–

7

6

Water is another commonly encountered molecule, which is lost. Thus, a product isolated from the marine sponge Haliclona fascigera and identified as (+)helianane (8) [20] on the basis of extensive NMR studies (1 H, 13 C, HMBC, COSY, APT) and HR FABMS, was found after much synthetic work to be curcudiol (9), a natural product found in the marine sponge Arenochalina sp. [21].

OH O 8

9

OH

Although total synthesis is usually the most employed method to correct structural misassignments, in this case, several (up to seven) total synthesis studies agreed with the initially proposed structure and only in one case did the authors report an important difference between the optical rotation (OR) of both products, +33.4∘ and +80∘ , for the synthetic and natural one, respectively. A final synthetic study showed that all previous studies failed to disclose the real structure. Although the biomimetic synthesis of the ethereal ring for helianane from curcuphenol, as proposed in the original paper [20], was unsuccessful, the eightmembered ring could be synthesized by a different synthetic strategy. In doing so, several inconsistencies when comparing the NMR spectra of the natural product and the synthetic one were detected. The most obvious differences were that many of the carbon resonances were broad, as a consequence of conformational flexibility of the ring on the NMR time scale and there was a 10 ppm difference

13.4

Tools: Solution NMR Spectroscopy

in the resonance of the aliphatic carbon atoms bearing the oxygen in 8 and 9. Interestingly, the molecular formula of the natural product was determined to be C15 H22 O by HR FABMS – datum that could be explained by a dehydration process. Similar ethereal-dihydroxy misassignments were discovered by Takahashi et al. (compounds 10, 11) [22, 23]. In these cases, the splitting pattern of certain methylene protons is what drew the attention of researchers, because, in general, such protons should not be equivalent if they are embedded in a ring and would ultimately lead to two complex signals in the 1 H NMR spectra. The original structure proposed, 10, was thus incompatible with the NMR evidence, and 11 was found to be the correct structure. EtO2C

EtO2C

O

O OH

n

HO

O

n

HO

R 10 n = 3, R = Et n = 4, R = Me

OH

R

11 n = 3, R = Et n = 4, R = Me

13.4 Tools: Solution NMR Spectroscopy

NMR is the most important and widely used method for structure determination of natural products in solution. The change from continuous wave (CW) to Fourier transform (FT) NMR spectrometers was a milestone for NMR spectroscopy. This fact allowed the use of pulse sequences, permitting the detection of isotopes of low natural abundance and low sensitivity and also the development of two-dimensional experiments. The most commonly studied nucleus is 1 H, which has the highest sensitivity among all magnetic isotopes, followed by 13 C (lower sensitivity, a quarter of that of 1 H, and less natural abundance, 1 against 100% in the case of 1 H). Differences in the chemical shifts and coupling constants of nuclei can be interpreted to yield chemical structures. Chemically equivalent nuclei must resonate at the same chemical shift and have the same chemical properties, while magnetically equivalent nuclei must have the same couplings, known as scalar couplings, to all other nuclei, mainly via two- or three-bond connections. Couplings over more bonds are generally referred to as long-range couplings, although three bond (vicinal) coupling is the most used in structure determination. Direct coupling is known as dipolar coupling and, although not seen in solution spectra because it averages to zero, its presence can be detected using suitable experimental techniques [24]. Dipolar coupling provides the mechanism for one of the most useful NMR phenomena available, the nuclear Overhauser effect (NOE).

499

500

13

On the Search for the Appropriate Techniques for Structural Elucidation of Small Molecules

The concurrence of several NMR techniques allowed the full characterization of vitamin B12 structure (12) in 1956 [25] and its biosynthetic pathway in 1994, both constituting milestones [26]. Constitution (bond connectivity) is commonly determined by qualitative chemical shift analysis and data from a plethora of 1D and 2D experiments, being the last ones in the foundation of the most contemporary structure determinations. A 2D NMR spectrum shows the correlation of two frequency variables and is obtained by performing the Fourier transform twice. 2D NMR experiments can be divided into three groups: J-resolved spectra (correlating chemical shifts with coupling splittings, also known as J,δ-spectroscopy, whose main application field is the analysis of crowded spectra with strong signal overlapping), chemical shift correlation (correlating chemical shifts in both frequency axes, homonuclear and heteronuclear COSY and 2D-NOE being the key 2D NMR experiments, which offer relevant structural information via spin connectivities shown by the crosspeaks), and multiple quantum spectra (correlating heteronuclear chemical shifts where a special pulse sequence is used to excite a non-allowed transition for which to be detected its magnetization has to be transferred to a single-quantum transition, such as in 1 H-detected HMBC). As Kerry L. McPhail et al. have shown in their review [3], the basis of the majority of misassignments is from NOE data, followed closely by interpretation of HMBC data. O

H2N

H2N O H C 3 H2N

O CH3

H CH3 CN

N

H3C O H H

N Co + N

N

H2N

H

NH2

CH3 CH3

CH3 CH3 H

H N H3C O

H

O

O

O

O P O OH –O

N N

NH2

CH3 CH3

O HO

12

Since HMBC experiments use a predefined scalar C–H coupling constant (3 J CH ), the differentiation of geminal (two-bond) scalar C–H coupling constant (2 J CH ) from 3 J CH and four-bond scalar C–H coupling constant (4 J CH ) from 3 J CH correlations is a difficult task in HMBC spectra. The combination of HMBC and 1,1- or 1,n-ADEQUATE experiments differentiates 2 J CH from 3 J CH correlations

13.5

Tools: Solid-State NMR Spectroscopy

because in ADEQUATE experiments carbons and protons that are ONLY two bonds apart are correlated and therefore H–C–C moieties are detected. Thus, it is now possible to circumvent the limitations imposed on determining the structure when a ratio of 1 H to 13 C and other heavy atoms is below two, the carbon molecular skeleton is broken into two parts by heteroatoms or there is a quaternary carbon that is four bonds apart from the nearest proton. In the difficulties derived from this low ratio may reside some of the incorrectly assigned structures reported in the literature. Gary E. Martin and coworkers [27] have shown the utility of the combination of inverted 1 J CC 1,n-ADEQUATE with cryoprobe technology to solve the structure of the highly proton-deficient alkaloid, staurosporine (13).

HN O

O

N

N O NH 13

Routinely, the relative configuration (RC) of stereogenic centers is established by a combination of NOE-based experiments and torsion angle determination through vicinal scalar couplings and/or derivatization protocols [28]. However, in some cases, such as complex natural compounds, unequivocal determination of the RC cannot be achieved due to the high structural complexity. In this regard, the quantum-chemical prediction of NMR chemical shifts and quantitative comparison with those experimentally obtained provide invaluable information for the verification of constitution, conformations, and RCs [10, 29]. Another technique gaining relevance in determining configurational and conformational issues is the use of residual dipolar couplings (RDCs) obtained by partial alignment of molecules inside an anisotropic medium [30]. This technique has proved to be extremely powerful for the one-shot determination of configuration in molecules with many stereogenic centers (Chapter 8).

13.5 Tools: Solid-State NMR Spectroscopy

Solid-state NMR spectroscopy is a powerful tool for structural elucidation of samples that cannot be dissolved or melted, and it can be applied not only to crystal powders but also to amorphous materials (Chapter 6). Its utility can be highly improved when used in combination with other techniques, such as computational chemistry. The main differences between fluid- and solid-state NMR spectra come from how molecular motion affects the different interactions

501

502

13

On the Search for the Appropriate Techniques for Structural Elucidation of Small Molecules

that nuclear spins experience when they are under the influence of an external magnetic field. In fluid-state NMR, molecular tumbling eliminates the inherent anisotropy of interactions such as chemical shift, dipolar (through space) spin–spin couplings, and electric quadrupolar coupling for nuclei with nuclear spin I > 1∕2 leading to high-resolution NMR spectra. However, in the solid state, all these anisotropic interactions contribute to broadening the spectral lines and result, in most cases, in featureless broad humps from which it is not possible to extract any useful information. However, paradoxically, these spectra contain much information. Consider the simple case of a pair of protons separated by a distance r and under the influence of an external magnetic field B0 (Figure 13.2a). The dipolar coupling between both nuclear spins produces a splitting described by Δν(Hertz) = (3𝛾 2 ℏ∕4πr3 )(3cos2 𝜃 − 1)

(13.1)

where 𝛾 is the magnetogyric ratio of the proton and 𝜃 is the angle formed by the internuclear vector and the external magnetic field. The maximum splitting, 180 kHz, will occur when cos𝜃 = 1 (𝜃 = 0∘ ) and for an internuclear distance of r = 1 Å, being one order of magnitude larger than the entire chemical shift range commonly used for protons. If instead of a pair of protons we were dealing with a macroscopic powdered sample, the NMR spectrum will consist of a superposition of many lines corresponding to the couplings between pairs situated at different distances and with different values of 𝜃 giving an anisotropically broadened spectrum. This is illustrated in Figure 13.2, in which the 1 H solution and solid-state NMR spectra of adamantane are compared on the right side. An interesting case arises when a solid-state NMR spectrum of a powdered sample containing isolated nuclear spin pairs with a fixed r value is recorded. This is the case for the 1 H NMR spectrum of solid CaSO4 ⋅ 2H2 O, in which the distance between hydrogen atoms belonging to different water molecules is too long to produce a measurable coupling. In this case what is observed is a typical

(b)

20 kHz

B0 θ r (a)

(c)

770 Hz

Figure 13.2 Through-space dipolar coupling (a). A comparison of the static solid-state (b) and solution-state 1 H NMR spectra of adamantane (c).

13.5

Tools: Solid-State NMR Spectroscopy

B0 90° (d)

Magic angle spinning

B0 54.74°

(c)

B0 0° (b)

Powder all orientations (a)

Hz Figure 13.3 (a) Solid line: Pake doublet for the case of dipolar interaction of 1 H–1 H spin pairs randomly oriented. The doublet is composed of two mirror images subspectra due to couplings with 1 H site with mI = ± 1∕2 spin states. Dotted line: subspectrum for couplings with 1 H site with mI = 1∕2.

(b–d) Dipolar interaction of a spin pair at different orientations of the internuclear vector respect to B0 ; (b) 𝜃 = 0∘ , maximum splitting, minimum intensity; (c) 𝜃 = 54,74∘ , no splitting, magic angle spinning; and (d) 𝜃 = 90∘ and 270∘ , maximum intensity.

“powder pattern,” also known as a Pake doublet (Figure 13.3), derived from all the possible orientations of the internuclear vector with respect to the external field. From the distance between the two horns (𝜃 = 90o and 270∘ ) the internuclear separation can be evaluated [31]. It is worthy of note that the splitting disappears when 𝜃 = 54.74∘ . This value can be easily extracted from Equation 13.1 by solving 3 cos2 𝜃 − 1 = 0, and is called magic angle because when a solid sample is physically rotated around an axis inclined at this angle with respect to B0 , a line narrowing is obtained because the anisotropic broadening is averaged to zero.

503

504

13

On the Search for the Appropriate Techniques for Structural Elucidation of Small Molecules

σ 33 σxx σxy σxz σ MOL =

σ 11 σ PAS

σyx σyy σyz

=

σzx σzy σzz (a)

0

0

0

σ 22

0

0

0

σ 33

σ 22 σ 11

(b) B0

(c)

σ 33 B0

θ σ 22 φ (d)

σ 11

(e)

Figure 13.4 The shielding tensor 𝜎: (a,b) matrix description; (c) graphic representation; and (d,e) orientation with respect to B0 .

When the sample does not contain quadrupolar nuclei and the nucleus to be studied is isolated either because it is a nucleus with low natural abundance (e.g., 13 C, 15 N, etc.) or the molecule contains only one nucleus of this type (e.g., 31 P), the only interaction that broadens the spectrum is the chemical shift anisotropy (CSA), because the resonance frequency of the nucleus depends on the orientation of the molecule. This orientation dependence of the CSA (as well as those of dipolar and quadrupolar couplings) can be represented by a second-rank tensor, meaning that the interaction can be mathematically described by a 3 × 3 matrix, 𝜎 MOL (Figure 13.4a). This, in turn, can be graphically represented by an ellipsoidal surface (Figure 13.4c). The distance from the center to where B0 intersects the surface of the ellipsoid is a measure of the chemical shift for this particular orientation of the molecule with respect to B0 Figure 13.4 d-e. This matrix can be diagonalized, meaning that, by means of an adequate coordinate transformation, a new tensor 𝜎 PAS (Figure 13.4b) (PAS comes from the principal axes system) with three principal components can be obtained. These components are the three major axes of the ellipsoid and they are labeled in order of increasing shielding (i.e., 𝜎 11 ≤ 𝜎 22 ≤ 𝜎 33 ). The average of these values gives the isotropic chemical shielding, 𝜎 iso , which is coincident with what is measured in solution: 𝜎iso = 1∕3 (𝜎11 + 𝜎22 + 𝜎33 ) The powder pattern that contains the frequencies corresponding to all the possible orientations of the chemical shift tensor with respect to B0 (Figure 13.5) can be

σiso (a)

σ

σiso

σ

(b)

σ

13.5

Tools: Solid-State NMR Spectroscopy

σiso

σ

(c)

σ11 σ22 σiso (d)

Figure 13.5 Theoretical powder patterns (a) isotropic, (b,c) axial, and (d) anisotropic.

calculated from the equation: ν = ν0 (𝜎11 sin2 𝜃cos2 𝜑 + 𝜎22 sin2 𝜃sin2 𝜑 + 𝜎33 cos2 𝜃) The shape of the powder pattern is governed by the values of the anisotropy (𝛿) and asymmetry (𝜂) parameters, defined by 𝛿 = 𝜎33 − 𝜎 − 𝜎iso 𝜂 = (𝜎22 − 𝜎 − 𝜎11 )∕𝛿 This shape provides information about the symmetry environment of molecular fragments (Figure 13.5). Thus, if the molecule presents spherical symmetry, the chemical shift tensor can be described as a sphere with three equal principal values (𝜎 11 = 𝜎 22 = 𝜎 33 = 𝜎 = 𝜎 iso ) and the shape of the powder pattern will resemble that of the liquid state (isotropic). If the molecule presents axial symmetry, the chemical shift tensor can be described as an ellipsoid of revolution with two equal principal values and different from the third one. If 𝜎 11 = 𝜎 22 ≠ 𝜎 33 the graphical representation will be a prolate and if 𝜎 11 ≠ 𝜎 22 = 𝜎 33 it will be an oblate. The two different principal values are usually indicated by 𝜎 ⊥ and 𝜎 ∥ , indicating the orientation (perpendicular or parallel) of the symmetry axis with respect to B0 . When the molecule under study contains different types of active nuclei (for example, different environments for carbon atoms), the powder pattern corresponding to each type of nucleus will overlap leading to featureless spectra from which it is not possible to extract any useful information. In these cases, the effects of the anisotropic NMR interactions can be suppressed by using the magic angle spinning (MAS) technique in order to obtain narrow line spectra. As an example, the polymorphism of 10-deacetyl-baccatin III (14), a molecule that forms the major portion of the anticancer drug Taxol, was investigated by solid-state NMR and it was compared with the computed and experimental principal values (𝜎 ii ) of 13 C tensors of different polymorphs [32]. This molecule presents two polymorphs, one that includes a DMSO solvate (with a known X-ray structure) and another crystalline form, whose X-ray structure is unknown. By comparing the computed tensors for the two geometries (the X-ray geometry

505

σ33

506

13

On the Search for the Appropriate Techniques for Structural Elucidation of Small Molecules

and a minimum-energy structure) with experimental values it was possible to describe the structure of the “unknown” polymorph. O CH3 OH

HO H3C

CH3

HO

CH3 HO O

H O

O O

O CH3

14

Combining different solid-state NMR techniques, isotope labeling, and computational techniques permits extracting structural information in amorphous phases, which is a very challenging task, in particular in the mesoscopic range of 10–100 Å. This information is needed to understand glass structures, nucleation and growth mechanisms, self-organization, and so on. However, in this way, it was possible to unravel the distribution of conformers in two amorphous phases of triphenylphosphite (TPP) (Figure 13.6a). TPP presents four accessible solid-state phases [33], two amorphous, a-1 and a-2, and two crystalline, c-1 and c-2; c-1 is the commonly found modification. The amorphous state a-2 contains highly correlated domains consisting of clusters that are a few molecules in size and parallely arranged as seen in the crystalline phase c-1. The nature of the phase transformation a-1 → a-2 has been associated with a change in molecular conformation, so a conformational analysis of the different phases is crucial to understand this transformation. A DFT study of TPP shows overall eight structures of similar energy [33]. This information permitted a conformational description of TPP molecules in phases a-1, a-2, and c-1. The isotropic shift (𝜎 iso ), the anisotropy (𝛿), and asymmetry (𝜂) parameters could be extracted for the labeled sites of TPP and they allowed a conformational analysis by comparison of the ab initio calculated values with experimental data. The small differences found in these parameters for the different conformers do not allow a conformational analysis based on the 13 C nuclei, but it can be done using the corresponding parameters for the 31 P nuclei, which show greater differences. In Figure 13.6b, the theoretical simulation of 31 P wide-line NMR spectra for different conformational distributions in a-1, a-2, and c-1 phases is displayed. As can be seen, the simulation [33] (Figure 13.6b) and actual spectra [34] (Figure 13.6c) match very well. Thus, the glassy phase a-1 contains a broad distribution of seven possible conformers, phase a-2 has mainly two conformers, and c-1 has only one conformer.

13.6

O

P

Chiroptical Spectroscopies

O

O

–200 –150 –100 (b)

(a)

(c)

–200

–150

–100

–50

0

Figure 13.6 (a) Tri-(1-[13 C]phenyl)phosphite. Asterisks indicate labeled positions. (b) Theoretical simulations of 31 P spectra for different conformational distributions in a-1 (dotted line), a-2 (dashed line),

50

–50

0

100

50

150

100

150

200

200

and c-1 (solid line) phases. (Adapted with permission from Ref. [33]) (c) 31 P spectra of a-1, a-2, and c-1 phases. (Adapted with permission from Ref. [34].)

13.6 Chiroptical Spectroscopies

The interest in determining the AC of a chiral compound stems from the fact that stereochemistry determines important chemical, biological, and physical properties mainly through molecular and supramolecular interactions. Due to the inherent symmetry of magnetic fields, NMR gives exactly the same observables for mirror-image compounds unless a chiral medium (solvent, chiral ligands) is present. However, it is extremely difficult to assign the AC to each enantiomer since this may involve detailed knowledge of the interaction between the chiral agent and the molecule being studied. As in the case of NMR, ab initio computational methodologies have shown their power in the application of chiroptical spectroscopies to the problem of AC determination in chiral compounds [35, 36], namely, electronic circular dichroism (ECD) [37, 38], optical rotatory dispersion (ORD) [39], vibrational circular dichroism (VCD) [40], and ROA, (see Chapters 3, 5, and 7 and below). The axial chirality in one ellagitannine,

507

508

13

On the Search for the Appropriate Techniques for Structural Elucidation of Small Molecules

roxbin B, (15), was misassigned due to errors in the interpretation of the ECD spectrum [41]. OH HO OH

OH

HO OH

OO

HO

OH

O O

O

O

O O O

HO

O

OH O

HO OH HO

OH OH

15

Chiroptical responses can be accurately predicted using affordable computational methodologies based on DFT if configurational and conformational information are already available, in most cases, from NMR experiments. Therefore, the combined use of NMR, chiroptical spectroscopies, and computational techniques may constitute a complete toolkit for structural analysis from constitution to conformation and to relative and absolute configurations of complex organic compounds. An example of a compound whose chiral discrimination poses great difficulty is a saturated quaternary hydrocarbon bearing similar substituents on the asymmetric carbon atom. Van’t Hoff, in his first publications, recognized that the degree of difference between the four substituents at the asymmetric center might determine whether optical activity would be observed or not; he introduced the term “optically inactive chiral compound.” Although such hidden chirality, which was called cryptochirality, cannot be distinguished using any contemporary technique, it can be transmitted into a visible chirality using asymmetric autocatalysis [42]. A representative example of a cryptochiral molecule is 5-ethyl-5-propylundecane (or (n-butyl)ethyl(n-hexyl)(n-propyl)methane), a naturally occurring compound found in Phaseolus Vulgaris L. that exhibits practically no optical rotation (|𝛼| < 0.001) between 280 and 580 nm [43]. 10

9

11

2

6

8

4 1

3

5

7

16

Another example of such a compound is 4-ethyl-4-methyloctane 16 or (nbutyl)ethylmethyl(n-propyl)methane) whose [α]D 25 and [α]365 23 values of (+)-16

13.6

Chiroptical Spectroscopies

509

of +0.19 (neat) and +0.70 (neat), respectively, show the utility of measuring the optical rotation at shorter wavelength for cryptochiral compounds [44, 45]. While the observed CD of 16 is too small to make a clear (R) or (S) assignment, VCD proved to be suitable because, as for all compounds, it is active in the IR spectral region (Chapter 11) [46, 47]. ROA is a spectroscopic technique that measures vibrational optical activity (VOA) based on the difference in intensity of Raman scattered light, which is right and left circularly polarized due to molecular chirality (Chapter 5). When monochromatic radiation of frequency 𝜈 0 is incident on a non-absorbing sample molecule, some scattering of the radiation occurs. It is a two-photon process (one incident and one scattered) in which the incident photon is annihilated. In most of the scattered radiation, both photons have the same energy, and they account for the Rayleigh scattering or elastic scattering. However, a small portion of the scattered radiation (1 × 10−7 ) perturbs the molecule, producing a transition between different vibrational levels and creating a new photon with different energy (inelastic scattering or Raman scattering). Although the scattered radiation can be measured by observing it in all directions, in an ROA experiment three geometries can be used (Figure 13.7a): forward scattering (when the angle 𝜃 between the incident and scattered radiation is 0∘ ), right-angle scattering (𝜃 = 90∘ ), and backscattering (𝜃 = 180∘ ). Backscattering is the most preferred geometry and it is the geometry chosen to build, until now, the only commercially available ROA apparatus (ChiralRAMAN, BioTools, Inc., USA). Raman scattering can be used to measure VOA because the intensity of Raman scattering from chiral molecules is slightly different for right and left circularly polarized incident light. The parameter used to measure this difference is the dimensionless circular intensity difference (CID), defined as Δ = (I R –I L )∕(I R + I L ) nt ide Inc ght li

d ere att Sc light

Incident light Forward scattering θ = 0°

(a)

Chiral sample

Backscattering Θ

Right-angle scattering θ = 90°

Incident light

θ = 180°

ICP

Chiral sample Scattered light DCP (b)

Sc SCP

Figure 13.7 (a) Directions in which scattered radiation is measured. Θ: angle between incident and scattered radiation. (b) ICP, SCP, and DCP polarization schemes for ROA measurement.

Inc id lig ent ht

att e lig red ht

510

13

On the Search for the Appropriate Techniques for Structural Elucidation of Small Molecules

where I R and I L are the scattered intensities in right and left circularly polarized incident light, respectively. The numerator is the intensity of an ROA band and the denominator is the conventional Raman scattering intensity of the parent band [48]. Because Δ values are ≤10−3 , and Raman scattering is intrinsically very weak, ROA is a very small effect. As a result, ROA spectra are highly susceptible to artifacts, and some ROA spectra are incorrect [49]. ROA was predicted theoretically by Atkins and Barron in 1969 [50], and it was experimentally established by Barron et al. in 1973 [51]. There are three ways by which the diastereomeric interactions between left and right circularly polarized light and a chiral molecule can be measured (Figure 13.7b). Incident circular polarization (ICP) was the original form of ROA to be established theoretically [48] and experimentally [51]. In this method, the incident radiation is modulated between right and left circular polarization, but the scattered radiation is not analyzed with respect to its circular content. Scattered circular polarization (SCP) was first described in 1985 [52] and the first measurement was carried out 3 years later by Nafie et al. [53]. In this case, the circular polarization of the scattered radiation is analyzed while the incident radiation is linearly or naturally polarized. In 1991, the first measurement of dual circular polarization (DCP) was reported [54]. In this method, the incident and scattered light beams are synchronously (DCPI ), or anti-synchronously (DCPII ) modulated between right and left circular polarization states. SCP was the design chosen for the above-mentioned commercial Chiral RAMAN spectrometer. A design extension of this apparatus that permits simultaneous acquisition of all four forms of circular polarization ROA was recently reported [55]. This ICP–SCP–DCP instrument allows comparison of results for the different designs. High-level quantum mechanical calculations are required to unravel the molecular information encrypted in ROA spectra. Although adequate software is nowadays available, there is still a shortcoming when the molecule presents a large number of conformers. In addition, the application of theoretical methods can be limited by the influence of environmental effects and the presence of experimental artifacts. Thus, different solvents can change the conformations, cause the formation of optically active complexes between solvent and solute molecules and, in some cases, dominate chiroptical properties [56]. Fortunately, in the case of VOA spectroscopies, the solvent vibrations can be often distinguished from those of the solute. Enantioenriched (R)-[2 H1 , 2 H2 , 2 H3 ]-neopentane is the archetype of all organic molecules that are chiral due to a dissymmetric mass distribution. It consists of an sp3 carbon chiral center with four methyl substituents that differ only in their isotopic pattern (Figure 13.8a) [57]. This molecule displays a highly symmetric electron distribution and has nine nearly equally weighted conformers (Figure 13.8b) with mutually canceling optical activity that makes the determination of its AC very challenging. Empirical or relative methods, such as chemical correlation, X-ray crystallography, or 1 H NMR anisotropy, in which a reference with known AC is necessary (Chapter 11), cannot be used because of the chemical inertness of the compound. On the other hand, neither X-ray Bijvoet method (no

13.6

Chiroptical Spectroscopies

CH2D

H3C C D2HC

(a)

CD3

(b)

Figure 13.8 (a) Chirally deuterated neopentane. (b) The nine conformers of chirally deuterated neopentane can be obtained by changing the relative positions of CH2 D and CHD2 groups. Hydrogen: white small spheres and deuterium: gray small spheres.

heavy atoms in the molecule to produce the anomalous scattering effect; see Chapter 11) nor electronic optical rotation (EOR) or circular dichroism (CD) (no chromophoric groups in the molecule), is suitable. Then, only VOA may offer a way for its AC determination. In particular, ROA combined with quantum chemical computations makes AC possible. The ROA spectrum of a sample of (R)-[2 H1 , 2 H2 , 2 H3 ]-neopentane has been recorded on an SCP instrument designed and constructed by J. Haesler [58], in which both back- and forward-scattering geometries were used. Theoretical calculations for the ROA spectra of the nine rotamers and their average showed two remarkable aspects that made the analysis of the results even more challenging. On the one hand, the ROAs of the nine rotamers often display bands with opposite signs. On the other hand, their intensity exceeds that of the mixture by more than one order of magnitude. Thus, a very high precision in the calculation of the relative size and relative position of the ROA bands of the nine rotamers is mandatory. Theoretical calculations also indicate that the small value of Δ for the mixture of the nine rotamers makes ROA not measurable except in the rocking motions of methyl groups (720–950 cm−1 ) and the C–C bond stretching and deformation methyl groups (1150–1340 cm−1 ) spectral regions. Although, the size of the computed Δ values in these regions is approximately 10−5 in backscattering, it is smaller for other scattering geometries; backscattering is the preferred geometry. The extent of the agreement between the computed and the measured ROA is striking, and confirms the AC of the sample to be (R)-[2 H1 , 2 H2 , 2 H ]-neopentane [57]. 3 The inherently weak cross section of normal Raman scattering can be increased extraordinarily by the surface-enhanced Raman scattering (SERS) effect. This effect is observed for molecules placed in contact with a “plasmonic” surface (nanosized gold, silver, or copper structure usually as a colloidal suspension or a nanostructured film) due to the intense local electromagnetic field created by an efficient coupling between the nanostructure system and the incident radiation. The efficiency of SERS scattering can be, in some cases, 15 orders of magnitude higher in comparison to the conventional Raman scattering [59], allowing for measurement of Raman spectra of samples at very low concentrations, and,

511

512

13

On the Search for the Appropriate Techniques for Structural Elucidation of Small Molecules

in some cases, permitting the observation of Raman spectra, even of single molecules [60–62]. Extending SERS to optically active Raman scattering (SEROA) was proposed a decade ago, but while the theoretical bases for ROA are well established, only a few preliminary theoretical treatments of SEROA have been developed [63]. Also, the number of SEROA experiments reported is very small. The first possible SEROA spectrum was published in 2006, but the high noise level and the fact that mirror SEROA spectra of both enantiomers were not reported made these findings very controversial [64, 65]. It was not until 2010 that the first report of a presumed SEROA effect with the spectra of both enantiomers was presented [66]. Here, a SEROA enhancement of at least three to four orders of magnitude was found for cysteine adsorbed on electrochemically roughened silver electrodes. In any case, the complexity of the mechanism responsible for surface enhancement of the signal and the existence of factors that cannot be controlled still (for example, molecular motion, distance, orientation, and interactions between the molecule and the nanoparticles) indicates that this technique, although very promising, is still in its infancy. 13.7 Theoretical Calculations: Ab initio Calculations of NMR Shifts

The continuing improvements in computer power and knowledge of the applicability of quantum theory have expedited the potential applicability of calculations to structure determination of common (such as NMR and chiroptical spectroscopies) and uncommon (such as atomic-resolution SPM, powder X-ray diffraction, and VOA) techniques. The accurate calculation of NMR chemical shifts with quantum chemical methods has laid a solid foundation to reduce the number of structural misassignments provided the molecule in question does not contain heavy atoms (elements from the third or higher row) since NMR shift calculations neglect spin–orbit contributions from relativistic effects [67]. Geometry optimization constitutes a key step in the use of NMR predictions because all possible conformations need to be taken into account. Among NMR parameters, 13 C chemical shifts constitute a good sensor for compatibility between two structures because they are spread over a wide spectral range, are relatively insensitive to solvent effects, and are sensitive to steric and electronic influences. This methodology consists in comparing computational and experimental data to identify the molecular arrangement that best matched the experimental ones. There are different strategies to reach a structure assignment with different levels of confidence, depending on the availability of experimental data [68, 69]. One plausible way to reach a rapid and reliable structural identification is to combine GIAO (gauge including atomic orbitals) NMR chemical shift calculations with statistical analyses [69] or trained artificial neural network (ANN) pattern recognition [70, 71]. ANNs are computational algorithms that learn from known data (training process) and recognize patterns elsewhere afterwards. This does

13.7

Theoretical Calculations: Ab initio Calculations of NMR Shifts

not necessarily lead to a correct result. This approach would classify a putative molecular structure as correct or incorrect. In doing so, the number of structural misassignments that still appear in the literature would be greatly reduced. In fact, using 13 C chemical shift calculations together with ANN, the initially proposed structures of examples, such as hexacyclinol (17) and vannusual (18), would be classified as incorrect and the revised ones (19 and 20, respectively) would be considered as correct [70]. H

H

H O O

OH H

O

H

O

H

17

HO H O O MeO 19

OH OH OH

H OAc

O

O

O

O H

H

OH

18 O

O

OH

H O

OH OH

H H

H OAc

OH

20

Hexacyclinol, an unsaturated oxygenated molecule, was isolated in 2002 from Panus rudis strain HKI 0254. Its proposed highly strained endoperoxide polycyclic structure 17 [72] has caught the attention of synthetic chemists, especially after a provocative synthesis was reported [73]. Using Bifulco’s methodology [67], but in order to minimize computational cost and to maximize performance, a three-step computational analysis was used by Rychnovsky [74] to propose a new molecular structure for hexacyclinol (19), based on that of a compound isolated from the same organism. To do so, first, the best minimum was identified using a Monte Carlo conformational search with the Merck molecular force field (MMFF). This was the most critical step, because the best computed minimum did not always correspond to the experimentally observed minimum. Next, the minimum was calculated using the HF/3-21G method. This method led to accurate structures with moderate computational costs. Finally, the NMR chemical shifts were calculated with the GIAO option using the mPW1PW91/6-31G(d,p) DFT method. The performance of this approach was such that the average chemical shift differences for a set of known compounds were