Introduction to Magnetic Resonance

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English Pages [287] Year 1967

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Introduction to Magnetic Resonance

Table of contents :
Title Page
Short Bibliography
Table of Atomic and Magnetic Constants
1. Principles of Magnetic Resonance
1.1 Introduction
1.2 The NMR Experiment
1.3 The ESR Experiment
1.4 Thermal Equilibrium and Spin Relaxation
1.5 The Resonance Line Shape
1.6 Magnetic Interactions
Suggestions for Further Reading
2. Magnetic Resonance Spectra of the Hydrogen and Helium Atoms
2.1 Introduction
2.2 The Magnetic Hamiltonian
2.3 Perturbation Theory
2.4 The Basic Spin Functions and Zero-Order Energies
2.5 The First-Order Hyperfine Energies
2.6 The Second-Order Hyperfine Interaction
2.7 The First Order ESR Spectrum
2.8 The Second-Order ESR Spectrum - Forbidden Transitions
2.9 The Zero-Field Levels of Hydrogen
2.10 The NMR Spectrum of the Helium Atom
2.11 Chemical Shielding
2.12 Corrections to the g Factor
2.13 Anisotropic Effects
Suggestions for Further Reading
3. Nuclear Resonance in Solids
3.1 Introduction
3.2 The Dipolar Coupling Tensor
3.3 The NMR Spectrum of Two Coupled Protons
3.4 The Second Moment of an NMR Absorption Line
3.5 Structural Studies by the Method of Moments
3.6 Nuclear Quadrupole Resonance
Suggestions for Further Reading
4. The Analysis of NMR Spectra in Liquids
4.1 Introduction
4.2 The Chemical Shift
4.3 The Spin-Spin Coupling
4.4 The Analysis of Complex Spectra
4.4.1 Classification of Spectra
4.4.2 The Analysis of an AB Spectrum
4.4.3 The Analysis of an A2B2 Spectrum
4.4.4 Splitting from Magnetically Equivalent Nuclei
4.5 Practical Considerations
Suggestions for Further Reading
5. Interpretation of Chemical Shifts and Spin-Spin Couplings
5.1 Introduction
5.2 Origins of the Chemical Shift
5.2.1 Molecular Electronic Currents
5.2.2 Ramsey’s Formula
5.3 Proton Chemical Shifts
5.4 Shifts from Other Nuclei
5.4.1 Fluorine 19F
5.4.2 Carbon 13C
5.4.3 Nitrogen 14N and 15N
5.4.4 Other Nuclei
5.4.5 Solvent Effects
5.5 The Origin of Nuclear Spin-Spin Coupling
5.6 Proton Spin-Spin Coupling
5.7 Molecular Structure Studies by NMR
Suggestions for Further Reading
6. ESR Spectra of Organic Radicals in Solution
6.1 The Spin Hamiltonian: Hyperfine Splitting
6.2 Sets of Equivalent Protons
6.3 Hyperfine Patterns from Other Nuclei
6.4 Mechanism of the Hyperfine Coupling
6.4.1 The Unpaired Spin Density
6.4.2 Indirect Coupling Through a C-H Bond
6.4.3 McConnell’s Relation
6.4.4 Hyperconjugation
6.5 Spin Distributions in Alternant Hydrocarbon Ions
6.5.1 Delocalized Molecular Orbitals
6.5.2 Substituted Benzene Anions
6.5.3 The Pairing of Electronic States
6.6 Negative Spin Densities in Odd Alternant Radicals
6.7 Hyperfine Splitting from 13C and 14N Nuclei
6.7.1 Carbon 13
6.7.2 Nitrogen 14
6.8 Applications of ESR to Solution Chemistry
Suggestions for Further Reading
7. ESR of Trapped Organic Radicals in Solids
7.1 Introduction
7.2 The Spin Hamiltonian
7.3 The First-Order ESR Spectrum
7.4 Second-Order Effects
7.5 Experimental Determination of the Hyperfine Tensor
7.6 The Sign of the Electron-Nuclear Dipolar Coupling
7.7 α-Proton Coupling Tensor
7.8 Delocalized π-Electron Radicals
7.9 Hyperfine Coupling from β Protons
7.10 Hyperfine Tensors of Other Nuclei
7.10.1 Carbon 13
7.10.2 Nitrogen 14
7.10.3 19F Splittings
7.11 Randomly Oriented Solids
Suggestions for Further Reading
8. ESR of Organic Molecules in Triplet States
8.1 Introduction
8.2 Electron Spin-Spin Interaction
8.3 The Triplet Energy Levels
8.4 Transitions with Δms = 2
8.5 Hyperfine Structure
8.6 Further Studies of Excited Triplet States
8.7 Organic Molecules with Triplet Ground States
8.7.1 Methylene and Nitrene Derivatives
8.7.2 Triplets with One Localized Electron
8.7.3 π-Electron Triplets
8.8 Triplet Excitons
8.9 Radical-Ion Clusters in Solution
Suggestions for Further Reading
9. Theory of the g Tensor and the ESR Spectra of Inorganic Radicals
9.1 Determination of the g Tensor in Crystals
9.2 Theory of the g Tensor and the Effective Spin Hamiltonian
9.3 A Simple Example
9.4 The g Tensor in Molecules
9.5 The CO2- Radical
9.5.1 Experimental Results
9.5.2 Molecular Orbitals
9.5.3 Interpretation of the T and g tensors
9.6 Other Inorganic Radicals
Suggestions for Further Reading
10. ESR of Transition Metal Ions and Complexes
10.1 Introduction
10.2 Energy Levels of the d Electrons
10.2.1 The d Orbitals of a Free Ion
10.2.2 The Ligand Field Splitting
10.2.3 Regular and Distorted Complexes
10.3 General Freatures of the ESR Spectra
10.4 Kramers’ Theorem
10.5 The g Tensor in Ions with S=1/2
10.5.1 The Ti3+ Ion in a Tetrahedral Complex
10.5.2 The Ti3+ Ion in an Octahedral Complex
10.6 The Zero-Field Splitting of Triplet States
10.6.1 The Origin of the Splittings
10.6.2 Zero-Field Splitting in the V3+ Ion
10.6.3 The Spin Hamilton
10.6.4 ESR Measurements of D
10.7 Ions with Spin S Greater Than One
10.7.1 Quartet States
10.7.2 Quintet and Sextet States
10.7.3 Summary
10.8 Hyperfine Splitting from the Metal Nucleus
10.9 Covalent Bonding and Ligand Hyperfine Structure
10.10 Electron Exchange Coupling
10.11 The Rare-Earth Ions
10.12 Spin-Lattice Relaxation
Suggestions for Further Reading
11. Spin Relaxation
11.1 Introduction
11.2 Bloch’s Equations
11.3 The Lorentz Line Shape
11.4 The Origin of Magnetic Relaxation
11.5 Nuclear Spin Relaxation in the Water Molecule
11.5.1 Perturbation Theory
11.5.2 The Power Spectrum of a Random Force
11.5.3 The Effect of a Local Field
11.5.4 Rotational Brownian Motion
11.5.5 The Calculation of T1 and T2
11.5.6 Short and Long Correlation Times
11.6 Other Nuclear Relaxation Mechanisms
11.6.1 Introduction
11.6.2 Anisotropic Chemical Shift
11.6.3 Nuclear Spin-Rotational Coupling
11.6.4 Electric Quadrupole Couplings
11.6.5 Unpaired Electron Spins
11.7 Spin Relaxation of Radicals in Solution
11.7.1 Relaxation Mechanisms
11.7.2 Anisotropic g Tensor and Hyperfine Tensor
11.7.3 Electron Spin Exchange
11.7.4 Zero-Field Splittings
Suggestions for Further Reading
12. The Study of Molecular Rate Processes
12.1 The Time Scale of Magnetic Resonance Experiments
12.2 The Line Shape for a Jumping Spin
12.3 Chemical Exchange Effects in NMR Spectra
12.3.1 Hindered Internal Rotation
12.3.2 Spin Coupled to a Relaxing Nucleus
12.3.3 Proton Exchange Reactions
12.4 Rate Effects in ESR Spectra
12.4.1 Modulation of the Hyperfine Coupling
12.4.2 Ion-Pairing in Solution
12.4.3 Electron Transfer Reactions
12.4.4 Time-Dependent Changes in the Direction of Spin Quantization
Suggestions for Further Reading
13. Nuclear Resonance in Paramagnetic Systems - Double Resonance
13.1 Introduction
13.2 The Knight Shift
13.3 Unpaired Electron Distributions by NMR
13.4 Relaxation by Paramagnetic Ions in Solution
13.5 Electron Nuclear Double Resonance
13.5.1 The Overhauser Effect
13.5.2 The Solid-State Effect
13.5.3 ENDOR
13.6 Spin Decoupling in NMR
Suggestions for Further Reading
Appendix A. Matrix Elements and Eigenvalues
Appendix B. Time-Independent Perturbation Theory
Appendix C. Spin Angular Momentum
Appendix D. Tensors and Vectors
Appendix E. Time-Dependent Perturbation Theory
Appendix F. Calculation of T1 and T2 for a Spin of 1/2
Appendix G. The Power Spectrum of a Random Function
Appendix H. The Diffusion Equation for Brownian Motion
Appendix I. Tensor Averages in a Rotating Molecule

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