X-Ray free electron lasers: applications in materials, chemistry and biology 978-1-78262-409-7, 1782624090, 978-1-78801-202-7, 178801202X, 978-1-84973-100-3

Table of contents :
Content: Review of X-ray Sources and Application in Energy Sciences
X-ray Laser Studies of Natural Photosynthesis
Ultrafast X-ray Laser Studies of Electron Excited States
X-ray Spectroscopy of Water and Absorbed Water on Metals
Electronic Dynamics in Photovoltaic Systems
Two-colour X-ray Studies in Energy Sciences
Electronic Structural Dynamics in Photochemical Processes
Material Structure and Motion Studies in Solar Energy Conversion
X-ray Studies of Charge Transfer and Excited Electronic Structure in Artificial Photosynthesis.

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Published on 11 August 2017 on http://pubs.rsc.org | doi:10.1039/9781782624097-FP001

X-Ray Free Electron Lasers

Applications in Materials, Chemistry and Biology

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Energy and Environment Series Editor-in-chief: Published on 11 August 2017 on http://pubs.rsc.org | doi:10.1039/9781782624097-FP001

Heinz Frei, Lawrence Berkeley National Laboratory, USA

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1: Thermochemical Conversion of Biomass to Liquid Fuels and Chemicals 2: Innovations in Fuel Cell Technologies 3: Energy Crops 4: Chemical and Biochemical Catalysis for Next Generation Biofuels 5: Molecular Solar Fuels 6: Catalysts for Alcohol-Fuelled Direct Oxidation Fuel Cells 7: Solid Oxide Fuel Cells: From Materials to System Modeling 8: S  olar Energy Conversion: Dynamics of Interfacial Electron and Excitation Transfer 9: P  hotoelectrochemical Water Splitting: Materials, Processes and Architectures 10: Biological Conversion of Biomass for Fuels and Chemicals: Explorations from Natural Utilization Systems 11: Advanced Concepts in Photovoltaics 12: Materials Challenges: Inorganic Photovoltaic Solar Energy 13: Catalytic Hydrogenation for Biomass Valorization 14: Photocatalysis: Fundamentals and Perspectives 15: Photocatalysis: Applications 16: Unconventional Thin Film Photovoltaics 17: Thermoelectric Materials and Devices 18: X-Ray Free Electron Lasers: Applications in Materials, Chemistry and Biology

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Published on 11 August 2017 on http://pubs.rsc.org | doi:10.1039/9781782624097-FP001

X-Ray Free Electron Lasers

Applications in Materials, Chemistry and Biology Edited by

Uwe Bergmann

SLAC National Accelerator Laboratory, CA, USA Email: [email protected]

Vittal K. Yachandra

Lawrence Berkeley National Laboratory, CA, USA Email: [email protected]

Junko Yano

Lawrence Berkeley National Laboratory, CA, USA Email: [email protected]

Published on 11 August 2017 on http://pubs.rsc.org | doi:10.1039/9781782624097-FP001

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Energy and Environment Series No. 18 Print ISBN: 978-1-84973-100-3 PDF eISBN: 978-1-78262-409-7 EPUB eISBN: 978-1-78801-202-7 ISSN: 2044-0774 A catalogue record for this book is available from the British Library © The Royal Society of Chemistry 2017 All rights reserved Apart from fair dealing for the purposes of research for non-commercial purposes or for private study, criticism or review, as permitted under the Copyright, Designs and Patents Act 1988 and the Copyright and Related Rights Regulations 2003, this publication may not be reproduced, stored or transmitted, in any form or by any means, without the prior permission in writing of The Royal Society of Chemistry, or in the case of reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency in the UK, or in accordance with the terms of the licences issued by the appropriate Reproduction Rights Organization outside the UK. Enquiries concerning reproduction outside the terms stated here should be sent to The Royal Society of Chemistry at the address printed on this page. Whilst this material has been produced with all due care, The Royal Society of Chemistry cannot be held responsible or liable for its accuracy and completeness, nor for any consequences arising from any errors or the use of the information contained in this publication. The publication of advertisements does not constitute any endorsement by The Royal Society of Chemistry or Authors of any products advertised. The views and opinions advanced by contributors do not necessarily reflect those of The Royal Society of Chemistry which shall not be liable for any resulting loss or damage arising as a result of reliance upon this material. The Royal Society of Chemistry is a charity, registered in England and Wales, Number 207890, and a company incorporated in England by Royal Charter (Registered No. RC000524), registered office: Burlington House, Piccadilly, London W1J 0BA, UK, Telephone: +44 (0) 207 4378 6556. For further information see our web site at www.rsc.org Printed in the United Kingdom by CPI Group (UK) Ltd, Croydon, CR0 4YY, UK

Published on 11 August 2017 on http://pubs.rsc.org | doi:10.1039/9781782624097-FP005

Preface On April 10, 2009, the Linac Coherent Light Source (LCLS) at SLAC National Accelerator Laboratory achieved lasing at a wavelength of 1.5 Å.1 This day marked the birth of a revolutionary new source, an X-ray free electron laser (XFEL). An XFEL provides ultrafast X-ray pulses that are about ten billion times brighter than those obtained from a synchrotron source. Combining the unique properties of X-rays, namely to probe the atomic and electronic structure of matter, with the extreme brightness and femtosecond time resolution of an XFEL, has opened a new window into the inner workings of many fundamental processes. This book consists of a collection of chapters written by some of the experts and first users of XFELs. It describes the properties, methods and applications of XFELs with special focus on biological systems and chemical materials, many of them related to photochemistry. Photochemistry is centrally important to life on Earth and human society because, ultimately, almost all the energy the world uses (nuclear and geothermal energy are exceptions) is provided one way or the other by the Sun. As the pressing challenges of climate change, energy and environment need to be addressed in the coming decades, it is the intelligent use of the energy provided by the Sun that may hold the key to the future of our planet and the thriving of human society. And this is actually possible. First, the Sun delivers more than enough energy to Earth by almost a factor of 10 000. (Approximately 1017 W of Sun power reaches the Earth compared to ∼1.6 × 1013 W of all the power currently used by mankind.) Second, we are making progress in gaining an atomic and molecular level understanding of the mechanisms that convert energy from sun light—directly or indirectly—into other forms that we can control and use. It is the understanding of such processes that will ultimately ensure a sustainable future for our energy and environmental challenges, and the ultrafast, ultra-bright X-ray pulses provided by XFELs might play a critical role in providing such understanding.   Energy and Environment Series No. 18 X-Ray Free Electron Lasers: Applications in Materials, Chemistry and Biology Edited by Uwe Bergmann, Vittal K. Yachandra and Junko Yano © The Royal Society of Chemistry 2017 Published by the Royal Society of Chemistry, www.rsc.org

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X-Rays are a unique tool to characterize the atomic and electronic structure of many materials, including artificial and natural, and periodic/ordered and non-periodic/disordered systems. While X-ray microscopy methods provide structural information of complex non-periodic systems down to about 10 nm resolution, X-ray diffraction and scattering methods provide structural information of mainly periodic systems down to atomic resolution. A wide variety of X-ray spectroscopy methods provide detailed insights into the local electronic and atomic structure and bonding energetics of the absorbing atom in an element-specific manner. For the last 40 years, it has been the development of ever more powerful and brighter synchrotron radiation (SR) sources that has pushed the limits in resolution and sensitivity of these X-ray methods. Currently, there are about 50 SR facilities, often called Light Sources, operational worldwide, serving tens of thousands of scientists annually (see, for example, www.lightsources.org). X-Rays beams created by a synchrotron consist of short pulses (∼100 ps) and are bright, monochromatic, polarized and tunable in energy. While these unique properties of SR have pushed the elemental sensitivity and spectral, as well as spatial resolution in many areas of science, including energy and environment, the 100 ps timescale of SR pulses has not been sufficient to access the fundamental timescale for many atomic and molecular processes. Here, even shorter pulses in the femtosecond range are needed. There are efforts to create femtosecond pulses at synchrotrons by slicing techniques, but the applications are limited because of the lack of sufficient photons per pulse. In the optical regime, this time regime was made possible with ultrafast lasers, giving birth to the field of femtochemistry, the study of chemical reactions at femtosecond timescales.2,3 Yet, while ultrafast optical laser spectroscopy can obtain molecular information, it is the short wavelength and high energy of X-rays that can directly probe atoms and molecules on the atomic scale. Therefore, combining the femtosecond timescale with the atomic resolution of X-rays provides simultaneous spatial and temporal access to probing molecular systems during their various functions. The ultrafast, ultra-bright pulses generated at an XFEL have exactly these properties. Before the first XFEL turned on, it was anticipated in the “LCLS First Experiments” report4 that the ability to directly follow the evolution of bond lengths and angles could have a profound impact on the field of femto­ chemistry. The authors speculated that such experiments would advance fundamental understanding of many processes, including photochemically induced bond breaking, photosynthetic processes and dynamics in nanoparticles. The extremely bright, ultrashort X-ray pulses could potentially also image important biological structures at atomic resolution, in some cases without the need for crystallization. A critical question had to be addressed for most studies using ultra-bright X-ray pulses: can matter be probed before the onset of damage? Calculations were performed to understand the intensity and timescale limits above which damage-induced changes in the sample would occur and compromise, for example, diffraction data.5 From these

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calculations and from numerous XFEL experiments performed over the last 7 years, we know now that the allowable dose limit with femtosecond X-ray pulses exceeds the limit for conventional X-ray methods by several orders of magnitude. Consequently, XFELs can not only access ultrafast timescales, they also can probe systems, whose characterization with synchrotron X-rays is limited by radiation damage, or simply not practical at a realistic time­ scale. These include many radiation-sensitive biological systems, such as viruses, bacteria, proteins, metalloenzymes and synthesized/manufactured chemical materials, in particular if they have to be studied under ambient and functioning conditions in real time. While the use of an XFEL has the potential to provide unique new insights, such experiments, as well as the XFEL operation itself, are very challenging and generally much more complex than, for example, SR-based work. These challenges can be summarized in three points:    (1) The interaction of extremely intense X-ray pulses with matter can create fundamentally new phenomena and experimental challenges. First, the physical phenomena during the interaction need to be understood in order to learn about the sample and its state, and second, intense X-ray pulses often destroy the sample, requiring a replacement after each shot. Hence, extensive research in the area of the fundamental interaction of X-rays with matter, as well as new individually specialized methods of sample environment and delivery, is required. (2) The stochastic nature of the self-amplified spontaneous emission (SASE) process that is generally used to create XFEL pulses causes a variety of experimental challenges. These include a complex spectral and temporal pulse profile, as well as significant shot-to-shot spatial, spectral, temporal and intensity fluctuations. Furthermore, many experiments are carried out in a pump-probe manner, where an ultraviolet/visible/infrared (UV/visible/IR; or even X-ray, in some cases) laser pulse is used to initiate a process or reaction, and the XFEL pulse subsequently probes its temporal evolution. Consequently, each pumpprobe event is treated as its own separate experiment. This requires shot-to-shot spatial and temporal pump-probe synchronization, spectral and spatial beam diagnostics, detection, and data processing. The data volume produced in this shot-to-shot approach, especially when combined with large pixel detectors, can be extremely high. (3) In storage rings used in SR facilities, electrons are repeatedly used in insertion devices placed around the ring to create X-ray beams that are fed into simultaneously used experimental stages. In contrast, an XFEL uses a single pass of electrons from a linear accelerator through a long undulator producing just one X-ray beam. Although there are schemes to share the X-ray beam between multiple experiments and new high repetition rate accelerators can feed several undulators simultaneously, the available capacity in XFEL experiments is

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presently severely limited compared to SR facilities. Fortunately, by the end of the decade there will be about ten independent XFELs operational worldwide (see Chapter 1) and this enhanced capacity will allow the build-up and growth of more and more robust experimental programs based on XFEL research. However, the capacity of SR facilities, let alone lab-based techniques, will not be reached until entirely new, much more compact accelerators are available. At present, the XFEL time availability, and the promise and potential for far-reaching advances and applications in science are at a similar place that SR-based science was about 40 years ago, when SR sources were considered rare and esoteric. We are optimistic that the explosive growth we saw in synchrotron-based research over the last several decades is an indicator of what we can expect from XFEL-based research in the near future.

   These unique characteristics and challenges of XFEL-based research and the judicious approaches to exploit and address them will be the common theme throughout the book. Indeed, we feel extremely fortunate and thankful that many of the pioneers of XFEL science have agreed to contribute to this book. We have grouped the chapters into six larger sections, namely Properties of XFELs, Biological Structure Determination, Photochemistry in Biological Systems, Photochemistry in Materials, Sample Delivery Methods and New Directions. While these sections are thought to give a loose structure and flow to the book—starting with a historical perspective on XFELs and ending with an outlook of soft X-ray science enabled by the future high repetition rate XFELs—the reader will find that, in fact, each chapter is its own stand-alone paper. We find that this will make it easier for the reader to follow the discussions, although there are unavoidably some repetitions of methods, systems and concepts in the various chapters. In the following we will briefly describe the range of topics these chapters cover. In the first section Properties of XFELs a historical introduction to XFELs is given and their physical principles and main characteristics are reviewed in the very comprehensive Chapter 1 by Geloni, Huang and Pellegrini. Here, the principles of the SASE process to produce ultra-bright, ultrafast X-ray pulses, and the critical parameters of the injector, linear accelerator and undulator that comprise an XFEL are described in detail. The chapter closes with a description of the present status and some exciting new developments in XFEL-related accelerator research, in particular new compact XFEL machines, which could dramatically reduce costs and widen the applications of ultrafast X-ray pulses. The general reader, as well as the expert in accelerator physics, will find in this chapter many useful parameters and physical principles of XFELs and a beautifully illustrated layout and description of each XFEL facility currently operating or under construction. Applications of XFELs to biological systems have really thrived because the “probe-before-destroy” concept of ultra-short pulses has opened the door to studies under functional conditions, and we have dedicated the next

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two sections to this topic. The section on Biological Structure Determination contains four chapters describing various X-ray methods that have been specifically developed for XFELs. We begin with Chapter 2 by Spence, who gives a comprehensive overview of various XFEL-based methods for the study of biological systems. The chapter builds a link between new sample delivery methods (described in a dedicated section in Chapters 16–18) and new experimental techniques that were specifically developed to take advantage of the unique properties of ultra-bright, ultra-short XFEL pulses in structural biology. The first 7 years of XFEL-based research in this field are reviewed and their historical context is provided. This chapter also gives a broad overview of XFEL-based techniques to study the protein dynamics of molecular machines under physiological conditions. Chapter 3 by Sauter and Adams focuses on the methods of using XFELbased protein crystallography to study the structure and dynamics of biological macromolecules under physiological conditions. XFEL experiments face challenges as compared to synchrotron work due to many differences, including the nature of the exposures (still shots instead of rotational image series), and the authors show how data analyses are re-examined and modified in order to achieve the ultimate goal, namely to produce the best possible electron density maps from the recorded data. In Chapter 4 by Ekeberg, Maia and Hajdu, XFEL-based high-resolution imaging of non-periodic biological objects is described. Specifically, the data analysis required to reconstruct an object in three-dimensions (3D) from many single shot two-dimensional (2D) projections is discussed in detail. An understanding of these algorithms is critical for assessing the origin of spatial resolution limits in single particle imaging. The authors discuss to what extent these limits are imposed by experimental parameters (for example, object size and elemental composition, X-ray wavelength, pulse brightness, detector resolution, etc.) or by the reconstruction methods. Such knowledge will guide the design parameters of XFEL machines and instrumentation, and is critical for developing a strategy for XFEL-based single particle imaging. The second section on the biological application of XFELs focuses specifi­ cally on Photochemistry in Biological Systems. The section starts with Chapter 5 by Moffat describing the study of biological systems in solution, driven far from equilibrium by optical pulses, and the structural course of their return to equilibrium. These changes can be monitored by dynamic, time-resolved X-ray scattering in the femtosecond to nanosecond timescale, and the principles of this technique and its application at SR and XFEL facilities is presented in the chapter. This is followed by Chapter 6 by Dods and Neutze, where the study of ultrafast structural motions in photosynthetic reaction centers is described. These ubiquitous and important proteins use sunlight to drive reactions with remarkably high quantum yield and energy efficiency. The authors describe how X-ray scattering techniques at XFELs can probe real-time, ultrafast structural changes in these biomolecules and their functional role in photosynthesis.

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The section closes with Chapter 7 by Alonso-Mori and Kern describing the simultaneous use of X-ray spectroscopy and X-ray scattering/diffraction for electronic and geometric structure determination in metalloproteins using XFELs. The authors provide a review of recent experiments, with an emphasis on the structure and function of photosystem II, targeted toward understanding the reaction mechanism of light-induced water oxidation in oxygenic photosynthesis. The next section contains eight chapters that focus on the XFEL-based studies of Photochemistry in Materials. While these chapters also include the discussion of new X-ray methods, they are each centred on specific systems and related scientific questions. The section starts with Chapter 8 by Wolf and Gühr, where experiments on ultrafast dynamics in isolated molecules are described. These gas phase photochemistry studies use element- and site-specific soft X-ray K-edge spectroscopy on C, N and O in organic molecules. The authors review recent pioneering studies using “indirect” methods, such as Auger spectroscopy, and point out future opportunities for studies employing “direct” methods, such as near-edge X-ray absorption fine structure (NEXAFS) spectroscopy. In Chapter 9 by Ogasawara, Perakis and Nilsson chemical dynamics studies in liquid water and at catalytic surfaces based on X-ray scattering and soft X-ray spectroscopy are discussed. This chapter highlights a series of XFELbased studies on bond formation, breaking and rearrangement. The next three chapters focus on 3d transition metal systems studied by various X-ray spectroscopy techniques, including X-ray absorption spectroscopy (XAS), X-ray emission spectroscopy (XES) and resonant inelastic X-ray scattering (RIXS), which is a combination of XAS and XES. In Chapter 10 by Chen the study of ultrafast photochemical reaction trajectories in Ni compounds by transient XAS is discussed. The study is used as an example to demonstrate how XFELs can help in resolving electronic configurations for initial excited states before thermalization on the timescale of 100 fs or shorter. Such studies can help to capture intermediates of potential photocatalytic significance. A slightly different approach, namely the use of Kα and Kβ XES and X-ray diffuse scattering (XDS), is described in Chapter 11 by Kjaer and Gaffney. This work focuses on tracking excited state dynamics in photo-excited transition metal molecular systems. Notably, the XES and XDS techniques, which are uniquely sensitive to electronic and structural dynamics, respectively, are applied simultaneously in these XFEL-based studies on ultrafast dynamics. An even more detailed look at electronic structure dynamics can be obtained by transition metal L-edge RIXS using soft X-ray pulses. This is described in Chapter 12 by Wernet, which focuses on the orbital-specific mapping of chemical interactions and dynamics of the photochemically activated prototypical metal complex iron pentacarbonyl [Fe(CO)5] in solution. XFELbased RIXS is sensitive to the frontier–orbital interactions and populations in the system with atomic specificity and femtosecond temporal resolution. The method enables the correlation of metal–ligand coordination with

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orbital symmetry, spin multiplicity and reactivity, and could eventually help explain photochemical catalysis of actual functional systems in real time. A different way of visualizing chemical reactions in solution by femtosecond X-ray scattering is described in Chapter 13 by Adachi and Ihee. The study of bond formation in the solution phase has been especially challenging due to the difficulty of initiating and probing such diffusion-limited bimolecular processes with ultrafast time resolution. The advent of XFELs has opened the possibility for femtosecond time-resolved X-ray liquidography (TRXL) to obtain real-time radial distribution functions that can visualize the photo­ induced bond formation, such as the formation of a covalently bonded gold trimer complex. While the majority of ultrafast pump-probe experiments aim at studying photoinduced changes, one can also use ultrafast light pulses to coherently control the structure in solid-state systems. This intriguing possibility for modulation of material properties on timescales many orders of magnitude faster than conventional methods is discussed in Chapter 14 by Johnson. Here, an overview of some possible mechanisms for how such control over atomic-scale order can be achieved is given, along with selected examples of their application and how to quantitatively characterize them by X-ray diffraction measurements recently made possible by XFELs. The section on Photochemistry in Materials concludes with Chapter 15 by Techert et al., where XFEL-based studies of complex electronic and structural chemical and biochemical reactions in space and time are described. The chapter includes a discussion of various X-ray methods and systems, including liquid phase reaction dynamics, its applications to photocatalysts, applications in biophysics and ultrafast imaging of gas phase reactions. The section Sample Delivery Methods contains three chapters that focus entirely on novel ways to introduce samples into the XFEL beam. This topic is critically important to the success of an XFEL experiment. In fact, we have painfully learned during the first 7 years of XFEL operations how much of a bottle neck this part of the experiment can be. It is no exaggeration to state that most of the inefficiency and time lost during early XFEL experiments was directly related to the sample delivery and environment, and even today these methods are still rapidly evolving. Chapter 16 by DePonte describes how liquids and gases can be delivered at high speed and positional accuracy in order to allow for rapid replenishment of sample between the arrival of X-ray pulses. The chapter provides a brief overview of liquid and gas sample delivery at the LCLS along with some recent developments, including liquid injection in the form of cylindrical jets, drops and sheets with thickness down to 100 nm, as well as pulsed liquid and gas sources. In Chapter 17 by Weierstall a different type of delivery method of microcrystals for serial femtosecond crystallography at an XFEL is discussed. This chapter focuses specifically on the delivery of microcrystals embedded in a high viscosity microstream in order to minimize the sample consumption compared to low viscosity liquid jets. This method allows the use of

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membrane protein crystals grown in lipidic cubic phase, as well as crystals mixed in other high viscosity matrixes. Yet another, rather different strategy of sample delivery is presented in Chapter 18 by Orville. He describes acoustic droplet ejection (ADE), which is an on-demand sample delivery technique that uses focused sound waves to launch tiny droplets from the surface of a liquid. For XFEL applications, the ADE launched drops can be deposited either on a stationary, solid substrate, a moving conveyor belt, or are synchronized to arrive on the fly at the XFEL pulse interaction region. This method minimizes sample consumption and allows for good control of time delays in biological pump-probe experiments. While most chapters contain a brief discussion about future opportunities, we have grouped five chapters in the last section of the book on New Directions as they specifically focus on emerging methods and future science opportunities. We begin this section with Chapter 19 by Bucksbaum, who provides a discussion and outlook of ultrafast, laser-pumped, X-ray-probed quantum dynamics at short-pulsed light sources. Using three examples, the chapter describes how X-rays from synchrotrons and XFELs are used to study impulsively excited systems in condensed matter, as well as in molecules in the gas phase. The chapter concludes with an outlook on the exciting prospects of future sub-femtosecond pulses to study electronic coherences. New opportunities to expand quantum and nonlinear optical processes, such as lasing to the X-ray domain, are described in Chapter 20 by Rohringer. XFEL sources are intense enough to create a population inversion in an atomic system following photoionization of the inner-most electronic shell. After giving an overview of inner shell atomic X-ray lasers, focusing on a Kα neon X-ray laser, the chapter describes various phenomena and potential future applications, including stimulated hard X-ray emission spectroscopy to the liquid and solid phase. The determination of near atomic resolution structures of biomolecules without the need for crystallization by short intense XFEL pulses has been one of the drivers to build XFELs, and aspects of this topic are discussed in several chapters of the book. In Chapter 21 by Chapman the more methodological advances required to reach this goal are described. After discussing the challenges and opportunities of single-particle imaging, the chapter presents, among others, a potential method to simultaneously obtain multiple-view images of an object, and how this and other methods relate to the parameters of future XFEL sources. Chapter 22 by Ourmazd is a discussion of new theoretical approaches aimed to maximally exploit the increasing body of experimental data from XFELs and cryogenic electron microscopy. This approach based on machine learning is aimed to provide insights into energy landscapes and the conformational changes involved in the function of nanomachines. Here, states corresponding to high energy barriers play a critical, rate-limiting role. We conclude the book with a comprehensive outlook on new science opportunities and experimental approaches enabled by high repetition rate

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soft X-ray lasers as described in Chapter 23 by Schoenlein et al. Such studies will become possible once the new generation of XFELs, such as LCLS-II, based on continuous-wave radio frequency (RF) superconducting accelerator technology, become available. These machines provide ultrafast X-ray pulses at a high repetition rate (∼MHz) in a uniform and controllable time structure. The chapter highlights research opportunities identified and developed through a series of workshops over the past years. As we are approaching the end of the first decade of XFEL science, we have already witnessed many high impact results and the emergence of exciting new research areas.6 Yet, the applications of these machines are still in their infancy and their full scientific impact beyond demonstration experiments with applications to challenging systems (beyond model systems) is still to come. We hope that the work described in the following pages of this book will stimulate the reader to think about new methods to develop, new systems to study and new research areas to pursue, so that the full potential of these amazing and powerful machines can be realized. We thank Philippe Wernet for a critical reading of the Preface and for his input. This work was supported by the Director, Office of Science, Office of Basic Energy Sciences (OBES), Division of Chemical Sciences, Geosciences and Biosciences (CSGB) of the Department of Energy (DOE) under contract DE-AC02-05CH11231 (J. Y. and V. K. Y.), National Institutes of Health grants GM55302 (V. K. Y.) and GM110501 (J. Y), the Human Frontiers Science Project Award No. RGP0063/2013310 (U. B. and J. Y.), and the Linac Coherent Light Source (LCLS), a division of SLAC National Accelerator Laboratory and an Office of Science user facility operated by Stanford University for the U.S. Department of Energy (U. B.). Uwe Bergmann, Vittal K. Yachandra and Junko Yano

References . P. Emma, et al., Nat. Photonics, 2010, 4, 461. 1 2. A. H. Zewail, J. Phys. Chem. A, 2000, 104, 5660. 3. A. H. Zewail, Angew. Chem., Int. Ed., 2000, 39, 2586. 4. G. Shenoy and J. Stöhr, Report No. SLAC-R-611, 2003, p. 9. 5. R. Neutze, R. Wouts, D. van der Spoel, E. Weckert and J. Hajdu, Nature, 2000, 406, 752. 6. C. Bostedt, S. Boutet, D. Fritz, Z. Huang, H. Lee, H. Lemke, A. Robert, W. Schlotter, J. Turner and G. Williams, Rev. Mod. Phys., 2016, 88, 015007.

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Quote     The basis of science is observation. The most fundamental way of observation is by light. X-Rays are a form of light that can probe atoms and molecules. X-Ray lasers can probe atoms and molecules on their fundamental time scales, femto­ seconds. X-Ray lasers are therefore one of the fundamentally most powerful tools for science.     Tetsuya Ishikawa, Director, RIKEN SPring-8 Center, Sayo, Hyogo, Japan SLAC National Accelerator Laboratory, Menlo Park, California, USA, May 2nd, 2014

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Contents Section I: Properties of XFELs Chapter 1 The Physics and Status of X-ray Free-electron Lasers  Gianluca Geloni, Zhirong Huang and Claudio Pellegrini

1.1 Introduction  1.1.1 Early Work on X-ray Lasers and the Development of XFELs  1.1.2 Undulator Radiation Characteristics  1.1.3 Introduction to FELs  1.1.4 FEL Physics as Collective Instability  1.2 Three-dimensional (3D) FEL Theory  1.2.1 Characteristics of XFELs  1.3 Present Status  1.3.1 Hard X-ray FELs  1.3.2 Soft XFELs  1.3.3 Novel Developments  1.4 Conclusion  Acknowledgements  References 

3 3 3 5 7 9 14 16 21 22 29 32 37 37 38

Section II: Biological Structure Determination Chapter 2 Imaging Protein Dynamics by XFELs  John C. H. Spence

2.1 Introduction: Seeing Atoms Without Using Crystals  2.2 Radiation Damage Limits Resolution 

  Energy and Environment Series No. 18 X-Ray Free Electron Lasers: Applications in Materials, Chemistry and Biology Edited by Uwe Bergmann, Vittal K. Yachandra and Junko Yano © The Royal Society of Chemistry 2017 Published by the Royal Society of Chemistry, www.rsc.org

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2.3 Serial Crystallography at XFELs for Structural Biology  2.4 Molecular Machines and Single-particle Imaging  2.5 Time-resolved Serial Crystallography, Optical Pump-probe Methods and Photosynthesis  2.6 Time-resolved SFX for Slower Processes: Mixing Jets and Other Excitations  2.7 Fast Solution Scattering and Angular Correlation Methods  2.8 Data Analysis  2.9 Summary  Acknowledgements  References 

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Chapter 3 Overcoming Data Processing Challenges for Breakthrough Crystallography  70 Nicholas K. Sauter and Paul D. Adams

3.1 Introduction  3.2 Data Measurement Challenges Intrinsic to SFX Experiments  3.3 Data Processing Tools Aimed at Still-shot Signal Integration  3.3.1 The Universal Approach of Modelling the Lattice  3.3.2 The Difficulty of Deducing the Lattice Model from Partial Spots  3.3.3 An Approach to Compensate for Missetting  3.3.4 Models of Crystal Imperfection  3.3.5 Post-refinement  3.3.6 Outlier Rejection and Consistent Lattice Alignment  3.3.7 Lessons from Validation  3.3.8 Detector Geometry  3.4 Future Outlook  Acknowledgements  References  Chapter 4 3D Imaging Using an X-ray Free Electron Laser  Tomas Ekeberg



4.1 Background  4.2 The Challenge  4.3 Methods to Orient Diffraction Patterns  4.4 Expand, Maximize and Compress  4.4.1 Updating the Orientations 

70 71 73 73 74 76 76 78 79 80 83 84 85 85 88 88 89 91 92 93

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4.4.2 Updating the Model  4.4.3 Choosing the Similarity Function d  4.4.4 Photon Fluency  4.5 Validation  4.6 The 3D Reconstruction of the Mimivirus Particle  4.7 The Resolution Limit  4.8 Dynamics  Acknowledgements  References 

95 96 97 98 100 102 103 103 103

Section III: Photochemistry in Biological Systems Chapter 5 Dynamic and Static X-ray Scattering from Biological Systems on the Femtosecond to Nanosecond Time Scale  Keith Moffat

5.1 Introduction  5.1.1 The Biological Part  5.1.2 The Physical Part  5.1.3 Structure and Dynamics  5.1.4 Dynamic X-ray Crystallography  5.2 Example: Dynamic Structural Studies of the Photocycle of the Bacterial Blue Light Photoreceptor, PYP  5.3 Summary  Acknowledgements  References  Chapter 6 Elucidating Ultrafast Structural Motions in Photosynthetic Reaction Centers with XFEL Radiation  Robert Dods and Richard Neutze



6.1 Photosynthetic Reaction Centers  6.2 Conformational Stabilization of the Charge Separated State  6.3 Evidence for Structural Changes Using Synchrotron Radiation  6.4 Ultrafast Structural Gating in Photosynthetic RCs  6.5 Studies of Protein Structure Using X-ray Free Electron Laser (XFEL) Radiation  6.6 Time-resolved SFX  6.7 Time-resolved Wide Angle X-ray Scattering Using XFEL Radiation  6.8 Concluding Remarks  References 

107 107 107 109 112 117 121 125 125 125 128 128 130 130 132 133 134 136 138 138

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Chapter 7 Damage-free Electronic and Geometric Structure Determination of Metalloproteins  Roberto Alonso-Mori and Jan Kern

141

7.1 Introduction  141 7.2 Methods  143 7.2.1 Triggering Reactions  143 7.2.2 Diffraction  144 7.2.3 X-Ray Spectroscopy  147 7.2.4 Sample Delivery  149 7.3 Applications  151 7.3.1 Processes Relevant to Metalloenzyme Systems  151 7.3.2 Studies on Myoglobin and Related Systems  153 7.3.3 Studies on Cytochromes and Related Systems  155 7.3.4 Cu and Non-heme Fe Enzymes  157 7.3.5 Studies on Photosystem II  159 7.4 Conclusions  165 Acknowledgements  166 References  166

Section IV: Photochemistry in Materials Chapter 8 Gas Phase Photochemistry Probed by Free Electron Lasers  173 Thomas J. A. Wolf and Markus Gühr

8.1 Introduction  8.2 Different Ways of Probing the Molecular Dynamics: Direct vs. Indirect  8.2.1 Indirect Methods  8.2.2 Outlook: Direct Methods  8.3 Future Opportunities  Acknowledgements  References  Chapter 9 Chemical Dynamics in Liquid Water and at Catalytic Surfaces  Hirohito Ogasawara, Fivos Perakis and Anders Nilsson



9.1 Introduction  9.2 Surface-mediated Catalysis  9.3 Water  9.4 Conclusion  Acknowledgements  References 

173 174 176 179 182 182 183 187 187 188 192 197 198 199

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Chapter 10 Ultrafast Photochemical Reaction Trajectories Revealed by X-ray Transient Absorption Spectroscopy Using X-ray Free Electron Laser Sources  201 Lin X. Chen

10.1 Introduction  10.2 Experimental  10.2.1 Characteristics of X-ray Pulses and the XAS Signal at the X-ray Pump-probe (XPP) Station of LCLS  10.2.2 Sample Considerations and Data Collection for XANES Spectra  10.3 Results and Discussion  10.3.1 Excited State Structural Dynamics  10.3.2 Identity of the T′ State: The Transient Ni(i) Center  10.3.3 Implications and Significance  10.4 Conclusion  Acknowledgements  References 

Chapter 11 Tracking Excited State Dynamics in Photo-excited Metal Complexes with Hard X-ray Scattering and Spectroscopy  Kasper S. Kjær and Kelly J. Gaffney

11.1 Introduction  11.2 Experimental Techniques  11.2.1 XES  11.2.2 XDS  11.2.3 Combined Experimental Setup  11.3 Experimental Results  11.3.1 Characterizing the Decay of Metal-to-ligand Charge Transfer (MLCT) States in Fe-centered Molecular Systems  11.3.2 Characterizing Electron Transfer and Spin State Dynamics of Co-centered Molecular Systems  11.3.3 Characterizing Structural and Solvation Dynamics in Photocatalytic Molecular Systems  11.4 Summary  Acknowledgements  References 

201 205 205 206 209 209 213 215 218 218 219

225 225 226 226 227 227 228 228 232 236 238 239 239

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Chapter 12 Orbital-specific Mapping of Chemical Interactions and Dynamics with Femtosecond Soft X-ray Pulses  Philippe Wernet

242



242 246 259 261 261

12.1 Introduction  12.2 Results and Discussion  12.3 Summary and Outlook  Acknowledgements  References 

Chapter 13 Visualizing Chemical Reactions in Solution with Femtosecond X-ray Scattering  Shin-ichi Adachi and Hyotcherl Ihee

264



264 266 266 270 271 275 279 280 281

13.1 Introduction  13.2 Experimental  13.2.1 Data Collection  13.2.2 Data Processing  13.2.3 Data Analysis  13.3 Results and Discussion  13.4 Conclusion  Acknowledgements  References 

Chapter 14 Perspectives for Ultrafast Light-induced Control of Atomic-scale Structure in Condensed Matter Systems  Steve L. Johnson

14.1 Introduction  14.2 Phenomenological Treatment for Classical Control of Order Parameters  14.3 Indirect Control  14.3.1 Via Electronic States  14.3.2 Via Phonon–Phonon Coupling  14.4 Direct Control by THz Excitation  14.5 Prospects for Further Progress  Acknowledgements  References 

284 284 286 287 288 296 297 298 299 299

Chapter 15 Ultrafast Time Structure Imprints in Complex Chemical and Biochemical Reactions  301 Sadia Bari, Rebecca Boll, Krzysztof Idzik, Katharina Kubiček, Dirk Raiser, Sreevidya Thekku Veedu, Zhong Yin and Simone Techert

15.1 Introduction  301 15.2 The Concept: Filming Chemical Reactions in Real Time Utilizing Ultrafast High-flux X-ray Sources  304

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xxi

15.3 Crystallography with Ultra-high Temporal and Ultra-high Spatial Resolution Allows Study of the Photochemical Reactions Beyond Conventional Quantum Chemical Approaches  15.4 Applications in Energy Research  15.5 The “from Local to Global” Approach: Ultrafast X-ray Spectroscopy and Ultrafast X-ray Diffraction Shake Hands and Allow the Study of Complex and Bimolecular Reactions  15.6 Ultrafast X-ray Studies of Solution Chemical Reactions  15.7 Applications in Biophysics  15.8 Ultrafast Imaging of Gas-Phase Chemical Reactions  15.9 Summary  Acknowledgements  References 

305 307

309 311 313 313 316 318 319

Section V: Sample Delivery Methods Chapter 16 Sample Delivery Methods: Liquids and Gases at FELs  Daniel P. DePonte

325



325 326 326 332 333 333 334 334 335 335

16.1 Introduction  16.2 Methods Overview  16.2.1 Liquid Jets  16.2.2 Gas Phase Jets  16.3 Automation  16.3.1 Sample Handling  16.3.2 Injector Automation  16.4 Summary  Acknowledgements  References 

Chapter 17 High Viscosity Microstream Sample Delivery for Serial Femtosecond Crystallography  Uwe Weierstall

337



337 338 338 339 343 344 346 346 346

17.1 Introduction  17.2 Crystal Delivery in a Liquid Stream  17.2.1 Low Viscosity Liquid Streams  17.2.2 High Viscosity Injector  17.2.3 High Viscosity Media  17.3 Results and Discussion  17.4 Conclusion  Acknowledgements  References 

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Chapter 18 Acoustic Methods for On-demand Sample Injection into XFEL Beams  Allen M. Orville

18.1 Introduction  18.2 Evolution of Sample Delivery Methods at XFELs  18.3 Acoustic Droplet Ejection (ADE) Method Development  18.4 On-demand Acoustic Injectors at XFELs  18.5 Ongoing Research and Development: Future Outlook  Acknowledgements  References 

348 348 350 352 355 359 361 361

Section VI: New Directions Chapter 19 Ultrafast Laser-pumped, X-ray-probed Quantum Dynamics at Short-pulsed Light Sources  Philip H. Bucksbaum

19.1 Introduction  19.2 The Pump-probe Method  19.2.1 Basic Properties  19.2.2 The Quantum Description of Pump-probe Methods  19.2.3 Ensemble Effects  19.2.4 Hierarchy of Time Scales in Molecules  19.3 First Example: Impulsive Excitation of Coherent Acoustic Phonons Probed by Ultrafast Picosecond X-rays at 3d Generation Synchrotrons  19.4 Second Example: Impulsive Rotational Raman Excitation  19.5 Third Example: X-ray Production of Molecular Movies  19.6 Conclusion and Outlook: Moving Towards Future X-ray Detection of Attosecond Electron Motion  Acknowledgements  References 

367 367 368 368 369 369 370 371 372 375 376 378 378

Chapter 20 Photoionisation Inner-shell X-ray Lasers  Nina Rohringer

380



380 383 389 392 395

20.1 Introduction  20.2 The Photoionisation Kα X-ray Laser in Neon  20.3 Molecular Soft X-ray Photoionisation Lasers  20.4 Outlook and Conclusions  References 

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Chapter 21 Opportunities for Structure Determination Using X-ray Free-electron Laser Pulses  Henry N. Chapman

397



21.1 Introduction  21.2 Outrunning Radiation Damage  21.3 Single Shot 3D Incoherent Imaging of Unique Objects  21.4 Imaging Reproducible Objects  21.5 Continuous Diffraction from Single Molecules  21.6 Conclusion  Acknowledgements  References 

397 399 401 405 409 414 415 415

Chapter 22 Machine-learning Routes to Dynamics, Thermodynamics and Work Cycles of Biological Nanomachines  418 Abbas Ourmazd

22.1 Introduction  22.2 Geometric Machine Learning  22.3 Mapping Conformations of Nanomachines  22.4 Three-dimensional Conformational Movies over Energy Landscapes  22.5 Dynamics Beyond Timing Uncertainty  22.6 Conclusions and Future Prospects  Acknowledgements  References 

Chapter 23 New Science Opportunities and Experimental Approaches Enabled by High Repetition Rate Soft X-ray Lasers  Robert W. Schoenlein, Andy Aquila, Daniele Cocco, Georgi L. Dakovski, David M. Fritz, Jerome B. Hastings, Philip A. Heimann, Michael P. Minitti, Timor Osipov and William F. Schlotter

23.1 Introduction  23.2 Fundamental Dynamics of Energy and Charge in Atoms and Molecules  23.2.1 Dynamic Molecular Reaction Microscope  23.2.2 Nonlinear X-ray Approaches for Mapping Valence Charge Dynamics  23.2.3 LCLS Instrument NEH 1.1  23.3 Photo-catalysis and Coordination Chemistry  23.3.1 Excited-state Charge Dynamics via RIXS  23.3.2 LCLS Instrument NEH 2.2  23.4 Quantum Materials 

418 421 423 423 427 430 431 431

434

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23.4.1 Opportunities for Momentum-transfer- dependent RIXS at XFELs  23.4.2 Collective Excitations: Transient Fields and Time-dependent (Pump-probe) Approaches  23.4.3 LCLS Instrument NEH 2.1  23.5 Coherent Imaging at the Nanoscale  23.5.1 Single Particle Imaging  23.5.2 LCLS instrument NEH 1.2  23.6 Conclusion  Acknowledgements  References 

Subject Index 

448 450 451 452 452 453 454 455 455 458

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Section I

Properties of XFELs

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Chapter 1

The Physics and Status of X-ray Free-electron Lasers Gianluca Geloni*a, Zhirong Huangb and   Claudio Pellegrinib,c a

European XFEL, Holzkoppel 4, 22869 Schenefeld, Germany; bSLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025, USA; c UCLA, Department of Physics and Astronomy, 475 Portola Plaza,   Los Angeles, CA 90095, USA *E-mail: [email protected]

1.1 Introduction 1.1.1 Early Work on X-ray Lasers and the Development of XFELs Infrared (IR) and visible lasers were initially developed in the 1960s.1,2 Starting from the that time there has been a continued effort to extend the generation of coherent electromagnetic radiation to shorter and shorter wavelengths, with the ultimate goal of reaching the X-ray region. One important reason for these efforts is that an X-ray laser, generating a beam of coherent photons at the angstrom wavelength, would open a new window on the exploration of matter at a length scale corresponding to the atom size (the Bohr radius) and probe in great detail the structure of simple and complex molecules. If, at the same time, the X-ray pulse length could be reduced to a few femtoseconds (the Bohr time, the revolution time of a valence electron around the nucleus),   Energy and Environment Series No. 18 X-Ray Free Electron Lasers: Applications in Materials, Chemistry and Biology Edited by Uwe Bergmann, Vittal K. Yachandra and Junko Yano © The Royal Society of Chemistry 2017 Published by the Royal Society of Chemistry, www.rsc.org

3

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one could also explore the dynamics of atomic and molecular process on their own time scale. The dream of exploring atomic/molecular processes on their natural length and time scale would, for the first time, become a reality and open the exploration of new science for physics, chemistry and biology. The main impediment in the search for an X-ray laser based on inner level atomic transition are the very short lifetime of excited atom-core quantum energy levels and the larger energy required to excite electrons in the inner core levels. George Chapline and Lowell Wood3 of Lawrence Livermore National Laboratory, one of the most active research institutes for X-ray laser development, estimated the radiative lifetime of an X-ray laser transition to be about 1 fs times the square of the wavelength in angstroms. The way out of this difficult situation is offered by the generation of electromagnetic waves from relativistic electron beams and X-ray free-electron lasers (XFELs). A history of their development is found in ref. 4. Here, we summarize some of the steps that led in recent years to the successful demonstration of XFELs and their operation for novel experimental research in physics, chemistry, biology and materials sciences at the femtosecond/angstrom frontier.5 An important step on the way to XFELs was Hans Motz’s concept6 of obtaining nearly monochromatic coherent radiation from relativistic electrons moving through a periodic magnetic array, which he called an undulator magnet, as shown in Figure 1.1. Motz evaluated the wavelength (λ) of the radiation emitted at angle θ respective to the undulator axis by a relativistic electron moving along the axis. For the case of a helical undulator, the wavelength is given by    

    where

λ = λU(1 + K2 + γ2θ2)/2γ2,

(1.1)

   

K = eBUλU/2πmc2 (1.2)     is called the undulator parameter, λU is the undulator period, typically a few centimeters, BU is the undulator magnetic field on the axis, γ is the electron energy in units of the rest energy mc2. The undulator parameter is the normalized vector potential and is typically of the order one to three. The radiation wavelength can be easily tuned using the quadratic dependence on the electron energy and the undulator parameter.

Figure 1.1 Schematic arrangement of undulator magnets. Reprinted from ref. 6 with the permission of AIP Publishing.

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In 1953 Motz and co-workers observed coherent radiation at Stanford at a millimeter wavelength using a planar undulator with 4 cm period and 3 to 5 MeV electron beam, generated by a linear accelerator, with a bunch length shorter than the radiation wavelength.7 Raising the beam energy to 100 MeV, they observed incoherent radiation. Using Motz’s words: “the mm wave generation might have some practical importance. In this case, it is possible to bunch the electron beam so that groups of electrons radiate coherently. It was shown that the power level may be higher by a factor of the order of a million compared to non coherent radiation …”, can we do the same at a wavelength of about 1 Å? The answer is no, we do not know how to generate an electron beam with all electrons squeezed within λ/10 or separated by λ at X-ray wavelengths. But, in this case, nature is kind to us. Under proper conditions using a free-electron laser (FEL), the electron beam can go through a self-organization process and do just that, as we will see later.

1.1.2 Undulator Radiation Characteristics There are two main types of undulators used to generate radiation: helical and planar. A detailed description of electron trajectories and of the emitted radiation can be found in ref. 8. Assume a reference frame with z along the undulator axis and x,y in the transverse directions. Consider a relativistic electron with energy E = mc2γ, longitudinal velocity βz near to one and small transverse velocities βx, βy ≪ 1. In the case of a helical undulator with period λU, wave number kU = 2π/λU and magnetic field on axis B0, the field near the axis is approximated to the lowest order by Bx = −B0 sin(kUz), By = B0 cos(kUz), Bz = 0. The trajectory is a helix of radius a = K/kUγ, where the undulator parameter K, given in eqn (1.2), is typically of the order of one or a few. The transverse velocities are    

βx0(z) = ẋ0/c = −(K/γ)sin(kUz),     βy0(z) = ẏ/c = (K/γ)cos(kUz).     The longitudinal velocity is

(1.3) (1.4)

   

βz0 = {1 − (1 + K2)/γ2}1/2 ≃ 1 − (1 + K2)/2γ2, (1.5)     having assumed the relativistic factor γ ≫ 1. Notice that, in this case, the longitudinal velocity is a constant. To understand the FEL physics, it is important to characterize the radiation emitted by one electron as it traverses an undulator magnet on a trajectory near to the magnet axis. The radiation is peaked at a wavelength    

λr = λU(1 − βz)/βz ≈ λU(1 + K2)/2γ2 (1.6)     and consists of a wave train with a number of wave fronts equal to the number of periods, NU, in the undulator. The length of the radiation pulse is NUλr.

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For a helical undulator, the radiation is circularly polarized, only the fundamental is present on axis at the wavelength λr [eqn (1.6)], and the harmonics appear off axis. For planar undulators, only one of two transverse components of the magnetic field is present. The electron trajectory is a sinusoid of period λU in the plane perpendicular to the magnetic field. The radiation is plane (linearly) polarized instead of circularly polarized. The longitudinal velocity is not a constant as in the helical case and oscillates at twice the undulator period, leading to the presence of an odd harmonic on the axis. The resonant wavelength is still given by eqn (1.6) if we make the substitution of the undulator parameter [eqn (1.2)] with K rms  eBU U / 22πmc 2 . The undulator parameter is typically of the order of one to three. For a case like the Linac Coherent Light Source (LCLS), the beam energy is about 15 GeV and the undulator is planar, with λU = 3 cm, Krms = 2.8 and NU = 3500. The corresponding wavelength is λ = 0.15 nm. The radiation pulse length and duration for a single electron are NUλ ≈ 0.3 µm and 1 fs. The spectrum is a sum of harmonics of the fundamental. However, on axis, θ = 0, only the fundamental is present for a helical undulator and is given by    

    where

2

d I dd



2re mc

2

c

   



2

NU

2

K

2

2

1  K  2



  πN U 

 R

2

 sin   ,     



 1  .

(1.7)

(1.8)



    The factor ω2/ωR2 in eqn (1.8) is assumed to be equal to 1, a very good approximation. The full width at half maximum (FWHM) of the radiation line on axis is    



~



(1.9)

    We now estimate the number of photons emitted by one electron in the fundamental line and near the axis, within the line width 1/2NU. Since the frequency depends on the emission angle according to eqn (1.1), to remain within this line width the emission angle must be limited to    

   1  K 2  4 2 N U     corresponding to a solid angle of

 / 2U N U ,

(1.10)

   

ΔΩ = πσθ2 = πλ/2λUNU. (1.11)     If we consider transversely coherent photons within the phase space area σrσθ = λ/4π, the effective source radius is

   

   

r 

2U N U / 4π.

(1.12)

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7

Multiplying eqn (1.7) by the solid angle and by the line width, we obtain

r K2 I c  2π 2 mc 2 e .  1  K2     The corresponding number of photons is

(1.13)

   



N ph,c  π

K2 . 1  K2

(1.14)

    It is interesting to notice that the number of coherent photons emitted by one electron depends only on the fine structure constant α and the undulator parameter. For typical values of the undulator parameter, the number is of the order of 0.01, a small value. This result gives us a simple rule for evaluating the number of coherent photons emitted by one electron in crossing an undulator. In the case of many electrons, Ne, if there is no correlation between them and they are distributed over a length larger than the wavelength, the total number of photons scales linearly with Ne and is hence about 1% of the number of electrons. If, as in the case of the Motz experiment at millimeter wavelength, all electrons are in a length shorter than the wavelength, the number of photons emitted is about 1% of Ne2. For electron bunches generated in linear accelerators, the number of electrons is typically in the range of 107–109. The difference between the two cases is very large.

1.1.3 Introduction to FELs The next step was the introduction of the FEL concept9 in 1971 by John Madey, shown schematically in Figures 1.2 and 1.3. In an FEL an electromagnetic wave, co-propagating with the electron beam, is added to the electron beam-undulator magnet studied by Motz, opening new possibilities. FELs combine the physics and technology of the particle accelerator and lasers to generate electromagnetic radiation with very high brightness. Madey used the Weizsäcker–Williams method to calculate the gain due to the induced emission of radiation into a single electromagnetic wave propagating in the same direction of a relativistic electron through a periodic transverse magnetic field. Finite gain is available from the far IR through the visible region, raising the possibility of continuously tunable amplifiers and oscillators at these frequencies with the further possibility of partially coherent radiation sources in the ultraviolet (UV). Considering an extension to the X-ray region or beyond 10 keV, Madey noted in his paper: “The dependence of the gain on the square of the final state wavelength probably precludes the development of steady-state oscillations in the region beyond the ultraviolet …”. Madey’s group demonstrated the feasibility of the FEL concept with two experiments. The first, shown in Figure 1.2, was an FEL amplifier at 10.6 µm.10 It used a 24 MeV electron beam from a superconducting linear accelerator at Stanford, with a current of 5 to 70 mA. The undulator was of the helical

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Chapter 1

Figure 1.2 Schematic of the FEL amplifier experiment at Stanford. Reprinted with

permission from L. R. Elias, Physical Review Letters, 36, 717, 1976. Copyright (1976) by the American Physical Society.10

Figure 1.3 Madey’s FEL oscillator configuration. Reprinted figure with permission from D. A. G. Deacon et al., Physical Review Letters, 38, 892, 1977. Copyright (1977) by the American Physical Society.11

type obtained with a superconducting, right-hand double helix, a period of 3.2 cm and a length of 5.2 m. The single pass gain was as large as 7%. The second, shown in Figure 1.3, was an oscillator operating at a wavelength of 3.4 µm, a beam energy of 43 MeV, the same helical undulator and an optical cavity that was 12.7 m long.11 The two experiments by Madey and co-workers use the two basic configurations of an FEL: an amplifier or oscillator, and an external laser beam that seeds the amplifier. When there is no external seed the electron beam propagating through the undulator generates spontaneous incoherent radiation, as observed by Motz at high electron beam energy and short wavelength. The oscillator can also be seeded or it can start from noise generated by the spontaneous radiation. The analysis of these experiments was based on Madey’s quantum theory of the FEL as stimulated bremsstrahlung, valid only for small changes in the electromagnetic wave intensity, the small signal gain regime. However, Madey’s small signal gain formula does not depend on Planck’s constant, indicating that the FEL is essentially a classical system. A classical small signal gain theory, developed by William Colson,12 based on non-quantized Maxwell

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equations for the field and Lorentz equation for the electrons gives the same gain value as Madey’s quantum theory. The small signal gain theory shows that the FEL single pass gain depends on the electron beam six-dimensional phase space density. The scaling with wavelength of the required beam characteristics, as the electron bunch length, transverse phase space density and peak current, together with the lack of good optical cavities in the X-rays spectral region, precludes the possibility of pushing FELs to X-ray wavelengths in the small signal gain regime, as already mentioned.

1.1.4 FEL Physics as Collective Instability This situation changed with the development, by many authors, of the classical high gain theory in the 70s and 80s, removing the condition of a small change in the electromagnetic wave intensity and using the full dynamics of the electron beam-radiation field interaction.13–25 The paper by Saldin and Kondratenko15 is an important contribution. In this paper it was considered, for the first time, to use the high gain regime starting from spontaneous radiation to reach saturation in a single pass IR FEL using low energy electron beams (a few to 10 MeV). This approach would eliminate the need of an optical cavity. In a second paper (ref. 26) they proposed to use high gain amplification starting from noise for an FEL inserted in a storage ring to produce soft X-rays at 5 nm from electrons at 20 GeV for the purpose of generating electron polarization in a storage ring. Bonifacio, Pellegrini and Narducci19 gave another important contribution, analyzing the FEL physics as a collective instability and showing that, in the one-dimensional (1D) limit, the FEL equations can be written, by proper variables transformation, in a universal form, depending only on one parameter, ρ, the FEL parameter. This quantity is a function of the undulator and electron beam characteristics and does not depend explicitly on the radiation wavelength. Since it does not depend on the radiation wavelength, the theory can be verified experimentally at any wavelength. In their paper the authors also show and analyze the possibility of starting from noise and reaching saturation in a single undulator pass, a self-amplified spontaneous emission (SASE) FEL, avoiding the need of an optical cavity. The possibility of generating high-intensity coherent radiation in the soft X-ray and vacuum-UV region using a storage ring, the best electron source available at that time, was again analyzed in ref. 15. J. B. Murphy and C. Pellegrini showed that using a storage ring and considering collective instabilities limiting the beam phase space density, the radiation wavelength that can be obtained is limited to values larger than about 50 nm.27 The limit mainly comes from the large relative electron energy spread, ≈10−3, due to electron beam instabilities. The best option to reach angstrom wavelengths is to use a linear accelerator with a new electron source28 developed at Los Alamos as part of the Star Wars program: the RF photo-injector.29 This source can generate beams

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with 100 times better emittance and ten times smaller energy spread than the original SLAC linear accelerator (linac) thermionic source. It also reduces the energy spread to a value at least ten times smaller than that obtained in a storage ring. The photoinjector was used in the early experiments demonstrating the validity of the SASE theory. In the late 1990s and early 2000s, experiments done by the UCLA-Kurchatov,30 UCLA-LANL-Kurchatov,31 Argonne National laboratory,32 DESY33 and SLAC-UCLA-BNL-LLNL34 groups, covering a wavelength region from the IR to the near UV, verified all important aspects of the theory, including the start from noise, and validated the numerical codes used to simulate the experiments. The SASE XFEL gives the best, and so far the only, alternative to atomic transition with population inversion X-ray lasers.15,19,28 Claudio Pellegrini4,35 proposed in 1992 to build a SASE XFEL in the wavelength range 0.1 to 4 nm using one third of the 3 km long 40 GeV linear accelerator of the SLAC National Accelerator Laboratory.36 This proposal led eventually to the construction of the first hard XFEL, the LCLS, at SLAC and its successful operation at a wavelength as short as 1.5 Å.37 Since the first lasing was achieved at LCLS on April 10, 2009, another XFEL, the SPring-8 Angstrom Compact Free Electron Laser (SACLA), has been successfully commissioned in Japan38 and three more hard X-ray FELs are under construction in Korea,39 Switzerland40 and the European Union.41 Two soft X-ray FELs, FLASH42 and Fermi,43 are also in operation at DESY, in Germany, and Sincrotrone Trieste, in Italy. LCLS is being upgraded to LCLS-II,44 covering both the soft and hard X-ray regions. The characteristics and properties of these soft and hard X-ray FELs will be discussed in more detail in the last Section (1.3) of this chapter. The physics of the collective instability can be explained with a simple model. Consider the case of an electron beam propagating along the axis, z,  of a helical undulator. The electron beam interacts with a co-propagating circularly polarized electromagnetic wave. Let Ex = E0 cos[kr(z − ct)],  Ey = E0 sin[kr(z − ct)] be the electric field components; the transverse velocity of the electrons produced by the undulator magnet has components given by eqn (1.3) and (1.4); the interaction produces an electron energy modulation, on the scale λ, given by    

    where

mc 2

d ecKE sin ,   dt

(1.15)

   

Φ = kr(z − ct) + kUz (1.16)     is the relative phase of the radiation and the electron oscillation. The electron energy modulation changes the electron trajectory in the undulator magnetic field. As shown in Figure 1.4, high energy electrons have a shorter path than low energy electrons, generating bunching of the electrons at the scale of the radiation wavelength, λr = 2π/kr.

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Figure 1.4 Electron trajectories in the undulator, showing a longer path for lower energy electrons with respect to higher energy electrons (dashed curve).

Electrons bunched within a wavelength emit radiation in phase, thus producing a larger intensity. We close the loop by going back to step 1. The larger intensity leads to more energy modulation and more bunching, leading to exponential growth of the radiation; the intensity can reach the limit I ∼ Ne2 for the case of extreme bunching. The most important quantity is the bunching factor, or order variable    



B

1 Ne  exp(in ), Ne n  1

(1.17)

    where Φn = kr(zn − ct) + kUzn is the relative phase of the electromagnetic wave and of the nth electron oscillation in the undulator field, the same quantity appearing in energy exchange eqn (1.15). The bunching factor is zero for a uniform electron distribution, small (B ≪ 1) for a random distribution of the electron longitudinal position, and of the order of one for an FEL near saturation. The intensity of the electromagnetic field is proportional to the square of the number of particles in the electron bunch, times the square of the bunching factor, I ≈ Ne2|B|2. In the 1D limit, the FEL equations can be written, by proper variable transformation, in a universal form, depending only on one parameter:19 the FEL parameter, given by    



 [ JJ ] K P    4 kU c 

 

2/3

,

(1.18)

    where [JJ] = 1 for a helical undulator, [JJ] = {J0[K2/(4 + 2K2)] − J1[K2/(4 + 2K2)]}2/2 for a planar undulator,    

1/ 2



2  4πre c ne   3   

P  

(1.19)

    is the beam plasma frequency, ne is the electron density and re the classical electron radius. The instability just described leads to an exponential growth of the electromagnetic wave field amplitude, as shown in Figure 1.5. The instability can be triggered by an external wave, which is called a seeded FEL, or by a non-zero value of the bunching factor at the undulator entrance. For long wavelengths,

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Figure 1.5 Evolution of radiation power and of micro-bunching on a scale of the radiation wavelength, along the undulator for a SASE FEL. The gain length characterizes the exponential growth of the radiation power and of the bunching factor.

for instance, longer than the bunch length, we can prepare a non-zero initial bunching factor by manipulating the electron longitudinal positions. However, even at wavelengths much shorter than the bunch length, a random distribution of the longitudinal electron position at the undulator entrance gives an initial value of the bunching factor that can be small but not zero. In fact, for the random distribution case, the initial bunching factor has an average value equal to zero, but a root mean square value different from zero and depends on the number of electrons in a radiation wavelength. In particular, for the case of X-rays with wavelengths in the nanometer or sub-nanometer range, where there are no practical electromagnetic sources, starting the instability from the initial bunching factor due to the randomness of the longitudinal electron distribution on the scale of the radiation wavelength is the only practical way to operate an FEL. As this mode of operation is based on self-amplified spontaneous emission, the FEL is referred to as a SASE FEL. The electromagnetic power instability growth rate, or power gain length, is given approximately by    



LG0



U 4π

3

.

(1.20)

    The typical value of the FEL parameter for XFELs is about 0.001. The expression of the FEL parameter for a planar undulator will be given later. In addition to the gain length in eqn (1.20), all other important properties of the FEL, in the 1D limit, can be expressed using the FEL parameter, ρ. The saturation power is a fraction ρ of the beam power    

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Psat ≃ ρPbeam, (1.21)     where the beam power, Pbeam = EbeamIbeam/e, is the product of the beam current and energy. Hence, the FEL parameter is the efficiency of the energy transfer from the electrons to the radiation field. The saturation length is about ten times the gain length. The line width is about equal to the FEL parameter    



~



(1.22)

    The number of coherent photons per electron is also given by the simple formula    

Nph ≃ ρEbeam/ℏω, (1.23)     giving the ratio of the beam energy to the photon energy times the FEL parameter. Consider a case similar to the SLAC XFEL, LCLS: γ = 3 × 104, λU = 3 cm, Krms = 3, NU = 3500. In this case, we obtain λ = 0.1 nm. Near saturation, assuming the FEL parameter to be 10−3, a typical value for existing XFELs, we obtain from eqn (1.23) 103 coherent photons per electron. Comparing this number with the spontaneous radiation case in eqn (1.14), we see the large gain obtained from the FEL amplification effect. It is important to notice that, in the 1D limit, the theory does not depend explicitly on the beam and radiation characteristics. Its validity can be verified experimentally at any wavelength. As we will see later in detail by studying the FEL equations, in the 1D limit, neglecting diffraction effects, the process is characterized by one parameter and two length scales, the gain length, LG, the radiation intensity exponential growth rate of the instability, and the cooperation length, Lc, which is the distance over which the radiation emitted by one electron can interact with other electrons, considering the difference in velocity between electrons and photons. As we have seen in Section 1.1.2, a photon emitted by an electron moves (slips) ahead of it by one wavelength per undulator period. The cooperation length is the slippage in one gain length. The two lengths are proportional to each other, where L c = (λr/λU)LG. This implies that both gain and coherence length can be expressed by one parameter only:45 the FEL parameter. The amplitude of the radiation field grows exponentially along the undulator axis, z, as E = E0 exp(z/LG) if the following conditions, necessary for the validity of the 1D model, are satisfied:28     a. Beam emittance is smaller than the radiation wavelength:    

ε < λr/4π (1.24)     b. Beam relative energy spread, including contributions from the electron betatron oscillations, are smaller than the FEL parameter ρ:    

   

σE/E < ρ

(1.25)

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c. Undulator length is larger than the gain length:    

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NUλU ≫ LG0     d. Gain length is shorter than the radiation Rayleigh range:

(1.26)

   

LG/ZR < 1, (1.27)     where the Rayleigh range is defined using the minimum waist of a Gaussian radiation beam, πw02 = λrZR.     e. The quantum-recoil parameter:    

q = ℏωr/mc2γρ ≪ 1. (1.28)     This condition requires that the change in electron energy due to a single photon emission is small enough to move the electron off the FEL gain bandwidth, similar to what is required in the condition shown in eqn (1.25).

1.2 Three-dimensional (3D) FEL Theory The 1D theory was extended to the 3D case to take into account radiation diffraction and the electron’s betatron motion.46–48 The detailed 3D treatment is beyond the scope of this chapter, and the interested readers can refer to recent review articles.8,49 The collective particle dynamics under the influence of the combined undulator and radiation fields can be described by the Vlasov equation, while the radiation field is determined by the Maxwell equation driven by the collective motions of the electron beam. The most interesting feature is the emergence of a set of guided transverse modes in the radiation field.50 In general, there are many discrete solutions of Maxwell–Vlasov equations, and the radiation field can be written as an expansion of eigenmodes:    



Eν ( x ; z ) 



C

n0

n

An ( x )ei n 2  kU z .

(1.29)

    where cn is the mode expansion coefficient that can be determined by solving the initial value problem. The transverse modes and complex growth rate µn(eigenvalues) can be determined by solving the eigenmode equation, which depends on the electron beam and undulator characteristics. In the high-gain regime, a Gaussian-like fundamental mode (for n = 0) with the largest growth rate, Imµ0, usually dominates over other higher-order modes, i.e.,    

Eν(x;z) ≈ C0A0(x)e−iµ02ρkUz. (1.30)     Thus, the transverse profile of the radiation appears to be guided with exponentially growing amplitude, i.e., the transverse profile and size become independent of the undulator distance (z). We will discuss this remarkable feature of a high-gain FEL and its implication to the transverse coherence later.

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The growth rate of the fundamental mode can be expressed as  LG

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U  LG0 (1   ), 8(Im0 )π

(1.31)

    where LG0 is the 1D gain length discussed in Section 1.1.4 and eqn (1.20), and Λ is the gain length degradation factor, larger than 1. Based on the variational solution of the FEL eigenmode equation, Ming Xie48 obtained a very useful fitting formula for the power gain length of the fundamental mode that depends on three scaled parameters:    

d 

LG0 2kr  x2

(diffraction parameter),

 (angular spread parameter), r / (4π) L   γ  4π G0 E (energy spread parameter), U E

ε  kβ LG0

(1.32)

    where kβ is the transverse betatron wavenumber, determined by the quadrupole focusing in the undulator breaks. The frequency detune is optimized to yield the highest growth rate. The gain length degradation factor Λ is defined in eqn (1.33) as    

a6 a8 a9 a2 a4 a11 a12 a14 a15 a17 a18 a19   a1d  a3ε  a5 γ  a7ε  γ  a10d  γ  a13d ε  a16d ε  γ , (1.33)     where the fitting coefficients are

   

 a1 0.45, a2 0.57, a3 0.55, a4 1.6, a5 3, a6 2, a7 0.35, a8 2.9,  a9 2.4, a10 51, a11 0.95, a12 3, a13 5.4,  (1.34)  a14 0.7,  a15 1.9,  a16 1140,  a17 2.2,  a18 2.9,  a19 3.2.     The discrepancy between Xie’s fitting formula and numerical solutions of the FEL eigenmode equation is typically less than 10%. These positive fitting coefficients quantitatively show that all three scaled beam parameters in eqn (1.32) should be kept small to avoid a large gain reduction, corresponding to the qualitative beam requirements discussed in Section 1.1.4. The FEL power spectrum in the high-gain regime is given as    



dP  mc 2  dP g A  0  gs  d 2π  d

 z  2   exp ,    2    LG 2  

(1.35)

    where dP0/dω is the initial input power spectrum (due to seeding); ργmc2/ (2π) is the SASE noise power spectrum46 and can be identified as the spontaneous undulator radiation in the first two power gain lengths;51 gA and gS

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determine the input coupling to the fundamental mode and the effective start-up noise, respectively; and σω is the SASE bandwidth. In the 1D theory, the cold beam limit, gA = 1/9, gS = 1, and the root-mean-square (rms) SASE bandwidth is23 Published on 11 August 2017 on http://pubs.rsc.org | doi:10.1039/9781782624097-00001

   



 3 3  . kU z r

(1.36)

 z  P  g A Pn exp   .  LG 

(1.37)

    For a more general beam distribution, the SASE bandwidth can be found by solving the eigenmode equation and typically decreases to about ρ at the FEL saturation point. Integrating the SASE term over the frequency, we have the average SASE power as    



    Here, Pn  g S  mc 2  / 2π is the effective start-up noise for SASE. The radiation power growth is accompanied by the increased electron beam energy loss and energy spread. These effects inevitably slow down the gain process close to the FEL saturation. The saturation process cannot be described by the above linear theory. Numerical simulation codes have been developed to include 3D and saturation effects. These codes include GINGER,52 FAST53 and GENESIS.54 The FEL saturation power typically requires such numerical simulations but can be approximated in a fitting formula48 as    



Psat 

1.6

1   

2

 Pbeam .

(1.38)

    To estimate the saturation distance of a SASE FEL, we require that eqn (1.38) is equal to eqn (1.37). In the 1D limit, we obtain    



zsat 20 I etc  ln , LG e

(1.39)

    where Ie is the electron peak current, e is the charge of the electron and tc  π /   is the coherence time. Thus, the saturation distance is a numerical factor, times the power gain length. The numerical factor depends logarithmically on the number of electrons within one coherence time, Nc = Ietc/e, and typically varies little from 18 to 20. Therefore, the SASE saturation length is simply λu/ρ if LG ≈ LG0.

1.2.1 Characteristics of XFELs All short-wavelength SASE experiments measured the characteristic “gain curves” and obtained very good agreement with the theory and simulations.32–34,40 Two examples of experimental results are shown in Figures 1.6 and 1.7. The first shows the average energy in the radiation pulse and the rms energy fluctuation in the radiation pulse as a function of the active undulator

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Figure 1.6 Average radiation pulse energy (solid circles) and rms radiation pulse

energy fluctuation (empty circles) as a function of the active undulator length in the TTF experiment. The wavelength is 98 nm. Circles denote the experimental results while the curves are from numerical simulations. Reprinted with permission from V. Ayvazyan et al., Physical Review Letters, 88, 104802. Copyright (2002) by the American Physical Society.33

Figure 1.7 LCLS FEL power (red points) at 1.5 Å vs. active undulator length. The

measured gain length is 3.3 m and a GENESIS simulation is overlaid in blue with electron beam parameters measured. The X-ray image on the yttrium aluminum garnet screen downstream of the undulator is shown in the inset. Reprinted by permission from Macmillan Publishers Ltd: [Nature Photonics] ref. 37, Copyright (2010).

length in the Tesla Test Facility (TTF) experiment (the precursor to the FLASH FEL facility at DESY). The SASE intensity fluctuation are discussed below. Figure 1.7 shows the exponential growth and saturation of the LCLS FEL at the radiation wavelength of 1.5 Å vs. undulator length.

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As shown in the inset of Figure 1.7, the X-ray image on the yttrium aluminium garnet screen downstream of the LCLS undulator illustrates a nearly perfect Gaussian transverse mode for the LCLS beam. Such an excellent mode quality comes from the effects of gain guiding that select a single transverse mode, eqn (1.30). As a result, typical SASE FELs can reach almost full transverse coherence at saturation. Compared to the third-generation storage ring hard X-ray sources, the degree of transverse coherence is improved by about one to two orders of magnitude. The peak brightness improvement of the XFEL is even more impressive when compared to third-generation storage rings. The exponential amplification of FEL radiation increases the number of photons by about a factor of a million, while the X-ray pulse duration also decreases from the picosecond level to tens of femtoseconds. Altogether, the XFELs provide nine to ten orders of magnitude higher peak brightness than offered by existing synchrotron radiation facilities in the hard X-ray regime. The graphic comparison of XFELs vs. synchrotron radiation sources from storage rings is shown in Figure 1.8. Because of the start-up from noise, the temporal property of a SASE FEL is that of a chaotic light.56,57 Such a chaotic light can be analyzed by statistical methods since the radiation field is a fluctuating function of time. The first-  order correlation of the electric field yields the coherence time tc  π /   .56 In the exponential growth regime, the energy of a SASE pulse W with a flattop duration T fluctuates according to the gamma probability distribution:57    



p(W ) 

M M W M 1 W   exp   M , W    ( M ) W  M 

(1.40)

    where 〈W〉 is the average radiation energy and Γ(M) is the gamma function. The relative rms energy fluctuation σW is given by    

M 

1  2

W

W  2  W   W  2 2

T when T  tc or 1 when T  tc . tc

(1.41)

    Thus, the M parameter characterizes the degree of freedom or the temporal “mode” of the pulse. For hard XFELs, typically tc is in the sub-femtosecond regime, so T ≫ tc and M ≫ 1, and the gamma distribution of the shot-to-shot pulse energies approaches a Gaussian distribution with a small relative rms fluctuation given by 1 M . Figure 1.9 illustrates the simulated temporal power profile for a LCLS hard X-ray pulse with T = 20 fs and M ≈ 50.  When an extremely short X-ray pulse is generated with M = 1, the SASE approaches a single spike regime with the statistical fluctuation following a negative exponential distribution. The measured rms energy fluctuation in the TTF radiation pulse in both exponential and saturation regimes is shown in Figure 1.6. Note that M is not a constant since the FEL bandwidth (and hence the coherence time) changes with undulator length. The intensity fluctuation maximizes at saturation and reduces significantly after saturation, as also shown in Figure 1.6.

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Figure 1.8 Peak brightness of various XFEL facilities (see Section 1.3) and several

third-generation synchrotron radiation facilities. Reproduced from Z. Huang, “Brightness and Coherence of Synchrotron Radiation and FELs”, in the Proceedings of the 4th International Particle Accelerator Conference, Shanghai China 2013.55

The ability to generate coherent harmonic radiation is an important aspect of an XFEL. In a planar undulator, the electron trajectory is not a pure sinusoid due to the fact that the longitudinal velocity oscillates at one-half of the undulator period. This fact leads to odd harmonic emission along the undulator axis. The FEL interaction introduces both energy and density modulations of the electron beam with the period λr. Close to saturation, strong bunching at the fundamental frequency λr produces rich harmonic bunching and significant harmonic radiation in a planar undulator.58,59 A 3D analysis of nonlinear harmonic generation60 shows that the gain length, and transverse and temporal properties of the first few harmonics are eventually governed by those of the fundamental after a certain stage of exponential growth. For instance, driven by the third power of the radiation mode at the fundamental wavelength, the third nonlinear harmonic radiation grows three times faster than the fundamental with a narrower coherent transverse mode and a spikier temporal structure. The third harmonic power can reach 1% of the fundamental power level and has been quantified in several short-wavelength FEL experiments.61–63 As discussed earlier, both electron beam energy loss and energy spread increase due to the FEL interaction, and lead to the saturation of the radiation power. The FEL efficiency at saturation is about ρ [from eqn (1.10)] and is only on the order of 10−3. As first shown by Kroll, Morton and Rosenbluth,64 it is possible to extract more electron energy by varying the undulator parameter K after saturation to keep the resonant condition for a large fraction of the

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Figure 1.9 Simulated temporal profile of a 20 fs LCLS hard X-ray pulse at the undulator distance (a) z = 25 m, (b) z = 50 m, and (c) z = 75 m.

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Figure 1.10 Comparison of the simulated radiation power for the LCLS FEL at 1.5 Å

for a tapered monochromatic (seeded) amplifier (blue), tapered SASE (green), and untapered SASE (red). Reprinted from Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 483(1–2), W. M. Fawley, Z. Huang, K.-J. Kim, N. A. Vinokurov, Tapered undulators for SASE FELs,  537–541, Copyright (2002) with permission from Elsevier.68

electron bunch. In order to maintain the resonant condition, the undulator parameter K should be gradually decreased as this group of electrons continues to lose their energies. This is referred to as undulator tapering. FEL experiments from microwave frequencies to hard X-rays have demonstrated that tapering an undulator substantially increases the output power and extraction efficiency of a single-pass FEL amplifier.65–67 Simulations68–70 have also shown that a seeded FEL amplifier with a more uniform temporal profile can extract more energy using a tapered undulator than a SASE FEL and can potentially generate an XFEL that reaches TW peak power (Figure 1.10).

1.3 Present Status As discussed in the previous section, an FEL can be considered as an amplifier, where the input signal is fully specified by a given combination of electron energy modulation, electron density modulation and electric field at the entrance of the FEL undulator. During the FEL process, these three quantities interact self-consistently. The electron beam itself acts as an active medium and, during the FEL amplification process, energy is extracted from the beam to the advantage of the output radiation pulse. The process itself is parametric and heavily depends on the local electron beam properties: current, energy, energy spread and emittance, as discussed in Section 1.1.4 and later. The shorter the FEL wavelength is, the more stringent the requirements on the beam properties for the FEL instability to develop. Because of this reason, XFELs are driven by linear accelerators that ensure the best electron beam quality. Different accelerator designs are possible, with currents up to several thousands of Amperes,

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energies up to about 20 GeV, repetition rates from a few hundred Hz to MHz, relative energy spread down to a fraction of the FEL parameter ρ defined in eqn (1.18) and normalized emittances smaller than 10−6 mrad. The low repetition rate of room temperature linacs can be increased to the MHz range by using superconducting accelerators, operating in burst or continuous-wave (CW) mode. The choice and the preparation of the input signal for the FEL process plays a central role in the output characteristics of the radiation generated. In fact, since the FEL acts as an amplifier, many of the properties of the input signal are inherited by the output. For example, if one uses an external seed laser pulse as the input signal, one obtains a fully transversely and longitudinally coherent output signal. However, the success of external seeding techniques is currently limited to X-ray wavelengths above the nanometer range, while much shorter wavelengths can be obtained exploiting the SASE mode of operation. In this case, the input signal is constituted by the electron beam density modulation due to shot noise, which has a white spectrum and is always present in electron beams. Then, due to the mode-selection mechanism discussed in Section 1.2, the output radiation is highly transversely coherent, while longitudinal coherence is lost due to the amplification of many modes during the FEL process. In what follows, we focus our discussion on two different spectral ranges: the hard X-ray and the soft X-ray range. The boundary between the two ranges is set, in a somewhat arbitrary way, around one to a few nanometer wavelengths, which is the present limit for external seeding techniques.

1.3.1 Hard X-ray FELs The typical mode of operation of XFELs at wavelengths shorter than 1 nm is SASE, as discussed in detail in Sections 1.1.4 and 1.2. The efficiency of an FEL at saturation is measured by the ratio of electron beam power and X-ray pulse power, and is of order of the FEL parameter ρ. Typical ρ values for hard X-ray FELs are between 10−4 and 10−3. Typical electron beam energies range from a few GeV up to about 20 GeV, with currents between about 1 kA up to several kA. Using these numbers, we can easily estimate the X-ray pulse power at saturation to be in the order of several tens of GW. The electron bunch duration is usually tunable by selecting different charges from tens of pC up to about 1 nC, and compressing them to the same peak current. One thus obtains typical X-ray pulse durations between a few and a few hundred femtoseconds. In the remaining part of this section we will focus more in detail on the performance, at the fundamental harmonic, of several major hard X-ray facilities based on the SASE principle, either in operation or about to start operation.

1.3.1.1 LCLS The LCLS, located at the SLAC National Accelerator Laboratory, began operations in 2009 and was the first facility in the world to lase in the hard X-ray range, at 1.5 Å.37 It is driven by a normal conducting linac with a maximum repetition rate of 120 pulses per second (see Figure 1.11). Electron bunches can be accelerated

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Figure 1.11 The layout of the LCLS from gun to experiments71 [Reprinted with permission of the author from: H. Loos, LCLS Beam Diagnostics, Proceedings of IBIC2014, Monterey, CA, USA, Fig. 1 (distributed under the terms of the Creative Commons Attribution 3.0 License)].

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up to 14 GeV (recently up to 17 GeV), with typical charges varying from 20 pC to 250 pC, peak currents of 2–4 kA, normalized slice emittance depending on the charge and smaller than 1 mm mrad, and typical uncorrelated energy spread of 1–2 MeV. The linac serves a single planar fixed gap undulator with a period of 30 mm, composed of thirty-three 3.4 m-long segments, with intersections, including focusing elements, diagnostics and correctors, for a total undulator length of 132 m. The LCLS produces radiation between 280 eV and 12.8 keV at the fundamental, with a pulse duration between 2 fs and 500 fs, and up to 6 mJ energy (depending on the pulse duration).72,73 Longitudinal coherence properties vary between a single and many modes, depending on electron bunch duration and the operation wavelength. The LCLS includes a soft X-ray self-seeding setup74 (SXRSS) based on a grating monochromator for operation between 500 eV and 1 keV and a hard X-ray self-seeding75 (HXRSS) based on a single diamond monochromator76 for operation between 5.5 keV and 9.5 keV, yielding a typical pulse energy of 0.3–0.6 mJ, and an increase in brightness of a factor of 2–5 with respect to SASE. The setup can also be used for the production of multiple color FEL pulses, both in self-seeded and SASE mode.77,78 Multiple colors were also obtained by modulating the gain in the undulators.79 Multiple colors with energy separation of the order of 100 eV and a temporal separation up to tens of femtoseconds is possible by creating two identical bunches accelerated off-crest in the same bucket.80 A 3.2 m-long Delta-undulator afterburner has been recently added to the LCLS capabilities.81 It allows the production of circularly polarized X-ray pulses with energy of a few hundred microjoules in the soft X-ray range between 500 eV and 1500 eV.81 By 2019 LCLS will be upgraded to LCLS-II.44 LCLS-II will be driven by (a) a new superconducting CW linac with up to 1 MHz repetition rate and 4 GeV electron energy, producing X-rays in the range of 200 eV and 5 keV, and (b) the existing LCLS copper linac with 120 Hz repetition rate and up to 17 GeV electron energy, producing X-rays up to 25 keV. It will have two variable gap undulators: a hard X-ray (HXR), with 32 segments, 3.4 m length each, 0.6 m-long break sections, and a 26 mm period; and a soft X-ray (SXR), with 21 segments of 3.4 m length and 1 m long intersections, and a 39 mm period. The copper linac will feed the HXR line, while the superconducting linac will feed both HXR and SXR undulators.

1.3.1.2 SACLA The SACLA XFEL, shown in Figure 1.12, is located in Hyogo, Japan, and began operation in 2012.82,83 It is driven by a normal conducting linac, currently operating at a maximum repetition rate of 30 Hz. Tests are in progress to increase it to 60 Hz. Electron bunches can be accelerated up to 8.5 GeV, with charges between 0.2 nC and 0.3 nC, and peak currents above 3 kA. The linac serves a planar, in-vacuum undulator (BL3), with 18 mm period composed of 21 variable-gap segments, each 5 m long. The SACLA XFEL delivers radiation pulses in the photon energy range between 4 keV and 20 keV, with a duration between 2 and 10 fs, and saturation power between 6 GW and 60 GW,

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Figure 1.12 Schematic of the SACLA XFEL. Adapted with small modifications and

with permission of the authors from Fig. 1 in ref. 86 (distributed under the terms of the Creative Commons Attribution 3.0 License).

corresponding to a maximum pulse energy of about 0.5 mJ at 10 keV. Energy fluctuations are smaller than 10% rms, with a spectral bandwidth of about 0.5%. The BL3 line is equipped with a single crystal HXRSS setup,84 which is currently under commission. The chicane is used also to produce twocolor pulses with large (about 30%) spectral and spatial separation.85 A second hard X-ray undulator line with the same parameters (BL2) lased in 2014, while a XUV/SXR line (BL1) is under commission. A switching magnet before the undulators86 selects the line in operation. Space for accommodating two more beam lines is part of SACLA. It should also be noted that SACLA shares one beam line with the adjacent SPring-8 synchrotron facility to accommodate experiments using both XFEL and synchrotron pulses simultaneously.

1.3.1.3 Pohang Accelerator Laboratory (PAL) XFEL The PAL XFEL, located in Pohang, Korea, is at an advanced stage of construction and achieved lasing in the summer of 2016.87,88 It is driven by a normal conducting linac, with a repetition rate of 60 pulses per second. Electron bunches can be accelerated up to 10 GeV, with charges between 20 pC and 200 pC, peak currents of 4 kA, normalized slice emittance of about 0.4 mm mrad, and a few MeV energy spread. The expected pulse duration is between 5 fs and 100 fs. The linac will feed two variable gap planar undulators, as shown in Figure 1.13: an HXR, with 26 mm period, dedicated to the generation of X-rays between about 1.2 keV and 20 keV, and an SXR, with a 35 mm period, for

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Figure 1.13 Schematic of the PAL XFEL, reprinted with the permission of In Soo Ko. X-rays between about 270 eV and 1.2 keV at the fundamental. Tuning of the X-ray wavelengths will use both changes in electron beam energy and undulator gap. All undulators are made with 5 m-long magnetic segments separated by 1 m-long intersections, including focusing elements, phase shifters, diagnostics and correctors. The HXR line will initially consist of 20 segments (expandable to 28 segments) and lased in the summer of 2016. The SXR line will be complemented by an elliptical afterburner for polarization control. Photon pulses of 60 fs FWHM are expected at 0.2 nC charge, with a target peak power of 30 GW at 0.1 nm wavelength. The HXR line will be equipped with an HXRSS setup, which will be operational in the near future.89

1.3.1.4 SwissFEL The SwissFEL facility, shown in Figure 1.1490 and located at the Paul Scherrer Institute, in Villigen, Switzerland, is at an advanced stage of construction and has already started to lase in 2016. It is driven by a normal conducting linac, with a repetition rate of 100 Hz. Electron bunches can be accelerated up to 5.8 GeV, with charges between 10 pC and 200 pC, peak currents between 1.5 kA and 2.7 kA, normalized core slice emittance between 0.18 mm mrad and 0.43 mm mrad, and a slice energy spread of a few hundred keV. The normal conducting linac will serve, initially, the Aramis variable gap, an in-vacuum planar undulator with 15 mm period. After 2017, a second line using an APPLE-II type 40 mm period undulator, Athos, will be added. Athos will work at X-ray energies between 250 eV

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Figure 1.14 The SwissFEL layout, reprinted with permission from Nuclear Instruments and Methods in Physics Research Section A: Acceler-

ators, Spectrometers, Detectors and Associated Equipment, 798, J. Lee, C. H. Shim, M. Yoon, I. Hwang, Y. W. Parc, J. Wu, Optimization of the hard X-ray self-seeding layout of the PAL-XFEL, 162–166, Copyright (2015) with permission from Elsevier.89

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and 2 keV in SASE mode, iSASE/HB-SASE mode (this option will be enabled by the installation of little chicanes between each undulator module, see Section 1.3.3) and self-seeded mode, while Aramis will work in SASE and HXRSS mode91 (self-seeding options will be implemented at a later stage). The Athos line will be composed by 20 segments, each 2 m long, and will produce pulses with duration around 10 fs and several GW saturation power. The Aramis line will consist of 12 segments, each of them 4 m long, and will produce X-rays between 1.7 keV and 12.4 keV, with the option to upgrade the photon energy to the Fe Mössbauer line. At 1 Å, Aramis will produce pulses with a length between 2.1 fs (at 10 pC charge) and 21 fs (at 200 pC charge), with saturation power of 0.6 GW and 2.8 GW, respectively. Special modes of operation will allow the production of photon beams with large bandwidths (up to 3.5% FWHM) and/or ultrashort duration (60 as).

1.3.1.5 European XFEL The European XFEL,92–94 located between the states of Hamburg and Schleswig-Holstein, Germany, is at an advanced stage of construction and is expected to lase in the first half of 2017. It will be the first hard XFEL to use a superconducting linac based on TESLA cavities,95 with a maximum repetition rate of 27 000 pulses per second, distributed in ten trains with a maximum of 2700 pulses each, with an intra-train repetition rate of 4.5 MHz and the possibility of upgrading to the CW mode of operation. Electron bunches can be accelerated to 17.5 GeV, with charges varying from 20 pC to 1 nC, peak currents of about 5 kA, normalized emittance (depending on the charge) below 1 mm mrad, and a few MeV uncorrelated energy spread. The superconducting linac will feed two electron lines. The bunch pattern of these lines is fully and independently controlled by a very flexible beam distribution system, allowing for nearly simultaneous operation. Three planar, variable gap undulators are being installed: SASE1, SASE2 and SASE3, while space for more undulator lines and instruments is available, as shown in Figure 1.15: SASE1 and SASE2 are 40 mm-period undulators dedicated to the production of X-rays between about 3 keV and 25 keV in the fundamental, while SASE3 is a 68 mm-period undulator dedicated to softer X-ray energies between about 250 eV and 3 keV in the fundamental. The use of several electron energy points (8.5 GeV, 12 GeV, 14 GeV and 17.5 GeV) will allow continuous tuning of the X-rays over the entire frequency range. All undulators are composed of 5 m-long magnetic segments, separated by 1 m-long intersections, including focusing elements, phase shifters, diagnostics and correctors. SASE1 and SASE2 have 35 segments, while SASE3 has 21 segments. SASE3 will be equipped with an afterburner for polarization control below 3 keV. The X-ray pulse duration will range from a few femtoseconds for the lowest charges up to about 100 fs. The peak power obtainable will heavily depend on the electron energy and charge, and on the operation wavelength, with expected powers up to several tens of GW at saturation. Longitudinal coherence properties are expected to have a large variation, depending on

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Figure 1.15 Layout of the European XFEL. the electron bunch duration and the operation wavelength. At the longest wavelengths and for the shortest bunches a single mode is expected, with large shot-to-shot energy fluctuations, while at the shortest wavelengths and longest bunches, one expects up to several hundred modes. Also, the degree of transverse coherence is expected to vary from about 0.5 for the shortest wavelengths, highest charge and lowest electron energies up to about unity for the longest wavelengths, smallest charges and highest electron energies.96 Finally, the availability of long undulators opens up the possibility to implement two-color schemes,97 post-saturation tapering (see Sections 1.2.1 and 1.3.3), self-seeding98 (which will be installed at SASE2), harmonic  lasing99 and related advanced techniques (see Section 1.3.3).

1.3.2 Soft XFELs External seeding techniques can be employed for wavelengths longer than a few nanometers, complementing SASE. Two seeding principles and their combinations have been studied for a long time in lasers: high-gain harmonic generation (HGHG)100,101 and high-order harmonic generation (HHG).102,103 Novel external seeding techniques, for example, echo-enabled harmonic generation104 (EEHG), are briefly discussed in Section 1.3.3. In HGHG, an electron beam interacts in a modulator undulator with a laser at a long wavelength (typically, in the UV range), thus acquiring energy modulation. Subsequently, the electron beam travels through a dispersive element 

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(a magnetic chicane) where, due to energy-dependent trajectories, energy modulation is converted into density modulation. During this process, density modulation at harmonics of the initial laser wavelength is created, serving as the input signal into an FEL radiator with a properly tuned fundamental. HGHG is quite sensitive to the energy spread in the electron beam. An analysis of the dependence on energy spread shows a typical harmonic conversion of the order ρ/σγ, giving, in most cases, a limit of about one order of magnitude. In order to reach shorter wavelengths, one can resort to a cascaded scheme,105 where the output from a first HGHG setup is used to seed a second setup, with a fresh electron bunch.106 However, a fundamental limitation for extending this technique below the nanometer range is related to phase errors of the laser, as they are transmitted down the HGHG setup and multiplied by the total harmonic conversion. In HHG101,102 a target, for instance xenon, is illuminated by an intense laser beam at a given frequency (for example, a Ti:Sa laser in the IR range). Electrons are initially tunnel-ionized, but after half an optical cycle of the driving laser, when the electric field changes direction, they are accelerated back and can recombine with the original atom, emitting wide-bandwidth radiation. The maximum energy that can be gained by the ionized electron determines the cutoff of the HHG emission and can be in the extreme UV (EUV)/SXR range. Radiation, which must be intense enough to compete with shot-noise, is transported to the undulator and superimposed with the electron beam, thus acting as a seed for the FEL. Research on HHG focuses on increasing the cutoff energy to provide the possibility of seeding at shorter wavelengths. The first HHG experiment in the soft X-ray region was done at the SPring-8 Compact SASE Source (SCSS),107 an FEL located in Hyogo, Japan, active from 2005 to 2013. SCSS began operation as a proof of principle for compact XFELs in SASE mode and it also hosted an HHG setup.108,109 The SCSS normal-conducting accelerator will be relocated108 into the undulator hall of SACLA and will independently drive the BL1 SACLA undulator to produce FEL pulses in the EUV to SXR range under the name of SCSS+. SCSS+ is shown in Figure 1.12 and is currently under commission. The HHG experiment at the SCSS107 delivered pulses up to 20 µJ, around 60 nm with a bandwidth of 0.06 nm, a successfully seeding electron beam, delivered with 30 Hz repetition rate and a 20–30% hit-rate. In the next paragraphs, we will consider in more detail the performance of two soft X-ray facilities: Free-Electron LASer (FLASH; Hamburg, Germany) and FERMI (Trieste, Italy). HGHG is routinely used at FERMI. An HHG/HGHG setup is installed at FLASH.

1.3.2.1 FLASH in Hamburg The FLASH facility is located in Hamburg, Germany, and has been in operation as a user facility since 2005. It is the result of upgrades to the TTF that lased, in 2000, at 109 nm, thus demonstrating the competitivity of SASE FELs compared to other lasers at short wavelengths.110–113 It is driven by a superconducting linac based on TESLA technology94 (the same technology was later adopted at the European XFEL), accelerating

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Figure 1.16 The soft X-ray user facility FLASH; reprinted with permission from Schreiber, S. and Faatz, B. (2015) “The free-electron laser FLASH”, High Power Laser Science and Engineering, volume 3.114

electrons up to 1.25 GeV in ten trains per second, with up to 800 bunches/ trains, a tunable inter space between 1 µs and 25 µs, and a bunch charge between 20 pC and 2 nC. Typical peak currents of several kiloamperes with an energy spread of a few hundred kiloelectron-volts and normalized emittances below 2 µrad are obtained. The FLASH accelerator currently serves two soft X-ray UV (XUV) undulators:113 FLASH1 and FLASH2, see Figure 1.16. FLASH1 is a fixed gap undulator. By tuning the electron energy, one can produce FEL pulses in SASE mode between 4.2 nm and 52 nm in the fundamental, with a variable pulse duration between 30 fs and 200 fs (FWHM), and typical peak powers between 1 GW and 5 GW. FLASH2113 is a variable gap undulator and lased115 in 2014 at a wavelength of 40 nm. It produces FEL pulses between 4 nm and 90 nm, with energies up to 500 µJ. Simultaneous operation of FLASH1 and FLASH2 was demonstrated in 2015.116 User operation of FLASH2 started in the spring of 2016. The FLASH facility also hosts a seeding section117 composed of two modulator sections with a 20 cm period for a total effective length of 1.2 m—separated by two magnetic chicanes—and a variable gap radiator, sFLASH. This is a 10 m-long undulator with a period of 3.14 cm. The seed is constituted by a 266 nm laser beam with up to 280 µJ pulse energy and a pulse duration of 120 fs FWHM, generated using the third harmonic of near IR Ti:Sa pulses. Direct HHG seeding at 38.2 nm was demonstrated in 2013,116 albeit with limited contrast ratio due to the low hit rate. After that, seeding efforts focused on HGHG and on possible, future EEHG applications. The HGHG mode was recently operated at 38 nm, the seventh harmonic of the seed laser.118

1.3.2.2 FERMI FERMI, located at Basovizza, Italy, is the first user facility exploiting HGHG as the main mode of operation, while still allowing for SASE mode of operation.119–122 A normal conducting linac accelerates electrons up to 1.5 GeV, with a repetition rate between 10 Hz and 50 Hz, bunch charges up to 700 pC and an energy spread around 100 keV. Peak currents around 700 A are obtained, corresponding to a duration of about 1 ps, with normalized emittances of

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Figure 1.17 The layout of FEL-1 and FEL-2 at the FERMI user facility. Reproduced with permission from Enrico Allaria and the FERMI Team, 37th International Free Electron Laser Conference.

about 1.4 mm mrad. FERMI is seeded by the third harmonic of a Ti:Sa laser at 261 nm, delivering up to 0.2 mJ energy per pulse, or by a tunable optical parametric amplification (OPA) system delivering pulses between 230 nm and 260 nm, with energies up to 0.1 mJ per pulse. Pump-probe experiments with very low jitter are enabled by transporting a fraction of the pump laser in the IR region to the experimental hall.123 Two FEL lines, FEL-1 and FEL-2,  are available, using APPLE-II type undulators that grant full polarization  control,124 as shown in Figure 1.17. FEL-1 relies on a single stage HGHG.118 It generates pulses of energy between 50 and 300 µJ, wavelengths between 20 nm and 100 nm, with a relative bandwidth smaller than 0.1% FWHM, and a pulse duration between 50 fs and 100 fs.121 Special modes of operation at FEL-1 include short wavelength pulses and energy of 10 µJ at 12 nm wavelength (below the FEL-1 nominal reach), and two-color operation using two seed pulses and two sections of the radiator tuned to the harmonics of the two seeds.125 The high longitudinal coherence of FERMI also allows phase correlation of two-color pulses at different harmonics.126 FEL-2 uses a double stage HGHG cascade generating X-ray pulses of energy between 10 µJ and 100 µJ, and wavelengths between 4 nm and 20 nm, with similar relative bandwidth as for FEL-1 and a pulse duration between 30 fs and 70 fs.119 The double-stage relies on two modulators and two radiators. After the first HGHG stage, electrons pass through a delay line, so that radiation and a fresh part of the electron bunch, which has not been radiated yet, are superimposed at the entrance of the second modulator. In this way, the energy modulation at the wavelength of the radiation from the first stage is imprinted on the fresh part of the bunch, which then enters the dispersion section and the second radiator, tuned at a higher harmonic of the first stage output.

1.3.3 Novel Developments In the previous sections, we discussed the state-of-the-art performance of seeded and SASE modes of operation of XFELs. However, we have seen that HGHG and HHG techniques are currently limited in the maximum photon

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energy achievable, while SASE usually suffers from a poor longitudinal coherence. Another limitation of current FEL facilities is their large scale. Because of these reasons, significant research activity has focuses on increasing longitudinal coherence with a simultaneous increase of brightness in the SASE mode of operation, seeding at higher photon energies, and reducing the size of the FEL setup. In the following sections, we will briefly discuss novel developments in these areas of research.

1.3.3.1 Increasing the Longitudinal Coherence of XFEL Radiation Here, we will consider several techniques that can be employed to increase the longitudinal coherence of SASE radiation. These techniques may be applied in synergy with tapering in order to increase the output power of the SASE radiation. Tapering consists of a reduction of the strength of the undulator magnetic field so that the resonance wavelength is kept the same when the electron energy decreases due to the FEL process.127–133 By starting the FEL process from a monochromatic seed instead of noise, one expects a large increase in output power as the electron beam experiences a better-  behaved ponderomotive potential compared to the SASE case. Tapering can be easily implemented at facilities with long, tunable undulators like those at the European XFEL and the LCLS-II.134–139

1.3.3.2 Self-seeding A self-seeded FEL consists of two undulator parts and a frequency filter.140 The first undulator part is an FEL working in the SASE linear mode of operation, which still allows further lasing of the electron beam. After the first part of the undulator, radiation and electrons are separated by letting the electrons pass through a magnetic chicane with the length of a single undulator module, in order not to require changes in the external focusing system of the FEL. The electron beam density modulation due to the previous FEL process is destroyed by the dispersion introduced by the chicane, while the X-rays pass through a spectral filter. The filter narrows the SASE pulse to the width chosen by the spectral filter (not necessarily the final spectral bandwidth of the self-seeded FEL) and these monochromatic X-rays serve as a seed. This seed pulse is superimposed with the electron bunch at the entrance of the second undulator, which functions as an FEL amplifier. In practice, different self-seeding schemes have been realized, mainly differing in the filter used. In particular, a very compact grating monochromator is used74 in the soft X-ray range, whereas a single crystal or “wake” monochromator is used in the hard X-ray range.75,76 In this latter case, the single crystal acts to the first approximation as a narrow notch filter. In the time domain, the filtered FEL radiation is characterized by the presence of a monochromatic “wake”, following the main FEL pulse, which is used as the seed signal. From a practical viewpoint, “wake” monochromator filters consist of a thin, perfect-crystal diamond (typically around 100 µm thick). Different orientations of the

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crystal with respect to the beam are used to select different crystal planes at slightly different wavelengths within the FEL bandwidth, thus enabling the generation of multiple seed colors.77 In the case of a grating monochromator, as used for soft X-rays, the grating disperses the different frequency components of the X-ray pulse generated in the first undulator and a slit filters out one particular color, which is superimposed with the electron beam at the entrance of the second undulator (the electron beam itself may also act as a slit). HXRSS setups are currently in operation at LCLS,75 under commission at SACLA,84 and planned at European XFEL,97 Swiss-FEL90 and PAL-FEL.88 An SXRSS setup is in operation74 at LCLS. Self-seeding is sensitive to the electron beam quality141 and to jitter effects.75 In particular, a non-linear energy chirp in the electron beam leads to an increase in the spectral bandwidth beyond the Fourier limit, while energy jitter of the electron beam larger than ρ/2 increases the number of FEL shots yielding no output if the seed wavelength falls outside of a given SASE spectrum. Currently, the self-seeding setups at LCLS yield an increase in average spectral brightness by a of factor two to five compared to optimized SASE. Operation on high-repetition rate machines needs a special design due to heat loading of the self-seeding optics by the FEL pulse (see reference 134 for the HXRSS case) and spontaneous radiation.

1.3.3.3 Harmonic Lasing Harmonic lasing is an FEL instability driven by the nth harmonic of the fundamental.142–147 In order to saturate, the FEL process at the fundamental must be suppressed, which can be partly achieved by properly adjusting the phase delay of the phase shifters and partly by performing spectral filtering at different locations (e.g., complementing self-seeding chicanes with appropriate frequency filters). Saturation power and relative bandwidth both scale as 1/n compared to saturation power and relative bandwidth of the fundamental, while good transverse coherence is preserved and shot-toshot intensity fluctuations are comparable. Therefore, the pulse brilliance is comparable to that of the fundamental, yielding the possibility of lasing at shorter wavelengths with lower beam energy. After being recently reconsidered,148 the method is currently under active study as a possible asset for FLASH, the European XFEL and the LCLS-II. The increase in longitudinal coherence corresponds to that achieved by a monochromator, i.e., the brilliance is preserved. In order to increase the brilliance, it was proposed to first perform harmonic lasing in the linear regime in the first part of the undulator and then continue with the undulator retuned at the fundamental up to saturation.148

1.3.3.4 Purified SASE (pSASE) In the pSASE scheme a “slippage-boosted section” consisting of a few undulator segments resonant at a sub-harmonic of the FEL radiation is used in the middle of the exponential regime to amplify the radiation, while

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simultaneously reducing the FEL bandwidth or, equivalently, increasing the coherence length by increasing the slippage.149 Since the slippage-boosted section is located in the linear regime, the pSASE output should be independent of the position of the slippage-boosted section. In particular, if placed at the very beginning of the undulator, pSASE and the scheme proposed in ref. 148 to increase the brilliance coincide.

1.3.3.5 High-brightness SASE (HB-SASE) and improved SASE (iSASE) Several methods to increase the longitudinal coherence length of SASE radiation are based on the use of ad hoc phase-shifters to increase the total slippage of radiation with respect to the electron beam, up to the bunch length. In HB-SASE,150–152 one uses a periodic constant delay scaling as N + 1 times the cooperation length to clean up the sides of the spectrum, while in iSASE,153,154 one selects a geometric delay scaling as 2N times the cooperation length to narrow the central frequency region. Combinations of periodic and geometric delays have been considered as well. Proof-of-principle experiments for the iSASE scheme were successfully carried out at the LCLS using detuned undulators as phase shifters, which also showed the possibility of producing two-color iSASE pulses.79 Compared to self-seeding, the method is insensitive to electron energy jitter and all pulses present an improved temporal coherence. However, large electron energy jitter would lead to a jitter in the central bandwidth and a consequent increase of the FEL bandwidth averaged over many shots. For iSASE, no material medium needs to intercept the radiation (FEL and spontaneous), which is a clear advantage in the case of high-repetition rates. iSASE should be planned from the early design stages of a facility to provide the delays needed, since it requires phase shifters stronger than those used in conventional XFEL intersections.

1.3.3.6 EEHG EEHG155 is a seeding method that potentially allows reaching higher harmonic up-conversion compared to HGHG. The EEHG scheme is based on harmonic generation, but it includes two modulators and two dispersive sections. In the first modulator, a very particular longitudinal phase-space distribution is created, consisting of many beamlets, which are converted into bunching at high harmonics in the second. While HGHG is usually limited by the electron energy spread ρ/σγ, EEHG is not subject to that limitation. Intra-beam scattering and incoherent synchrotron radiation effects constitute conceptual limitations to the harmonic conversion factor but are still estimated to allow for a 100-fold conversion factor.156 One also has to consider the impact of the temporal and spatial quality of the seed laser beam, as phase errors are multiplied by a factor equal to the harmonic conversion factor. These considerations indicate that, while EEHG is intrinsically more efficient than HGHG, reaching EEHG radiation below 1 nm remains challenging.

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However, schemes to further increase the harmonic conversion number have been recently proposed using a triple modulator chicane (TMC).157 Successful EEHG experiments have been carried out at the Next Linear Collider Test Accelerator facility (NLCTA) at SLAC and at the Shanghai Deep-UltraViolet Free-Electron Laser (SDUV FEL) at the Shanghai Institute of Applied Physics (SINAP)158–160 up to the seventh harmonic. A direct observation of fine-scale energy banding in EEHG was made,161 where a conversion factor of 15 was reported, corresponding to an EEHG signal at 160 nm. In 2016, a conversion factor of 75 was demonstrated at NLCTA.162

1.3.3.7 Hard X-ray FEL Oscillator (XFELO) Building on the pioneering work of A. Luccio and R. Colella,163 the possibility of constructing an XFELO using Bragg mirrors to form an optical cavity has been studied again by K.-J. Kim, Y. Shvyd’ko and S. Reiche.164 Tunability can be obtained with a four Bragg mirror configuration,165,166 with diamond as the preferred crystal choice due to thermal and mechanical characteristics. An XFELO may be driven by an energy recovery linac or by a high-repetition rate CW superconducting linac. An XFELO would yield full transverse and longitudinal coherent laser pulses with a bandwidth in the order of a few millielectron-volts. For example, a CW linac with 25 pC bunches at 7 GeV and 0.5 ps rms durations could yield about 6.5 × 108 photons pulse−1 in a 3 meV FWHM bandwidth at a repetition rate of 3 MHz,167 thus complementing the output characteristics of conventional FELs. Studies for possible integration of an XFELO setup at the European XFEL168,169 and at the LCLS-II170 have been recently performed using the high-repetition rate of these accelerators. The case discussed in ref. 167 suggests a peak brilliance comparable to that obtainable with a combination of self-seeding and tapering171 within a spectral bandwidth about two orders of magnitude narrower than the in the FEL amplifier case.

1.3.3.8 Compact XFEL Sources The success of XFELs is strictly linked to the availability of high-brightness, high-energy linear accelerators. Conventional accelerator technologies pose a limit to the compactness of the machine. Therefore, XFELs are large-scale facilities, often several kilometers long. In recent years172,173 laser plasma accelerator (LPA) technology has made great progress towards low repetition rate XFEL-class beams with peak currents reaching about 10 kA, energy in the GeV scale, pulse durations shorter than the coherence length in the soft X-ray range and an emittance below what is needed for lasing in the X-ray regime, about 0.1 µm. However, the energy spread is still at a few percent, and therefore is too high for a soft X-ray FEL. A part of research and development towards the construction of a suitable driver for XFELs in the soft (few nanometers) X-ray range focuses on decreasing the electron beam energy spread. Other efforts are based on the observation that due to the very small emittance provided by LPA beams, the overall phase space volume is small enough

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to drive an XFEL. Therefore, in principle, one only needs to redistribute the LPA beam phase space in order to enable lasing. It has been proposed to do so by means of different techniques. One possibility is collimation or emittance exchange.174 Another is longitudinal decompression, where the electron beam, passing through a chicane, is transformed into a chirped beam with slice energy spread smaller than the FEL bandwidth and then proceeds into a tapered undulator.175 Finally, the use of transverse gradient undulators (TGUs) has been suggested. In this case, the LPA electron beam is first dispersed in the transverse direction and then sent into a canted-pole undulator.176,177

1.4 Conclusion The operation of LCLS, SACLA, FLASH and FERMI has been very successful, with remarkable performance improvements and important scientific results obtained in the past 5 to 10 years in physics, chemistry, biology and materials science. The scientific results and FEL improvements of LCLS have been discussed and reviewed recently in two Review of Modern Physics articles.5,8 In this chapter, we first reviewed the basic physical principles of XFELs, introducing the subject also from an historical perspective. We discussed 1D and 3D theories to give a compact but overall complete description of the working principles of XFELs. We also described in Section 1.3 their output characteristics, considering aspects like pulse brightness and statistical properties, and examined the present status of XFELs facilities, in operation or under an advanced stage of construction, summarizing the main properties of the pulses they generate. Lastly, we considered the research being carried out to improve the X-ray pulse coherence properties, the generation of multicolor spectra, the reduction of pulse duration and the production of very large peak power in the multi TW region. These improved FEL characteristics will push even further the frontier of scientific research in many areas of physics, chemistry, biology and materials sciences, including those concerned with fundamental processes critical to energy and the environment.

Acknowledgements G. G. thanks Enrico Allaria (FERMI), In So Koo (PAL-XFEL), S. Reiche (SwissFEL), S. Schreiber (FLASH) and M. Yabashi (SACLA) for reviewing the text dedicated to the description of their facilities and for useful updates. The support from EU 6 Multihybrids (IP 026685-2), Nanofire (NMP3-CT 2004505637) projects, Hungarian Research Found OTKA T049121, Fund of European Union and Hungarian state GVOP/3.1.1.-2004-0531/3.0, Public Benefit Association of Sciences and Sport of the Budapest University of Technology and Economics are acknowledged. C. P. wishes to thank SLAC National Accelerator Laboratory for its generous hospitality and the USA Department of Energy for its support under grant DE-SC0009983:0003. The work of  Z. H. and C. P. was supported by the USA Department of Energy under grant DE-AC02-76SF00515.

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Section II

Biological Structure Determination

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Chapter 2

Imaging Protein Dynamics by XFELs John C. H. Spence Arizona State University, Department of Physics, Tempe, Az, 85287-1504, USA *E-mail: [email protected]

2.1 Introduction: Seeing Atoms Without Using Crystals This review discusses applications of X-ray free-electron lasers (XFELs) to structural biology, with emphasis on approaches to imaging protein dynamics by time-resolved, atomic-resolution snapshot diffraction, with the briefest coverage only of topics treated more fully elsewhere in this book. First, some historical context. Richard Feynman once commented that, “Everything that living things do can be understood in terms of the jigglings and wigglings of atoms”. He believed that the atomic hypothesis, that matter consists of atoms, was mankind’s most important discovery. The first person to see an atom clearly was a student of Erwin Mueller’s at Penn State around 1951, using his field-ion microscope with a cooled tip.1 (Earlier work at room temperature had been less successful.) From the ancient Greeks to Robert Hooke’s “Micrographica” in 1665 (where the angles between the facets on microcrystals he saw in his new microscope suggested the packing of tiny spheres), the idea that atoms are the basic building blocks of matter has motivated efforts to see them in order to explain everything from biochemical   Energy and Environment Series No. 18 X-Ray Free Electron Lasers: Applications in Materials, Chemistry and Biology Edited by Uwe Bergmann, Vittal K. Yachandra and Junko Yano © The Royal Society of Chemistry 2017 Published by the Royal Society of Chemistry, www.rsc.org

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reactions to the performance of turbine blades in jet engines. The equally important challenge of understanding why atoms stick together in the particular arrangements they do, responsible for the properties of matter, from rusting ships to strong, light materials, explosives and protein–ligand interactions, has proven far more difficult.2–4 But it is the XFEL that now, for the first time, has allowed us to image molecules in motion at atomic resolution, with femtosecond time resolution, albeit within protein nanocrystals.5 The difficulties in making the required atomically sharp needles for field-ion microscopy soon spurred other efforts, and it was Albert Crewe in 1970 at Argonne National Laboratory who first saw an isolated atom, using a scanning transmission electron microscope (STEM).6 Crewe dedicated years of work to the imaging of dehydrated DNA on carbon films in a vacuum. Just prior to that work, the first three-dimensional (3D) reconstructions of stained viruses had been achieved by transmission electron microscopy (TEM),7 and in 1975 molecular images were obtained using two-dimensional (2D) unstained crystals of bacteriorhodopsin at 0.7 nm resolution,8 leading eventually to the modern method of cryo-electron microscopy (cryo-EM). This field has made admirably steady incremental progress since, with the development of fast computers and new algorithms, field-emission guns, frozen-hydrated samples in vitreous ice, automated sample-preparation methods, tomography and, now, single-electron area detectors, which are reviewed elsewhere.9,10 From the beginning,7 the emphasis on 3D imaging in biology, compared to the 2D projections (now possible at sub-Angstrom resolution using aberration-corrected instruments) common in materials science, is striking. In biology, DNA provides the ability to make unlimited numbers of identical copies of molecules, whose images may be merged to minimize radiation damage effects—no such method exists for making identical inorganic nanoparticles in materials science, so that other approaches must be used to minimize damage. There are important differences between the methods used to image dynamics in biology and materials science. The first-order phase transitions of greatest interest in materials science generally nucleate at special sites, spreading throughout a crystal, which is an entirely different situation from the chemical reaction cycles within a molecule of interest in biology. These may involve only a few atoms only at the center of a very large protein in each unit cell (containing mostly water) of a protein crystal, and can sometimes be triggered in many unit cells by a light flash. For smaller proteins, the nuclear magnetic resonance (NMR) method has proven very powerful and can also provide dynamical information.11 The cryo-EM method can also be used to image molecules quenched (or "trapped") from an equilibrium ensemble, then sorted by similarity, or optically excited before quenching. The field of XFEL applications to structural biology has been reviewed by Spence,12 Bostedt,13 Schlichting14 and, with emphasis on new approaches to time-resolved diffraction, by Spence in 2014.15 A simple explanation of the operation of the XFEL can be found in Ribic,16 with an outline of the history of that important invention. [The XFEL in self-amplified spontaneous 

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emission (SASE) mode operates on classical principles to achieve gain, quite unlike lasers based on quantum-mechanical atomic transitions.] The Linac Coherent Light Source (LCLS), for example, provides 120 pulses of hard or soft X-rays per second, each containing up to 1012 photons. With a pulse duration of 20 fs, this is sufficient to “out-run” radiation damage at atomic resolution, certainly for nanocrystal samples, and possibly for single particles (see below). Four main modes of data collection are supported at XFELs, as shown in Figure 2.1. These are: serial femtosecond crystallography (SFX) with one protein nanocrystal per shot, fast solution scattering (FSS; or “snapshot WAXS”), single-particle (SP) diffraction with one particle, such as a virus, per shot, and mixing jet studies for snapshot imaging of chemical reactions (this may use either solution scattering or nanocrystals). The gas-dynamic virtual nozzle (GDVN), which uses gas-focussing of a liquid stream to avoid clogging, is shown in Figure 2.2. Other delivery modes, such as viscous media “toothpaste” jets, conveyor belts, the electrokinetic injector17 and particle trap arrays on chips18 have also been developed, together with scanning “fixed” sample mounts for the study of 2D crystals, as discussed in the chapters by Weierstall and DePonte. For single particles, the most recent sample delivery has used the aerosol gas-focussing injector system,19 driven by a GDVN or electrospray. (The first offers lower background but an excessive thickness of the water jacket, the second reduces the jacket to a few monolayers but adds background scattering from the gases used in the electrospray.) A simple

Figure 2.1 (a) SFX with one protein nanocrystal per shot. (b) FSS with many similar

molecules per shot. (c) The SP mode with one particle per shot. (d) A mixing jet for snapshot imaging of slow dynamics.

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Figure 2.2 Environmental scanning electron microscopy (SEM) image of operat-

ing gas-dynamics virtual nozzle. The liquid can be seen to narrow as the outer jacket of high-pressure gas speeds it up as it enters vacuum at about 10 m s−1, where it breaks up into droplets which freeze.23,24 A Bragg beam is seen scattered to the upper left-hand corner.

convergent nozzle has given a 2 µm focus of 200 nm particles,20 while the possibility of running viruses along a hollow tube of light (a Bessel beam) has also been explored.21 New optical imaging methods now allow, for the first time, bioparticles to be directly observed during injection at XFELs, a most important advance to assist alignment.22 Diffraction patterns are read out at the repetition rate of the XFEL. Unless extensive modelling and prior information are available, we will see that only with the “Bragg boost” (the coherent amplification of intensity provided by crystals) is atomic-resolution imaging possible in 3D. This is a powerful effect, since the intensity at the Bragg peak (bringing the peak above noise level) is proportional to the square of the number of molecules in the crystal, so that even a nanocrystal consisting of 10 × 10 × 10 molecules will therefore provide a million times more peak intensity than one molecule, if instrumental and background effects are ignored. Since all these modes have time-resolved variants, the full taxonomy of data-collection modes might be labelled SFX, FSS, SP, time-resolved (TR)SFX, TR-FSS and TR-SP. The first TR-SP experimental results are expected in 2017. A double-focusing GDVN for TR-SFX at high repetition rate XFELS conserves protein.115

2.2 Radiation Damage Limits Resolution It has been clear since the early 20th century that radiation damage places a fundamental limit on resolution in practically all imaging and diffraction methods in biology (neutron diffraction excepted). SP cryo-EM deals with this issue by merging many real-space images of similar molecules, each of which receives less than a critical “damage dose”, which is a function of resolution.

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The images of individual molecules are then far too noisy to provide a useful image—only by merging thousands can a 3D high-resolution density map be obtained. Damage destroys fine detail first.25 Sophisticated sorting algorithms are used in cryo-EM to classify the molecules by orientation and into a number of possible conformations. The images of conformational change can then provide the basis for a molecular movie. Sequence information is obtained by assuming that the most similar images are sequential. It can also be obtained in certain cryo-EM quenching experiments for longer times, which use a timed light flash or chemical spray before freezing of the samples. The quenching time is typically about 1 ms. By comparison with similar XFEL SP data-merging algorithms, the cryo-EM real-space images present no phase problem and do not possess the additional Friedel symmetry present in diffraction patterns under single-scattering conditions. Imaging solves the phase problem. In 1970, shortly after Crewe’s paper, a second paper appeared,26 showing that single-atom imaging of molecules should never be possible using any form of scattered radiation (except, perhaps, neutrons and helium atoms, for which bright sources did not exist), because the radiation dose needed to do so would destroy the molecule. This follows from the ratio of elastic to inelastic cross-sections over a range of beam energies and types of radiation. The paper also contains the sentence “…this does not prevent molecular microscopy if the observations are made sufficiently rapidly…within 10−13 seconds”. This estimate of 100 fs for damage-free imaging has turned out to be remarkably prescient—recent XFEL crystallography using 50 fs pulses has shown 0.2 nm resolution scattering from crystals (where the images are periodically averaged) and 0.59 nm hard-X-ray scattering (limited by an aperture) from individual virus particles at the LCLS, summed over many shots.27 The resolution of 3D SP images is currently about 10 nm. The idea that one could “out-run” radiation damage, by collecting the useful elastic scattering for image-formation before significantly damaging inelastic scattering had occurred, was then further explored by Solem28 and, in detail, in response to the promise of the XFEL with its high-intensity femtosecond pulses, in molecular dynamics simulations by Neutze et al.29 (Recall that X-rays, unlike electrons, are scattered by the atomic electron cloud alone rather than the nuclei, whose positions are tracked in molecular dynamics simulations.) Since damage processes in crystallography occur on time-scales as long as a second (longer than synchrotron exposure times), the idea of out-running damage was not entirely new and had been appreciated in the synchrotron community, but the conceptual breakthrough here was to realise that with laser amplification, if an almost unlimited number of X-ray photons could be packed into a arbitrarily brief pulse, one could break the nexus between resolution, radiation damage and sample size, and so achieve damage-free atomic-resolution from arbitrarily small samples, such as a single virus, if a beam could be focussed down to those dimensions. And one could use samples in their native, room-temperature environment, avoiding the need to freeze samples to reduce damage. The first experimental evidence for this

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“diffract-then-destroy” mechanism came at lower resolution using the vacuum ultraviolet (VUV) laser FLASH at DESY in 2006,30 suggesting the possibility of high-resolution damage-free movies.31 High-resolution (0.8 nm) results from protein nanocrystals using a 1.8 kV XFEL beam were first published in 2011,30 together with the first single-particle XFEL results.32 Following initial elastic scattering, for samples larger than the inelastic mean free path of ejected photoelectrons, the photoelectrons thermalize, taking the sample temperature to perhaps 500 000 K and vaporization. For samples smaller than this size, photoelectrons escape, leaving a charged sample that undergoes a Coulomb explosion. The history and invention of the SFX method can be traced to early proposals for the delivery of samples in single file across a beam by  liquid jet,33 to the first application and development of that method (for the LCLS) at a synchrotron,34 and to its use in the first crystallography experiments at the first hard-X-ray XFEL.35 In this approach, femtosecond X-ray pulses diffract from successive hydrated nanocrystals, running in single file across the focussed XFEL beam in random orientations. Each nanocrystal is destroyed by the beam following diffraction. Diffraction patterns are recorded and read out at 120 Hz. Figure 2.3 shows the fading of high-angle scattering (corresponding to the finest detail in the sample) with increasing XFEL pulse duration at 1.8 kV for Bragg diffraction from the photosystem I protein.42 For the longest pulses, late-arriving X-rays are diffracting from already damaged crystal. As a rule of thumb, one cubic micron of protein crystal (without heavy atoms) produces about 106 scattered hard X-rays

Figure 2.3 Bragg peak intensity in merged SFX from photosystem I43 as a function

of resolution for several different X-ray pulse durations, normalized to the result at 50 fs.42 Fine detail is destroyed first, and the effective pulse duration is set by the time taken to attenuate the high-order Bragg peaks.

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at the tolerable damage limit of 30 MGy. The incident pulse may contain about 1011 hard-X-ray photons, over 98% of which pass through the crystal without interaction. For a 40 fs, 2 keV pulse with irradiance 1017 W cm−2, 10% of the carbon atoms in a protein crystal absorb a photon. A cascade of photoelectrons and Auger electrons releases this energy, followed by a cascade of low-energy electrons caused by secondary impact or field ionizations taking place on a 10–100 fs time-scale. Coulomb repulsion of the ions and an increase in electron temperature then cause displacement of both atoms and ions during the pulse. This heating leads to vaporization of the sample if the secondary electrons cannot escape, as the temperature can rise to over 500 000 K. Simulations by both molecular dynamics36 and hydrodynamic codes37 predict that 0.5 nm motions of the ions can occur in less than 100 fs, and that pulses as short as 10 fs may be required to achieve atomic resolution with one particle per shot, a more demanding requirement than that for SFX, which benefits from periodic averaging. It is found that doses of up to a thousand times greater than the Garman–Henderson “safe dose” can be used for similar resolution, if sufficiently brief XFEL pulses are used.38 More specifically, if the "safe dose" is about 30 MGy for cooled samples at synchrotrons (or 0.2 MGy at room temperature), then it is estimated to be about 700 MGy for an XFEL using 70 fs pulses (see Chapman39 for a full discussion). Recently, site-specific damage effects have been imaged in density maps around Fe metal clusters in ferredoxin using XFEL data40 and compared with synchrotron results. A sub-micron beam focus was used at maximum XFEL intensity, with beam energy above the iron K edge. This work, and supporting simulations,41 suggest that pulse durations of 20 fs or less may be needed to minimize some types of site-specific damage when using the smallest beam focus for highest intensity (as used in single-particle experiments). The XFEL has less influence on oxidation state than synchrotrons.116 The problem of out-running radiation damage must be understood differently in SFX and SP studies. Spot-fading studies (Figure 2.3) show how the disappearance of the outer Bragg reflections “gates” the time resolution of the process—the effective pulse duration that matters is the time taken for these spots to fade, destroying translational symmetry, not the duration of the pulse.42 For single particles, the onset of damage is more difficult to determine from the continuous distribution of scattering in the patterns (see ref. 25 for an analysis) and will need to be done either by the modelling of known structures, once reliable high-resolution data is obtained from  monodispersed particles, or by using the diffuse SP scattering present in some disordered crystals.55 This effect is described in more detail below; however, since the diffuse scattering resulting from purely displacive (not rotational) disorder is (except at low angles) equal to the SP diffraction pattern, a comparison of the fading curves (Figure 2.3), for different pulse durations, of the Bragg and diffuse scattering on the same diffraction  patterns will soon allow the resolution limits due to damage from crystals and single-particles to be compared.

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2.3 Serial Crystallography at XFELs for Structural Biology Why use an XFEL rather than a synchrotron for structural biology? By comparison with the highly stable modern synchrotrons, the SASE mode XFEL would appear to be highly unsuitable for crystallography, with its 15% shotto-shot intensity variation (from amplified noise), 0.1% bandwidth, noisy time structure, (different for each shot) and a focussed intensity, which immediately drills holes in steel. But new algorithms have now been developed that address these beam intensity fluctuations, variations in crystal size and errors in crystal orientation determination. In summary, XFEL crystallography has been found to offer the following advantages: (i) The reduction in radiation damage observed when using the shortest pulses allows crystallography at room temperature without the need for cooling and in a  controlled chemical environment, from the smallest (e.g., sub-micron) crystals, from which useful data cannot readily be obtained at synchrotrons. This opens the way for the study of dynamics at room temperature. The important point is that, when studied at room temperature, the correct thermal energy, representative of physiological conditions, is available to drive the chemical reactions as they are observed, which may not be the case for quenched or trapped samples. (ii) Showers of microcrystals are frequently observed during crystal growth trials, yet it may take months or years to find the conditions required to grow crystals large enough for conventional crystallography. Time-consuming screening trials can be avoided by direct injection of these microcrystals in a liquid jet or similar sample-delivery device. Since good diffraction patterns have been obtained from nanocrystals just a few dozen molecules on a side, research into the identification of protein nanocrystals too small to be detected by optical microscopy continues, using methods such as SONICC44 and Brownian motion tracking using NanoSight from Malvern Instruments Ltd. Methods of growing the required nanocrystals are under continuous development—these include growth in lipidic cubic phase (LCP)45 and growth in living cells, either extracted from the cells or with the cells themselves (containing nanocrystals of Bacillus thuringiensis) injected into the XFEL beam.46 (iii) The improved time resolution possible using an XFEL. (iv) Non-cyclic reactions can be studied (since each sample is destroyed), rather than requiring cyclic low-dose stroboscopic conditions on the same sample region. (v) When using sub-micron crystals, the optical absorption length for pump lasers is comparable with the crystal dimensions, allowing saturated pumping. (vi) For diffraction studies of nanocrystals reacting with a substrate, discussed in more detail below, diffusive mixing is possible, since the diffusion time of the substrate into the crystals is short.47,48 The use of nanocrystals, rather than the more common solution mixing, can then provide atomic-resolution data. (vii) In several cases, resolution appears to be better at XFELs than synchrotrons for similar protein crystals; however, detailed tests of these claims, which fully control for crystal quality, dose, temperature factors and beam diameter, remain to be done.

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(viii) Inner-shell X-ray absorption and emission spectra may be collected in synchrony with snapshot X-ray scattering from nanocrystals, allowing the chemical state of heavy atoms to be tracked through a chemical reaction in pump-probe experiments. Soon after the initial SFX results were obtained at LCLS (limited in resolution by the soft-X-ray beam energy), high-resolution results were obtained in February 2011.51 Since then, more than 100 structures have been determined using an XFEL and deposited in the protein data bank (PDB). Recent SFX examples include the angiotensin receptor [a G-protein coupled receptor (GPCR)] at 2.9 Å resolution52 and rhodopsin bound to arrestin,53 among many others. Serial crystallography has also been developed at synchrotrons, as discussed below and in the chapter by Weierstall. An important recent advance has been the realisation that, in crystals for which disorder consists solely of rigid-body displacements of proteins from the ideal lattice, the Debye theory54 of scattering from crystals with thermal motion predicts that the strong diffuse scattering seen between Bragg reflections in snapshots from molecular crystals is just the single-particle pattern from the primitive unit cell (apart from a rapid decrease in intensity to zero around the origin of reciprocal space). This diffuse scattering is an incoherent sum of the scattering from all the molecules in the crystal. Since this anisotropic scattering extends well beyond the Bragg reflections (and is not subject to thermal damping), this effect has now been used to extend the resolution of density maps of photosystem II from 0.45 nm to 0.35 nm.55 The continuous scattering can also assist solving the phase problem and opens up the possibility of solving imperfect crystals. Ideally, for this approach one wants something like a liquid crystal, which may possess orientational order but not translational symmetry. It also opens up the possibility, now under investigation, of pumping protein crystals with a large water content with an infrared (IR) laser to induce displacive disorder during the X-ray pulse.

2.4 Molecular Machines and Single-particle Imaging In this section, we consider the unique insights that the XFEL’s time and spatial resolution, and other characteristics, provide for our understanding of the molecular machines of life and briefly summarize progress in the relevant single-particle initiative at LCLS. Single-particle methods are also discussed in the chapters by Ekeberg, Maia and Hajdu, and Ourmazd, and are reviewed in Ekeberg,56 Bostedt,57 and Liu and Spence.58 Studies of the folded state of proteins in crystals have revolutionized structural biology. However, increasingly, it has been realized that under physiological conditions proteins sample a large ensemble of conformations around this average structure due to the availability of thermal energy, and that this dynamic behavior, consisting of near-equilibrium fluctuations, is crucial to their function. At higher temperatures, many proteins therefore switch rapidly between substates but are inactive at the temperatures around 100 K, where most crystal structures are now determined. The conformational

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states sampled by proteins are difficult to access by crystallography, which averages over the entire ensemble of states present in the crystals. Additional controlling conditions include solvent chemistry (e.g., pH), pressure, local electric fields and ligand binding. Protein function is then the result of a complex interplay between thermal motions, and their chemical and physical environment.59 The modern description of protein function is therefore based on a multi-dimensional energy landscape60 that defines the relative probabilities of the conformational states (the thermodynamics), the energy barriers between them (kinetics) and the work cycle. This landscape concept was taken from the original Eyring transition-state theory in chemical dynamics. Historically, studies on myoglobin have led the way (see Fenimore61 and references therein). Molecular processes depend on alterations in rates and populations in an ensemble, such as the enzymes facilitating reactions, or the changes in intracellular ion concentrations that trigger neurological processes. Very large rate increases can be achieved by very small changes in free energy (a few kT), so that breaking a few hydrogen bonds or van der Waals contacts in a protein containing thousands of such interactions can turn on a signaling cascade or catalyze a chemical reaction. Intrinsic protein dynamics occur only in this free-energy range of several kT. Reaction rates double for a 10 °C increase in temperature due to the exponential Boltzmann factor. As suggested elsewhere,59 the conformational substates sampled by a protein, and the pathways between them, are not random, but rather a result of the evolutionary selection of states that are needed for protein function. Signal transduction, enzyme catalysis and protein–ligand interactions occur as a result of the binding of specific ligands to complementary pre-existing states of a protein and the consequent shifts in the equilibria. In other words, the energy landscape is an essential, intrinsic property of a protein, encoded in its fold, and is central to its function: in one view, the ligand does not induce the formation of a new structure but, instead, selects from pre-existing structures, the result of evolution at the molecular scale. Several classes of protein dynamics may be distinguished, according to driving force, reversibility, speed, cyclic nature and thermodynamics. Certain molecular motors convert chemical energy, provided by adenosine triphosphate (ATP) hydrolysis (12 kcal mol−1, or 20 kT at 300 K, or 0.52 eV molecule−1) into mechanical motion. The molecular machines of life are otherwise mostly driven by thermal fluctuations (together with input of chemical energy due to bond breaking), operating on time-scales longer than microseconds. They might be thought of as molecular structures that focus Brownian motion. In equilibrium, buffeted by surrounding water molecules, these machines (such as the ribosome and kinesin) may be said to be idling. (An example is kinesin, which in equilibrium is equally likely to move to the left or right on tubules, but which moves only in one direction when provided with chemical energy.) A third class of systems is light-sensitive proteins, responding to large photon energies. Note that while time-sequence information is not needed to map out the energy landscape (since time has no meaning for an equilibrium ensemble), it is needed to determine the way the path adopted by a particular

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driven system is traversed. The relationship between the equilibrium energy landscape and non-equilibrium-driven processes is described elsewhere.62 Relative energies can be obtained from the frequency of the occurrence of particular conformations, via a Boltzmann factor, for molecular machines operating with energies around kT. A recent example of the determination of an energy landscape, for the ribosome, using cryo-EM data can be found in Dashti.62 While it may be some time before comparable spatial resolution can be obtained using the XFEL in SP mode, the point has been made (see the chapter by Ourmazd) that the much larger amount of data obtainable in XFEL SP experiments (especially when using the new high-repetition-rate machines) will give access, via this Boltzmann factor, to those much rarer, larger-energy and larger conformational changes not seen in cryo-EM imaging, which may be important to physiological function (and which go beyond the harmonic approximation commonly made in molecular dynamics simulations). These very large conformational changes would then be visible at a moderate resolution of, perhaps, 1 nm, and it is precisely these rare events involving larger energies that are the rate-limiting transition states. In this way, one may go beyond the small conformational changes imposed by the study of proteins that can be crystallized, which can only provide a periodic average over all conformers in the crystal. Pump-probe SP studies also have the important advantage of providing measured time intervals between movie frames. Since most biochemical reactions occur on a microsecond or longer timescale, the value of XFEL imaging on the femtosecond time-scale (other than for the reduction of damage) in biology has been questioned. But, in fact, as Moffat has pointed out for quantum-chemical reactions, all time-scales, from the excited-state lifetimes of the initial electronic excitation onward, are relevant.63 Enzymes, for example, rely on fluctuations that are much faster than the enzymatic constants. The binding of charged ligands can be electrostatically steered over very small diffusional distances, and therefore over very short times. Other reactions depend upon the formation of the correct cluster of ionizing groups with extremely short lifetimes. The crucial initial stages of light-driven processes, such as human vision and photosynthesis, clearly play out in the femtosecond regime. It is useful also to distinguish sub-nanosecond processes on the atomic scale (involving electronic excitations) as chemical reaction dynamics, to be distinguished from the kinetics described by rate equations and final states of thermodynamic equilibrium. All these insights deepen our understanding of biochemistry, and improved time and spatial resolution can also provide more accurate refinement of atomic potentials used in molecular dynamics simulations. In summary, some of the “Grand Challenge” problems in structural biology that might be addressed using XFELs include the following:     -- Image water molecules at protein surfaces in the hydration shell, with sub-picosecond time resolution. These surface waters may play a critical role in molecular recognition. THz radiation, which couples to the dipole moments of the surface waters, has been suggested for this.

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Refine atomic potentials used in simulations against high time and spatial resolution data. Trace photochemical reactions back to their origins in electronic excitation. Image rare, large conformational changes (perhaps at modest resolution), which are accessible because of the very large SP data sets that will become available with new XFELs. Image, at atomic resolution, the water-splitting event in photosynthesis with high time resolution. Image, at high spatial resolution and microsecond time resolution, the mechanism of enzyme catalysis. New double-focussing mixing jet designs, which mix solutions to allow movies of chemical reactions to be obtained, offer an excellent prospect of achieving this goal, as discussed below.

    The Single-particle Initiative (SPI) program at LCLS has set aside dedicated non-competitive beam times over a multi-year period to systematically trace, identify and rectify the resolution-limiting factors in SP diffraction at LCLS. Steady progress has been made in reducing beamline background scattering and improving detector performance, to the extent that the hard-X-ray SP facility (coherent X-ray imaging, CXI) has demonstrated scattering at 3.4 Å in diffraction patterns from a single virus (not enough scattering, however, to allow orientation determination and merging for a 3D reconstruction). For soft-X-ray data, where the scattering is stronger, data collected under different conditions at the LAMP chamber (at the AMO experimental station at LCLS), which could be merged and phased for 3D reconstruction, show about 9 nm resolution images of a virus capsid. With continued progress, it is reasonable to expect that 1 nm resolution or better will be achieved before long, with much larger amounts of SP data available soon from the new DESY facility. The important challenge is to increase hit rate, which remains about 1%, unlike the 40% or more obtained when using nanocrystals (for example, by reducing particle velocity), to reduce or identify background scattering (for example, by using a much larger pump in the vicinity of the sample) and to limit the precipitation of salts in the hydration fluids onto the particles. This might be done by using smaller droplets in the electrospray, which drives the aerodynamics stack (see the chapter by Ekeberg).

2.5 Time-resolved Serial Crystallography, Optical Pump-probe Methods and Photosynthesis Some of the most important successes of time-resolved, high-resolution imaging using an XFEL have resulted from the method of optically pumped, time-resolved serial femtosecond diffraction (TR-SFX). The subject is covered in several chapters throughout this book, including Chapter 6. In these experiments [see Figure 2.1(a)] on light-sensitive proteins, micron-sized

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protein crystals are excited in a liquid jet upstream of the X-ray pulse, where their snapshot is recorded. The time delay between excitation and X-ray interaction (which corresponds to one frame of a movie) may be determined either (most accurately) by timing electronics (with spatially extended pump illumination) or by the flow time in the liquid stream (less accurately, but allowing longer delays). Thousands of snapshots are required for each delay (movie frame) to provide a 3D diffraction dataset. The first TR-SFX results were obtained by Aquila64 for photosystem-I–ferredoxin. More recent examples incorporating the many advances in instrumentation and the 1000-fold improvement in time resolution over synchrotrons possible at an XFEL can be found in Young et al.111 (photosystem II), Barends et al.65 (for myoglobin), Kupitz et al.66 (for photosystem II), and Tenboer et al.67 and Pande et al.,5 both for photoactive yellow protein. It is a remarkable testament to the steady improvements in SFX data analysis algorithms (discussed below) that these improvements on simple Monte Carlo summation can now resolve the small changes of a few percent in structure-factor magnitudes due to optical illumination of a micron-sized protein crystal, given the scaling problems with continuous variation in crystal size and orientation, while working with partial reflections. Pande et al.,5 for example, achieved 200 fs time resolution in their remarkable TR-SFX study of photoactive yellow protein (which forms excellent crystals), sufficient to provide several frames of a 0.15 nm resolution movie of the trans/cis isomerization reaction that results from photon absorption in this light-sensitive protein. The mechanism is the same as that which occurs in the first event in human vision, when photons strike rhodopsin at the retina.68 Nango et al.114 have obtained a 13-frame movie of bacteriorhodopsin’s response to light. It should be noted that the simplified common description of pump-probe “molecular movies” glosses over multiple issues. For example, in a protein crystal excited by a femtosecond optical pulse with two reaction paths around a cycle (established by fast spectroscopy), molecules in different unit cells have certain probabilities of either not being excited at all, or initiating a reaction on either path. Each path, described by chemical rate equations, will produce different intermediate species with different rate constants. Measurement of lattice constants, temperature factors and overall resolution provide assurance that the crystal remains intact during the cycle, and that the outer envelope and contact points between molecules in different unit cells are little affected. (Destruction of the crystal by the photoelectron cascade comes later.) The observables, from a stream of nanocrystals, are the Bragg beams, which, after phasing, provide a periodic spatial average of charge density from the average of all illuminated crystals at one time point (pump-probe delay). The method, therefore, requires accurate knowledge of the un-illuminated (dark) ground state structure from prior crystallography at the highest resolution, so that methods, such as singular value decomposition (or perhaps modelling using molecular dynamics), can be used to separate the time-resolved charge densities along each path. From this, the amounts of intermediate species that come and go during the reaction cycle can be extracted based on the rate equations describing the reaction kinetics.

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It is clear that much more accurate results could be obtained if the Laue method, previously adopted for this work, could be used (e.g., Shotte69). Here, a wide energy spread in the beam is used to provide a “thicker” Ewald sphere, which spans the full angular profile of the Bragg peak, allowing each snapshot to record full reflections (for a single projection) at each time point and eliminating the need to scale Bragg peaks between different sized crystals of different partiality. The required large energy spread dE/E is, however, not normally possible using the highly monochromatic X-ray laser (for the LCLS, dE/E ≈ 0.001). Moffat70 finds that, to provide angle-integrated intensities from a crystal with mosaic disorder dϕ = 10−2 and Bragg angle β, one required dE/E > ϕ cot ϕ. For a high-angle reflection with β = 0.3, this requires dE = 260 eV at E = 8 kV, or less for more perfect crystals and more for low-  angle reflections. The suggestion has been made that the submicron-sized crystals sometimes used for SFX are more perfect, since their size is smaller than one mosaic block of the traditional model. However, this model may not apply to many proteins, whose defect structure is not well known.71 The use of a “chirped” beam (which changes energy during the pulse) and the use of “two-color” methods have also been proposed. Here, the XFEL generates pairs of pulses with a tunable femtosecond-scale delay at slightly different wavelengths ("colors"). For an analysis of errors in SFX using two colors,  perhaps with a pump pulse sandwiched between them, see Li.72 A promising approach is the use of genetic engineering to create light-  sensitive protein domains within a system of interest, known as opto-genetics. If nanocrystals can be grown, this would provide a general method of studying  protein dynamics;70 however, the structural change induced by the light must be small enough to be accommodated by the crystal. New approaches to XFEL time-resolved diffraction are reviewed in Spence,15 including the use of attosecond pulses. Here, the unavoidable broadening of the energy spread in a bandlimited beam could provide just the conditions needed for Laue diffraction, while the temporal coherence allows Bragg beams from different reflections diffracted into the same direction to interfere briefly, contributing to the solution of the phase problem by providing a three-phase invariant.

2.6 Time-resolved SFX for Slower Processes: Mixing Jets and Other Excitations A considerable literature exists on solution scattering experiments at synchrotrons, which provide snapshot diffraction from two solutions during a chemical reaction (see Van Slyke,73 for example, for work on the binding kinetics of RNA). The reaction may be triggered in some way or result from mixing, which normally needs to be turbulent, since this mixing time determines the time resolution of the method prior to chemical reaction of the species. In biology, because the entropy term in the free energy may be large, so that slower entropic work processes are important, reactions can occur on

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the microsecond, millisecond and longer time-scales. In solution, molecules have to find each other by diffusion before a reaction can start. For substrate diffusion into a crystal, diffusion times may be far greater, and depend on the water content of the crystal and the maze of interconnected waterways between molecules. This "mixing time" then sets the time resolution of the experiment. The reactions can be triggered by the photoelectrons generated by the X-ray beam itself, as in the well-studied case of horseradish peroxidase.74 The high brightness of modern synchrotrons and fast detector speeds have therefore recently enabled serial crystallography methods to provide “molecular movies” of enzyme mechanisms, triggered by the beam, in which the radiation dose is kept well below the Garman–Henderson “safe dose”, and resolution loss during the reaction is minimal.75 Using an XFEL in the serial crystallography mode, it becomes possible to use micron-sized crystals (which provide atomic resolution, not possible with solution scattering experiments using mixing cells at synchrotrons), so that diffusive mixing becomes possible with such small crystals that diffusion is fast—faster than the reaction time of interest. The diffusion time for glucose into a 1 µm crystal of lysozyme is about 80 microseconds.47 Radiation damage can be almost eliminated (thus disentangling the effects of damage from the chemical reaction). Most importantly, the chemical reaction can then be imaged by snapshot X-ray diffraction at room temperature under physiological conditions, where the correct thermal energy is available to take part (with other driving forces) in driving these reactions. A description of the first “mixing jet” for XFEL sample delivery is given in Wang et al.76a More recent designs (Calvey et al.76b) have now been tested successfully at LCLS beam times, and the first results of nanocrystal TR-mixing, drug binding to an enzyme (against tuberculosis),112 and ligand binding to mRNA, have appeared.113 We can foresee now a much wider range of methods being used to trigger reactions for imaging dynamics at XFELs in the near future. These might include Terahertz pumping, temperature jump and temperature equilibrium measurements, and, particularly, caged molecule release experiments,77 including pH changes driven by optical pumping of proton-release cages (e.g., Lommel78) and other photolabile compounds.

2.7 Fast Solution Scattering and Angular Correlation Methods Does the XFEL offer advantages for the small (and wide) angle X-ray scattering methods, SAXS and WAXS? (We might call XFEL WAXS “fast solution scattering”, or FSS. Other names include fluctuation X-ray scattering, or correlated fluctuation scattering.) Certainly, the well-documented radiation damage effects in these techniques might be minimized and superior time resolution obtained. As a result, we have seen remarkable studies of both water at low temperature79 and of photosensitive protein molecules studied by time-resolved pump-probe XFEL solution scattering.80 In that important

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study of the Blastochloris viridis reaction center, picosecond time resolution, and about 0.4 nm spatial resolution, were obtained in the difference between the optically pumped and dark states, allowing a molecular movie to be obtained following photon excitation. (Prior crystallographic work provided an accurate dark state structure, allowing extensive modelling by molecular dynamics.) The time-dependent diffraction provided details of the “quake” mechanism responsible for dissipating energy, following absorption of the large photon energy, which prevented unfolding of the protein. Two relaxation processes could be identified with different time-scales and scattering ranges. It has been pointed out that solution scattering from molecules frozen in time or space should be anisotropic, containing speckles (quite apart from the effect of coherent interparticle scattering), unlike WAX data, which is isotropic because the molecules rotate during the exposure. This is easily understood for the case of just a few particles per shot, if the spatial coherence of the beam spans only the particle size. Furthermore, a method exists for extracting the electron density map (image) of one particle using this anisotropic scattering from many identical, randomly oriented particles.81 Clearly, such 2D patterns contain more information than one-dimensional (1D) WAXS patterns (but are nevertheless deficient82), facilitating inversion to 3D images. An excellent tutorial review of this Kam theory and its history can be found in Kirian.83 The concept can be understood in the simple case of 2D identical objects lying flat on a plane normal to the beam, which differ only by random rotations about the beam direction, with one particle per shot. Then, the 2D angular correlation function (ACF) for each particle, formed from the SP diffraction pattern, will be independent of its orientation, allowing them to be added together. (The ACF is the autocorrelation of the diffracted intensity around each constant-resolution ring in the diffraction pattern.) With many particles per shot, it can be shown that this anisotropic ACF of one particle is added to a WAXS background,83 which can then be subtracted because it is isotropic. In principle, the resulting ACF can then be inverted to an image by phasing and Fourier transforming the data twice, once to convert the ACF to the diffracted intensity, and a second transform to give the real-space image.84 This anisotropy in FSS has been observed in X-ray scattering from colloidal glasses85 and from randomly oriented gold nanorods lying flat on a membrane,84 which was inverted using the Kam theory to provide an experimental image of a typical nanorod. For proteins in solution, the anisotropy in XFEL FSS data (with a recording time much shorter than the rotational diffusion time of the molecules) is usually swamped by other experimental artifacts causing anisotropy (e.g., scattering from the host liquid boundaries and stray X-ray sources in the beamline). Success has, however, been achieved using 2D lithographed structures86 at low resolution, and from data in the PDB for a ligand-gated ion channel (pLGIC) using an important new development of the Kam approach,87 which provides inversion to an image with a single iterative phasing step. A significant theoretical finding is that the results of

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this method, as originally suggested by Kam, are independent of the number of particles per shot;88 however, experimental resolution (in the absence of modelling) appears to be better using the SP method (one particle per shot) inverted by the expectation maximization and compression (EMC) approach. One cannot improve on the SP mode with beam diameter matched to particle size and a direct hit; however, experimental impact parameters are rarely zero and hit rates are low (e.g., 1% or less), whereas FSS has 100% hit rate. Thus, the optimum number of particles per shot (and analysis method) remains to be determined for real experimental conditions, including background scattering. The FSS method is particularly powerful for known structures when detecting differences between ground and excited state structure.89

2.8 Data Analysis The special features of SFX have required new algorithms for data analysis. The chapter by Sauter provides additional information on this topic. Since crystals (destroyed by each shot) cannot be rocked through the Bragg condition to provide the angular integration needed for a full estimate of a structure factor (so that goniometers are rarely used), new algorithms that address the scaling issues created by beam intensity fluctuations, variations in crystal size, and the precise determination of crystal orientation from diffraction pattern intensities and geometry had to be developed. Expressions for XFEL diffraction by protein nanocrystals were first derived from first principles by Kirian,90 which provided the basis for the serial crystallography method of data analysis. These expressions predicted the interference fringes, which run between Bragg spots for very small crystals, allow a scattering vector to be assigned to every Bragg spot and provide the rotation matrix that must be determined for each shot, between crystal and laboratory frame. Subsequent indexing has mostly been achieved using standard crystallography software (e.g., MOSFLM; see Winn91), allowing the data from many nanocrystals to be merged into a 3D diffraction volume. Indexing ambiguities can be resolved using the EMC method.92,93 A simplified version of this algorithm is implemented in CrystFEL. Initially, full reflections were obtained using a Monte Carlo approach, which relies on recording and merging randomly oriented crystals, whose orientations span and adequately sample the rocking curve for every Bragg reflection. The resulting error in structure factor measurement (e.g., Rsplit) then falls off inversely as the square root of the number of patterns, with some proportionality constant, as errors are added in quadrature due to variations in crystal size, orientation, and a combination of impact parameter and shot-to-shot variations in beam intensity, as shown in Figure 2.4. The proportionality constant has fallen dramatically over the past 5 years, as algorithms have improved and sources of error (especially associated with detector metrology, crystal size scaling and beam energy bandwidth) have been estimated or reduced. Nevertheless, this Poisson scaling does mean that 100 times more data are needed to add one significant figure. The method, which avoids the use of a goniometer at pre-set measured

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Figure 2.4 The experimental reduction in scattering factor error measurement

(Rsplit) with increasing number N of diffraction patterns follow a Poisson error law Rsplit = k/sqrt(N) law. For this SFX analysis of the photosystem II complex (PDB 3WU2), k = 18.5. Progress in SFX algorithm development, partial reflection analysis and scaling is measured by the reduction in k in recent years.

orientations, amounts to “shooting first, and asking questions later”. Much research has focussed on the very difficult measurement of partiality or “post-refinement”94 (the fraction of a full reflection that is intercepted by the Ewald sphere and the precise deviation of each reflection from the exact Bragg condition), as described in White,95 Uervirojnangkoorn,96 Kabsch97 and Sauter.98 A significant advance has been the method of Ginn,99 which has provided 0.175 nm resolution structures from a few thousand protein nanocrystals. A histogram showing the number of reflections predicted as a function of X-ray wavelength is used to refine the orientation matrix until a sharp peak is found in the histogram, which gives the beam energy spread. Partiality is based on a model angular profile for the Bragg peak and spot locations are refined. The phasing of SFX data has been achieved mainly by the molecular replacement (MR) method,100 which uses protein with similar sequence and fold found in the PDB for a model. Recently, success has also been obtained in several cases using the SAD method101 for native sulfur phasing  of XFEL data, demonstrating the increasing accuracy of SFX data analysis  (see Batyuk101 for sulfur phasing of a GPCR membrane protein and references therein). New de-novo approaches for experimental phase measurement include measurement of the intensity dependence of scattering factors

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from heavy atoms (including sulfur), which are predicted to saturate. By sorting the data according to pulse intensity, an analysis similar to SAD or isomorphous replacement may then be applied.102 Finally, it has been shown that the interference fringes seen running between Bragg reflections in the smallest crystals (similar to optical diffraction from a finite grating) provide the “oversampling” needed to solve the phase problem.103 For an experimental demonstration and additional references, see Kirian.104 For SP data analysis with one particle, such as a virus, per shot, the methods of coherent X-ray diffractive imaging (CXDI) have been adapted for XFEL data, including the hybrid input–output (HIO) algorithm and its variants (see Spence105 and Marchesini106 for reviews, and Millane and Lo107 for a review of related iterative phasing methods in crystallography). Unlike the CXDI problem, the orientational relationship between successive diffraction patterns must first be determined using randomly oriented particles of unknown structure (and requiring a certain minimum number of detected photons), whose accuracy may limit resolution, prior to solution of the phase problem. Approaches to these problems include manifold embedding108 and the remarkable EMC algorithm109 widely used in cryo-EM, which has been applied to SP XFEL data (see Ekeberg56 and references therein). The chapter by Ekeberg contains a full treatment of this topic, with details of available software.

2.9 Summary This is an exciting time for projects aimed at imaging protein dynamics using XFELs. From the above we can see at least three “Grand Challenge” projects emerging: (i) imaging the water-splitting event in photosynthesis; (ii) imaging single-pass enzyme dynamics to expose the mechanisms involved at atomic resolution as a basis for structural enzymatics;110 (iii) imaging large, rare conformational changes by single-particle methods. A wide range of methods is now being developed to trigger reactions, from THz radiation to caged-release compounds, optogenetics and spectroscopy, while new modes of imaging continue to be developed, from solution scattering, simultaneous snapshot diffraction and correlated fluctuation analysis, to mixing jet experiments based on diffusive mixing. As should be clear from this review, this new field of science is at that very exciting early stage, where many new ideas and techniques flourish, and the mature methodologies of the future have yet to be established. We are reminded of the words of Humphrey Davey in 1806: "nothing promotes the advancement of Science so much as the invention of a new instrument".

Acknowledgements Supported by NSF award 1231306. Thanks to N. Zatsepin for a critical review.

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Overcoming Data Processing Challenges for Breakthrough Crystallography Nicholas K. Sauter*a and Paul D. Adamsa,b a

Molecular Biophysics & Integrated Bioimaging Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA; bDepartment of Bioengineering, University of California Berkeley, Berkeley, CA 94720, USA *E-mail: [email protected]

3.1  Introduction X-Ray free-electron laser (XFEL) sources have generated tremendous interest within the structural biology community, due to their potential for avoiding radiation damage and performing time-resolved experiments, while exposing samples at room temperature under physiological conditions. Radiation damage has been a pervasive problem for macromolecular crystallography performed at synchrotron sources, where the energy deposited by the X-rays and the ensuing photoelectrons causes not only the general decay of the diffraction pattern,1,2 but also specific damage to protein sites, such as the loss of carboxylate groups,3 and the reduction of disulphide bridges and catalytic metal ions within enzymes.4–6 In contrast to synchrotron experiments, which are performed by exposing a rotating crystal over several seconds, XFEL experiments are accomplished by the serial exposure of numerous still crystals, each on a time scale of tens of femtoseconds. While it has been   Energy and Environment Series No. 18 X-Ray Free Electron Lasers: Applications in Materials, Chemistry and Biology Edited by Uwe Bergmann, Vittal K. Yachandra and Junko Yano © The Royal Society of Chemistry 2017 Published by the Royal Society of Chemistry, www.rsc.org

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shown that serial femtosecond crystallography (SFX) exposures at equivalent absorbed doses of 20–30 GGy (J kg−1) can damage the [4Fe–4S] clusters in ferredoxin,7 exposures at lower doses that are typically used for SFX (95 : 5. Therefore, a deep understanding of the electronic and nuclear structural response to excitation on femtosecond to picosecond time scales is needed to rationally design systems to utilize these potentially catalytic intermediates and could be pivotal to identifying a new regime of efficient metal-based photocatalysts, light sensitizers and electron donor/acceptors that might otherwise be neglected on the basis of selection criteria focused on triplet state lifetimes. It is, however, still challenging to obtain such detailed structural dynamics via optical spectroscopic measurements only because optical signatures of metal-centered electronic transitions for these critical TMC intermediates are frequently nonexistent or obscured by dominating optical signatures of ligand π → π* transitions, which are generally 10–1000 times stronger than metal-centered d–d transitions. For example, a multi-step, photoinduced electron transfer can take place in a sensitizer/TMC-catalyst supramolecular system, where the kinetics of electron transfer and charge recombination can be followed by the time evolution of optical signatures for the excited state sensitizer. But the fate of the TMC-catalyst is often unknown, because changes of the electronic and geometric structures of the metal catalytic centers may be optically “dark” or too weak to be detected. Even with strong MLCT or LMCT transitions, it is often the case that the optical absorption signals cannot directly reveal transient electronic configurations of the metal center during the photochemical reactions. Although electron paramagnetic resonance spectroscopy can probe the electronic configuration, including the spin states for the metal centers in TMCs, the time resolution of the technique (100 ns or longer) limits its applications in capturing transient species. X-Ray absorption near edge structure (XANES) and X-ray emission spectroscopy (XES) offer a new set of element-specific electronic transitions from inner shells (1s, 2s, 2p, 3s, 3p, 3d, etc.) to higher energy vacant orbitals and then to vacuum levels following the Fermi Golden Rule, from which the d electron occupation and metal–ligand bond covalency can be selectively probed.52–56 When the incident X-ray photon energy can be tuned in a sufficiently large range (i.e., 1 keV), extended X-ray absorption fine structure (EXAFS) measurements can selectively probe both dynamic electronic and local nuclear structures around the metal centers following photoexcitation without interference from ligand-localized transitions.20,57–64 Since the turn of the century, the laser pulse pump, X-ray pulse probe X-ray transient absorption (XTA) spectroscopy has been realized in various synchrotron sources and a number of studies on photochemical and photophysical processes of TMCs on the synchrotron X-ray pulse-defined time scale have been published.11,12,14,16,18,65–67 While these studies are viable in our understanding of light–matter interactions in TMCs, the 100 ps probe pulse duration limits studies of rich structural dynamics of initial excited states and their different relaxation pathways, including photochemical reactions. The emergence of XFEL sources capable of producing femtosecond X-ray pulses68,69 have opened new paradigms in studying electron and nuclear movements on the time scales from tens of femtoseconds to longer in

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parallel with those studies of optical transient spectroscopies. The most significant distinction of structural dynamics at X-ray free electron sources on a time scale of tens of femtoseconds and longer compared to those at synchrotron sources on time scales of 100 ps and longer is the capability of following the electron and nuclear movements in the real time far from thermal equilibrium and detecting thermally equilibrated, statistically averaged transient species. The first femtosecond XANES experiment in the hard X-ray regime was carried out in 2010 with a team of scientists from different parts of the world.19 This study was focused on structural dynamics of spin crossover iron(ii) complexes previously studied at the synchrotron sources,21,70–72 and detected a rise of the final spin state in about 150 fs.19 The results validated the capability and limitation of carrying out X-ray absorption spectroscopy measurements at the Linac Coherent Light Source (LCLS) under selfamplified spontaneous emission (SASE) conditions. The main limits are spectral windows available for XANES spectra and the intrinsic time resolution with the pulse-to-pulse temporal jitters. This study played an important role in helping users to evaluate the feasibility of X-ray absorption measurements and certainly helped us in designing the experiments presented here. Using ultrafast structural dynamics of a metalloporphyrin as an example, we describe our recent XTA studies of TMC photochemistry on the femtosecond time scale using the LCLS at the Stanford Linear Accelerator Center (SLAC). The example presented here is the excited state structural dynamics of NiTMP (Figure 10.2).

10.2  Experimental 10.2.1  C  haracteristics of X-ray Pulses and the XAS Signal at the X-ray Pump-probe (XPP) Station of LCLS The LCLS is also called the SASE-XFEL73 with stochastic distributions in energy and temporal profiles, varying randomly from shot-to-shot.68,69 According to the report at the XPP-LCLS station,74 the X-ray photon flux at a particular central energy is on the order of 1012 photons pulse−1 with a pulse duration of 50–70 fs (FWHM), running at 120 Hz. This results in an average flux of ∼1014 photons s−1, comparable to the total flux at an undulator beamline, and >6000 times enhancement from the pump-probe XTA measurements with a repetition rate of 1 kHz in the Advanced Photon Source (APS), a synchrotron source at Argonne National Laboratory. In addition to the short X-ray pulse duration of tens of femtoseconds at the LCLS, the SASE process results in an averaged spectral width of 30–50 eV at a particular central energy and an averaged variation of the pulse arrival time of ∼1 ps. Although such fluctuations seem to be undesirable for the time-resolved experiments, passing the incident X-ray through a monochromater (i.e., with Si 111 crystals) allows a step-by-step energy scan in an XANES spectral range near a transition edge in an available energy region defined by SASE at a central energy during

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one set of data acquisition. The spectral regions defined by SASE are energy dependent and usually 30–50 eV, which is sufficient to capture important inner shell electronic transitions of the specific element. The temporal fluctuations, the arrival time variations of individual X-ray pulses, are corrected by the “timing tool” that implements optical components to image the X-ray beam profile for each arriving pulse and encode the position of the image to the arrival times. This information is then used to make timing corrections during data analysis. Some details regarding femtosecond XANES data collection have been described by Lemke et al.19 and by Shelby et al.75 In the experiment described for the example shown in this chapter, spectral and temporal fluctuations are also considered in data acquisition. For each energy step, the 2 s integration time, or 240 individual shots, were collected and characterized according to initial intensity (I0) and fluorescence detector response (D1 and D2 on each side of the sample liquid jet). The amplitude of the X-ray fluorescence signal at each energy step was determined by taking averaged ratios of signals from D1 and D2 respectively to that of I0. Special care was taken to eliminate signals from those shots with signal deviated significantly from the median value. To correct the temporal fluctuation of the X-ray pulse arrival times, the time delay for each pulse respected to the laser excitation was corrected according to up-stream diagnostic radio frequency (RF) cavities (“phase cavities”) that record the average electron bunch arrival time. At the time of the experiment included in this chapter, the timing tool was not yet available. Therefore this alternative timing correction was implemented, which also accounted for the long-term drift in the average pulse arrival time relative to the laser delay. After this timing correction, the effective instrument response can be described by a Gaussian function with FWHM of 300 fs compared to 400 fs without the correction. Later at the LCLS, the FWHM was further shortened due to the implementation of the timing tool that encodes the profile of the radiation on a thin screen with an arrival time with much higher precision, enabling much higher time resolution closer to the X-ray pulse duration.

10.2.2  S  ample Considerations and Data Collection for XANES Spectra The high photon flux per pulse at the XPP station significantly increases the data acquisition efficiency and enables approximately a factor of 500–1000 enhancement for XTA data collection compared to the same experiments at synchrotron sources. Concerns have been brought up regarding sample damage by X-ray or pump laser pulse, as well as nonlinear optical effects due to intense laser pulse excitation, while X-ray nonlinear optical phenomena are at the research frontier, which is excluded here. From the laser excitation aspect, the pulse energy from the optical parametric amplifier output pumped by a Ti:Sapphire oscillator–amplifier system at the LCLS is 10–20 µJ pulse−1, which is 10–100 times higher than that used in optical transient absorption (OTA) experiments. However, sample concentrations used in LCLS experiments are

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generally much higher, resulting in similar average photons for each molecule used in laboratory OTA measurements. Because of a factor of 100–1000 lower absorption cross sections for X-ray photons than for laser photons, the optimized valence excitation and inner shell excitation conditions have significant discrepancy for the particular system studied here. For example, we used laser pulses at 527 nm aligned with the peak position of the Q-band for NiTMP to excite a solution of 8 mM, where the extinction coefficient is approximately 20 000 M−1 cm−1 and gives an OD527 nm ≈ 1.6, or 160 cm−1, with >97% laser photons absorbed. The estimated number of photons in each laser pulse of 10 µJ at 527 nm is ∼2 × 1013, while the number of 8 mM NiTMP molecules in a volume of 0.001 mm3 (with a cube of 0.1 mm on each side and 45° angle of the laser respect to the jet plane) is approximately 7 × 1012, giving ∼3 photons molecule−1. The X-ray absorption cross section at the Ni K-edge is much lower at 1.6 cm−1, which is approximately 100 times lower than that for the laser photons at 527 nm. Therefore, only about ∼4% X-ray photons are absorbed by the sample. As one can see, it is hard to have optimized excitation for both laser and X-ray photons. In the above example, the laser excitation is more optimized than the X-ray since ∼96% of X-ray photons are not absorbed by the sample. The sample solution was circulated by a pump system and delivered as a thin liquid jet with a sapphire nozzle of 100 µm thickness at which the laser pump beam and X-ray probe beam intersect in a nearly collinear configuration. The solution forms a thin sheet with 100 µm thickness and oriented at 45° with respect to the incoming beam. Therefore, the actual thickness of the solution that the pump laser and probe X-ray pass is about 140 µm. Considering the wavelength dependence of the speed of light inside the liquid jet of such a thickness, the time divergence between the laser wavelength of 527 nm and X-ray wavelength of 0.15 nm is approximately 140 fs (i.e., 1 fs µm−1). The laser pump pulses were generated from the output of an optical parametric amplifier (OPA) pumped by a Ti:Sapphire laser with a pulse duration of 50 fs (FWHM) with an average pulse energy of 10–18 µJ and a spot size of ∼300 µm diameter at the sample. As mentioned, the nonlinear optical effect of the excitation was a concern, such as two photon absorption (TPA) and exciton annihilation, but careful examination of the photon flux applied to the sample concluded that less than 1% of the NiTMP molecules may have TPA under the experimental conditions. Because the current configuration at the LCLS does not allow continuous shift of the central energy resulting from the SASE process, the measurements were limited to the Ni K-edge XANES spectra within ∼50 eV SASE bandwidth by aligning the central energy with the highest flux with the most interesting features of the XANES spectra. The monochromatic X-ray beam after a monochromater was focused to a ∼0.1 mm diameter spot at the sample by a series of beryllium lenses. Hence, the XANES spectra were collected by scanning the monochromater crystals step-by-step within the defined energy window. Because of this energy range limitation, the nuclear geometry of the transient species on the ultrafast time scales was measured by solution scattering using both wide and small angle X-ray scattering (WAXS and

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SAXS) approaches. Kinetics traces at characteristic X-ray photon energies were collected based on observed XANES features related to particular inner shell transitions, such as 1s → 4pz and 1s → 3d, while changing the delay between the laser pump pulse and X-ray probe pulse. In the example presented here, the pump-probe repetition was defined by the repetition rate of X-ray pulses at 120 Hz and the signal at each energy step or time step was collected with a 2 s integration time or 240 X-ray pulses with an accumulated number of monochromatic fluence approximately 5 × 1012 photons point−1 or 2.5 × 1012 photons s−1. In comparison, the same 2 s integration time using a monochromatic X-ray fluence at a synchrotron source (APS) with a 1 kHz pump-probe repetition rate has approximately 2 × 109 photons point−1 or 1 × 109 photons s−1. The usable X-ray probe photon flux at the synchrotron source could improve at a higher pump-probe repetition rate, but it is not the focus of the discussion here. The total fluorescence signal arising from the Ni K-edge absorption was collected using two solid state passivated implanted planar silicon (PIPS) detectors (Canberra, Inc.) at a right angle with respect to the incident X-ray beam and at both sides of the sample jet. The number of fluorescence photons expected can be calculated based on our previous publication80 using eqn (10.1):     Ω (10.1) I f  I a    k Det , 4π T    where If is the fluorescence signal; Ia is the number of photons absorbed by the sample; Ω is the solid angle covered by the detector; η is the quantum yield of the fluorescence; and µk and µT are the absorption cross sections of the atoms of interest and of the whole sample, respectively. ηDet is the detector efficiency defined as the fraction of the fluorescence photons among the total photons entering the detector. Using the above sample as an example for the calculation, an 8 mM Ni-containing sample with 0.01 mm2 area and 0.14 mm thickness, about 4% X-ray photons will be absorbed, which gives Ia as 1 × 1011 photons s−1. The solid angle Ω/4π is ∼0.04 for two detectors with a total 2 cm2 detection area situated 2 cm from the sample. The fluorescence quantum yield η for Ni is 40% and the fraction of Ni absorption in the sample is 4.8%. With all the above factors considered, there would be ∼107 X-ray fluorescence photons s−1 entering the two detectors, or 105 photons pulse−1, assuming ηDet is 100%. Such a high fluorescence flux demands a current mode other than the single photon counting mode detection. The above estimate did not include the elastic scattering signals, air absorption and other unpredictable factors, but provides an approximation of the signal intensity in helping detector selection. To minimize the contribution of background counts (elastic scatterings, etc.), a cobalt oxide filter (z-1 filter with six absorption lengths, EXAFS Materials Co.) was mounted on Soller slits designed for a fixed distance between the detector and the sample liquid jet (20 mm) and placed in front of each detector diode. So far, no sign of detector saturation was observed, as the sample illuminated by variation of the incident intensities of the X-rays. The incoming monochromatic X-ray

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pulse intensity was monitored for later pulse-by-pulse signal normalization by another PIPS detector located upstream of the sample chamber. Transient XANES spectra were obtained at different pump-probe delay times (e.g., −5 to 100 ps, the probe time minus the pump time). The sample integrity was checked by its ultraviolet (UV)–vis absorption spectra before and after the measurements, which was found to be identical.

10.3  Results and Discussion 10.3.1  Excited State Structural Dynamics In the example presented here, the excited state dynamics of NiTMP, like its analog NiTPP (nickel tetraphenylporphyrin), have been studied extensively by ultrafast OTA spectroscopy,81–84 Raman spectroscopy85,86 and X-ray transient absorption (XTA)13,87–89 at the synchrotron sources, such as the APS. The OTA studies suggested sequential excited state kinetics, S1 (π → π*) → T′ (π* → 3dx2−y2) → T (3dz2 → π) → S0 (3dx2−y2 → 3dz2), where the transitions inside the parentheses indicate the electron movement from one to another molecular orbitals, and the excited state trajectory and electronic transitions in valence and inner shell bands are shown in Figure 10.3.

Figure 10.3  From  left to right represents the excited state pathway of NiTMP. From the top to bottom are the structure and electronic configuration for each state including inner shell to valence orbital transitions drawn by purple arrows and valence excitation by the green arrow. Structures were obtained from TDDFT calculations.

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As mentioned earlier, our objective is to gain insight into excited state structural dynamics, especially the electronic configuration trajectories of the nickel center before the thermalization. The experimental XANES spectra, as well as the difference spectra (with laser – without laser) as a function of the pump-probe delay time are shown in Figure 10.4. The kinetic traces at selected characteristic X-ray photon energies were also collected at those energies showing the largest signal amplitudes in the

Figure 10.4  Ni  K-edge XANES spectra of NiTMP at different delay times (ps) follow-

ing 527 nm excitation. Energy E0 – E3 correspond to the 1s → 3d transition (“pre edge”) region, a transient rise and decay red-shifted from the ground state 1s → 4pz region, the 1s → 4pz transition for S0, and for T, and the white-line feature associated with shortened Ni–N bonds in the T(d,d) state. (A) XANES spectra at representative time delays with the full SASE spectral width, (B) The time evolution of the XANES spectra in the 1s → 4pz region, (C) Difference spectra relative to the S0 spectrum, showing the dynamics of the S0 bleach (E1), the rise of the T(d,d) 1s → 4pz peak (E2), the rise and fall of the transient at 8337 eV within 2 ps (E3), and the rise of the white-line feature (E4). Dashed lines correspond to energies at which kinetics traces were taken. Reprinted with permission from ref. 75. Copyright (2016) American Chemical Society.

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difference XANES spectra (Figure 10.5). There are two main aspects to consider: (1) the kinetics scheme in the time window of the experiment and (2) contributions of individual species to the signal at each X-ray photon energy. These considerations are completely analogous to what one normally deals with in the widely used OTA spectroscopy. The kinetics scheme in this example can be well described by a sequential reaction, S1 → T′ → T → S0, with the following time-dependent concentrations of different species:    d  S1  t  1 (10.2)    S1  t   d t          

d T   t   1 1     S1 t   T  t  1 2 dt

d T  t   1  1 T   t    T  t    3 dt 2  d S0  t  1  T  t .  dt

(10.3) (10.4) (10.5)

   This yields the populations S1(t), T′(t), T(t) and S0(t) for a specific set of time constants τ1, τ2, and τ3 values. S0(t) represents the ground state recovered from

Figure 10.5  (A)  Single-energy delays scans at (left to right) 8337, 8338, and 8341

eV with fits to kinetic model (1) (dark blue line). (B) Decomposed signal contributions from each electronic state accounted for in the fit of model (1) to the delay scans at (left to right) 8337, 8338, and 8341 eV determined by numerical integration of the rate expression for each species, in this case for the assignment τ1 = 1.0 ps, τ2 = 0.08 ps ( 20 ps, which is identical to the spectrum obtained from our previous synchrotron results. Therefore, only A1(E) for the T′ state is unknown and is treated as a variable in the fitting. Finally, the simulated traces for each energy are obtained by numerical convolution of Atotal(E,t) with a Gaussian instrument response function, the width of which is also fit as a variable. It has been shown from our kinetics scheme based on the sequential mechanism that the population of the second species T′ can be expressed by eqn (10.7):    T   t   k1  S1  0   e k1t  e k2t  (10.7)     k2  k1     where k1 = 1/τ1 = 0.08 ps−1 or 1 ps−1, and k2 = 1/τ2 = 1 ps−1 or 0.08 ps−1, and they cannot be distinguished solely base on eqn (10.7). The two seemingly exchangeable sets of rate constants can be distinguished by analyses using eqn (10.2)–(10.6), the kinetics equations with the spectral distributions. Kinetics traces at three characteristic X-ray photon energies at 8337, 8339 and 8341 eV dominated by the rise and decay of T′, the decay of S1 and the rise of T, respectively, were collected (Figure 10.5), which were fitted globally to simulated traces assuming a sequential kinetic scheme to describe the excited state decay, S1 → T′ → T → S0, and the time-dependent populations (e.g., [S1(t)], [T′(t)], [T(t)] and [S0(t)]) from the solution of eqn (10.2)–(10.5). Based on this scheme, the relative populations of each species as a function of the delay time were simulated by numerical integration of a system of differential equations. These are the differential rate expressions for each species included in the kinetic scheme. τ1, τ2 and τ3 are assigned to the first, second and third steps in the sequential scheme, respectively. These components were weighted by

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their relative absorption at each energy in eqn (10.6) and the total simulated kinetic traces were fitted to the experimental traces using a nonlinear least squares method to obtain time constants for each step. Ai(E)Pi(t) gives the contribution from the i-th species to the total signal. A fit of 1/τ1 = 1 ps−1 and 1/τ2 = 0.08 ps−1 is much better supported by the analysis, while the switching of the two time constants, 1/τ1 = 0.08 ps−1 and 1/τ2 = 1 ps−1, completely missed the signals at longer delay times. The result is not immediately obvious since the transient signal for T′ appears to have almost instant rise and a few picosecond decay time constants. Only in the global analysis combined with the experimental results (Figure 10.5) is this inverted kinetics for T′ revealed. The kinetics of the excited state NiTMP can be expressed by the following 1ps 

1

 

k1 scheme: S1  π,π    T



 0.3ps  k

1





  ps 

1

k

2 3   T1 3d z2 ,3d x2  y2   GS.

10.3.2  Identity of the T′ State: The Transient Ni(i) Center Although the kinetics analysis based on experimental results and eqn (10.2)– (10.6) clearly indicate the existence of T′ with inverted kinetics of 1 ps rise and 0.08 ps decay, its identity in terms of electronic configuration of the Ni center cannot be determined solely from the kinetics analysis. From the XANES spectra of the ground state S0 and the thermalized excited state T obtained from our previous synchrotron experiments and the current LCLS experiments at delay time t < 0 and t > 20 ps, significant and identifiable changes are shown in the 1s → 4pz at the middle of the transition edge (Figure 10.6A) and 1s → 3d at the pre-edge region (Figure 10.6B). The 1s → 4pz feature for T

Figure 10.6  Gaussian-broadened  calculated XAS transitions of relevant excited

electronic states compared to experimental spectra in (A) the rising edge regions where 1s → 4pz transitions dominate and (B) the preedge region. Reprinted with permission from ref. 75. Copyright (2016) American Chemical Society.

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is blue-shifted by ∼2 eV, while that for T′ is red-shifted by ∼2 eV from that for S0,1. The origins of these spectral changes are not immediately clear due to the influence of the 1s core-hole and possible molecular geometry changes that cannot be measured directly by XANES spectra at LCLS. In order to rationalize the experimental observations and identify the T′ electronic configuration, a series of computational investigations have been carried out. The first set of TDDFT calculations was the electronic and nuclear structures for all of the states involved in the excited state dynamic pathways, namely, S0, S1, T′ and T, with the results shown in Figure 10.3. The calculated geometry changes between T and S0 agree well with our previous X-ray absorption fine structure (XAFS) results, which can be highlighted by the transformation from the non-planar S0 to the planar T state accompanied by the ∼0.1 Å Ni–N bond elongation.42 The T′ state was constructed with Ni(i) electronic configuration as hypothesized. Based on the nuclear geometry from the TDDFT calculations, solutions to the self-consistent field (SCF) equations were obtained, which converge at a higher energy than ground state solutions.90–92 For the inner shell to higher energy transitions, the SCF solutions were obtained using a set of natural transition orbitals (NTOs)93 for the state of interest and first generated at the valence excited state geometry. The calculation details can be found from our publication,75 while the results are presented in Table 10.1. As shown by Table 10.1, the dipole-allowed 1s → 4p transitions are the dominant transitions in all calculated XAS (Table 10.1, Figure 10.6). Little changes have been found for the Ni 1s and 4pz orbital energies between the S0 and S1 states as expected because the π–π* transition does not involve Ni orbitals. The hypothesized Ni(i) configuration for T′ has its 1s orbital energies increase by ∼2 eV, which explains the red-shift of its 1s → 4p transition to 8337 eV. The blue-shift of the 1s → 4p transition for T can also be explained by the decrease of the 1s energies. The time evolution of the 1s → 3d transitions was collected by centering the SASE spectra around 8333 eV to obtain the optimal flux, because the transitions were only quadrupole-allowed and dipole-forbidden with weak signals. The expected 1s → 3d transitions for the excited state pathway are Table 10.1  Orbital  energies for the electronic ground state and changes in those energies in various excited states.

Inputs for excited-state XAS modeling Wavefunc. Geometry

S0 S0

S1(π,π*) S1(π,π*)

1s α 1s β 4pz α 4pz β

−8167.47 −8167.47 1.39 1.39

−0.05 −0.05 −0.07 −0.06

a

T′ T′

T (d,d) T(d,d)

S0 T′

S0 T1(d,d)

T(d,d) S0

T(d,d) S1

Calculated Ni orbital energies (eV)a 2.02 −1.17 0.37 −0.34 2.03 −1.17 0.37 −0.34 0.18 −0.23 0.06 −0.03 0.05 −0.44 0.06 −0.03

−0.67 −0.67 −0.15 −0.34

−0.61 −0.61 −0.16 −0.34

The values in the columns other than S0 are changes with regards to the S0 values.

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outlined in Figure 10.3. As observed by the previous synchrotron and the current LCLS experiments, the 1s → 3d transitions have only a single feature for S0 in the 3d8 configuration due to the two possible 1s → 3dx2−y2 transitions, which is also shown in the calculated results in Figure 10.6B. At a 50 ps delay, a double peak feature due to the 1s to 3dz2 and 1s to 3dx2−y2 transitions appears, which agrees with the T(d,d) configuration of two singly occupied 3dz2 and 3dx2−y2 electronic configurations. Although the data quality at the pre-edge is limited due to the weak transition, it is clearly observable that the experimental 1s → 3dx2−y2 feature at 1 ps delay is slightly red-shifted compared to the ground state and the amplitude of the feature is significantly reduced, which agrees with a transient Ni(i) configuration in T′, where 3dz2 is filled and 3dx2−y2 is half-filled or singly occupied. This trend is seen for the calculated transition for the T′ state with a notable red-shift in contrast with the blue-shift observed for the same transition at 50 ps and for the modeled T state. Because of the limit in the data quality, the featureless 1s → 3d transition at the 10 ps delay can be understood as the precursor of the double peak feature at longer delays due to the formation of the T state. On the other hand, the uncertainty of the data and the lack of direct measurements on nuclear geometry made quantifications of the electronic configuration difficult, and therefore the interpretation remains on the trend of the changes, which agrees with the assignment of T′ to a transient Ni(i) with an electronic configuration of 3d9, as shown in Figure 10.2.

10.3.3  Implications and Significance The structural dynamics of the initial excited state in TMCs before thermalization are crucial for understanding how their photochemical reactions start and which pathways on the potential energy surface the excited state molecules will take. Ultrafast OTA measurements on TMC excited states started about two decades ago94–97 and revealed important photochemical dynamics, such as ISC, electronic coherence and delocalization, but the evidence was frequently deduced from the valence orbital optical signature without details of the metal electronic configuration. OTA measurements are routinely carried out nowadays for excited state pathway kinetics that can fit different models based on valence transitions in UV/vis/near infrared (NIR) regions, but the method has limitations in extracting metal electronic configuration and in studying samples with poor optical quality. The introduction of a set of metal-centered inner shell transitions in XTA enables the probing of metal-specific transitions on the ultrafast time scale (10−15 s), which provides electronic movements between different orbitals that optical transient absorption measurements cannot directly detect, especially for those optically dark electronic states and samples with a poor optical quality. The above example demonstrates how ultrafast X-ray spectroscopy reveals structural dynamics of the excited state of NiTMP before vibrational relaxation and solvent cooling. In fact, this is one of a few examples currently available for a direct comparison of OTA/XTA results on the same time scale. In this study,

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energies of the 1s → 3d and 1s → 4pz transitions in Ni have been directly obtained for different electronic states from which these properties have been obtained for short-lived transient states that may be otherwise missed in synchrotron experiments. This information can be extremely helpful in understanding photoinduced electron transfer of TMCs for solar energy conversion to specifically determine the events happening at the metal center after the photoexcitation. Knowing the movements of electrons and nuclei during chemical reactions has been the frontier in chemical sciences. The emerging femtosecond X-ray and laser sources finally brought us to this frontier to face challenges in both experimental and computational methods. The example included here demonstrates that experimental observation and theoretical calculation are inseparable parts for understanding chemical reaction pathways. It is very exciting to compare the structural dynamics results from both approaches side-by-side. In the case of NiTMP, the femtosecond X-ray results could only suggest the existence of a transient state, and only through quantum mechanical calculations was the identity of the state revealed. The ultrashort X-ray pulses with tens of femtoseconds duration are on the same time scale of bond breakage and some of the low frequency vibrational motions. Hence, XFELs will enable detection of electron movement and nuclear movement simultaneously. However, unlike synchrotron sources where XANES and EXAFS spectra can be collected by scanning a monochromator in the ∼1 keV range from which the electronic configuration and nuclear geometry can be obtained in the same scan, the EXAFS spectra cannot be collected with the current capability at the LCLS. Therefore, the molecular geometry in solution has been obtained via WAXS at the LCLS. In the example presented here, the molecular geometry of T′ in NiTMP is from TDDFT calculations evaluated by direct comparison to our previous EXAFS results for S0 and T. The optimized geometries of the excited states (Figure 10.3) provide insight into nuclear responses to electronic configuration changes and the subsequent energetic rearrangement of Ni orbitals. Porphyrin macrocycle expansion and flattening in the T state is explained by electron density movement from 3dz2 to 3dx2−y2, resulting in more anti-bonding character in the Ni–N bonds. Consequently, the effective radius of Ni(ii) increases in T, which makes the Ni(ii) center fit better with a more planar porphyrin macrocycle instead of the constrained ruffled geometry in the ground state. Concurrently, the Ni 3dxz and 3dyz orbitals in a more planar porphyrin would overlap better with N 2pz orbitals. In this case, T relaxes to a more energetically favorable flattened conformation that allows greater delocalization of the π electrons. Interestingly, the weakening of the Ni–N σ bonds and strengthening of the π-conjugation in a planar porphyrin have opposite effects in stabilizing Ni(i) electronic configuration. The majority of the Ni–N bond length expansion has already occurred in the relaxed geometry of the T′ state, which has a flattened porphyrin conformation and an Ni–N bond length expansion of 0.08 Å. This suggests that the addition of an electron to 3dx2−y2 precedes and drives the Ni–N bond elongation and the macrocycle planarization.

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In order to separate the effects of electron density changes from those of geometry changes in the excited states around the Ni center, calculations using S0 wavefunctions for optimized T′ and T geometries or S0 geometry for T′ and T wavefunctions on the energies of 1s, 4pz and 3d orbitals shown in Table 10.1 were carried out, which could not reproduce the observed energy shift of 1s → 4pz transition energies for T′ and T. We can therefore conclude that the 1s → 4pz transition energies observed in the experiments reflect both electronic and nuclear structural changes that not only affect the valence orbitals but also inner shell orbitals, such as 1s, with its energy change dominating the observed transition energy shifts. It is worth clarifying the confusion regarding the insensitivity of the inner shell energies with respect to the valence orbital energies manifested by the “frozen core orbitals”, which is a key assumption in semi-empirical quantum mechanical calculations. Based on the calculated results shown in Table 10.1, we can conclude that the 1s core orbital energy is very sensitive to the valence orbital configuration and geometry with up to 2 eV in response to the 3d orbital configuration. However, for the “frozen core orbitals”, although they vary in energy with the valence electronic configurations, their variations have relatively small effects on the valence orbital energies. The example here suggests that the “frozen core orbital” concept needs to be taken with caution and the apparent energy shift observed in the pre-edge or edge regions in XANES spectra may be dominated by the energy change in the inner core orbital rather than the valence orbitals. The identification of transient Ni(i) in NiTMP and its corresponding nuclear geometry has important implications in molecular design to accommodate certain photogenerated transient oxidation states of the metal center that could be catalytically active. Based on the Ni(i) state’s lifetime and the corresponding structural evolution, we speculate the participation of the ring structure and conformation on the stabilization of this species. Metalloporphyrins with large out-of-plane distortions have photophysical properties deviated from those of its planar counterparts, which reflect interplays between the orbital energy order and the total molecular energy as a function of the distortion coordinates, as well as the electronic coupling/delocalization of the d orbitals with the π orbitals of the macrocycle. A TDDFT survey of Ni porphine, NiTPP and NiOEP singlet and triplet state energies showed that the lowest energy singlet states in all cases are CT states 1(π, 3dx2−y2) in origin, and the total energy is highest for NiTPP due to its higher degree of out-of-plane distortion.98 Meanwhile, the lowest energy triplet state, the T(d,d) state, is destabilized to a greater degree as ruffling increases, reducing the energy gap between the T′ and T states. Hence, the conversion between the Ni(i) T′ state to the Ni(ii) T state can increase in rate and the T′ lifetime would decrease due to larger electronic coupling between the two states. Based on this study, an ideal nickel porphyrin structure for a prolonged Ni(i) state should have a non-planar ground state structure and a sufficiently high potential energy barrier between the T′ and T states, but not too high as to prohibit the planarization of T. Such requirements may have conflicts among

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the different steps of the reactions. However, we would not be able to understand the design of the potential surface along a reaction pathway without the insightful information of the initial excited states before thermalization.

10.4  Conclusion The femtosecond X-ray pulses from XFEL facilities have brought in new opportunities for investigating electron and nuclear movements in photoexcited TMCs before the excited state thermalization via XAS. The time resolution and pulse flux provided by these sources enable XTA measurements to be carried out in parallel with optical transient absorption on the same time scale, based on electronic transitions in different energy regimes. Element-specific ultrafast XANES studies carried out at the LCLS with femtosecond time resolution combined with quantum mechanical calculations revealed the identity of a transient Ni(i) (π, d) electronic state (T′) with inverted kinetics. The observed and computed inner shell-to-valence orbital transition energies demonstrate and quantify the influence of electronic configuration on specific metal orbital energies. The applications in this area are of course not limited to XTA and have been developed in other X-ray spectroscopies, such as XES and resonant inelastic X-ray scattering (RIXS), as presented in other chapters of this book, especially chapters 7, 11 and 12. The strong influence of the valence orbital occupation on the inner shell orbital energies uncovered through quantum mechanical calculations and the XANES experimental results revises the assumption of “frozen core orbitals” in previous semi-empirical methods, in which the core orbital energies are strongly dependent upon the valence orbital configuration, while the valence orbital energies are much less sensitive to the inner core orbital energies. Thus, transition energies featured in XANES alone cannot be used to determine the d-orbital energies of different states. The study also suggests the interdependence of the Ni 3d electronic configuration and Ni local nuclear geometry. Based on the results from this example, a desirable excited state potential surface for a prolonged Ni(i) state is perceived, which should have a non-planar ground state structure and a sufficiently high potential energy barrier between T′ and T states, while it still allows nuclear movements to planarize the porphyrin ring in T. Such requirements may be necessary for clever design to achieve the balance between stabilization of T′ and conversion to T. Moreover, the influence of the porphyrin macrocycle conformation on excited state rise/decay kinetics may be significant enough to affect the kinetics that govern the limited population accumulation of Ni(i).

Acknowledgements We acknowledge support for this work from the Solar Energy Photochemistry program (experimental work) and Ultrafast Initiative (theoretical work) of the U. S. Department of Energy, Office of Science, Office of Basic Energy

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Sciences, through Argonne National Laboratory under Contract No. DE-AC0206CH11357 and MLS is supported by the National Institute of Health, under Contract No. R01-GM115761 (LXC) and R01-HL63203 (BMH). Use of the Linac Coherent Light Source (LCLS), SLAC National Accelerator Laboratory, is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC02-76SF00515. Computations on modeled spectra were facilitated through the use of advanced computational, storage and networking infrastructure provided by the Hyak supercomputer system at the University of Washington, funded by the Student Technology Fee. PJL is also grateful for support by the State of Washington through the University of Washington Clean Energy Institute. MLS also thanks the National Institute of General Medical Sciences of NIH for support through the Molecular Biophysics training grant administered by Northwestern University (5T32 GM008382). KH gratefully acknowledges support from DANSCATT and from the Villum and Carlsberg Foundations. The authors would like to thank Tim Brandt Van Driel for invaluable assistance with the phase cavity timing correction by providing a means to calibrate the phase cavity data.

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85. J. A. Shelnutt, K. Alston, E. W. Findsen, M. R. Ondrias and J. M. Rifkind, ACS Symp. Ser., 1986, 321, 232–247. 86. D. H. Jeong, D. Kim, D. W. Cho and S. C. Jeoung, J. Raman Spectrosc., 2001, 32, 487–493. 87. L. X. Chen, X. Zhang, E. C. Wasinger, K. Attenkofer, G. Jennings, A. Z. Muresan and J. S. Lindsey, J. Am. Chem. Soc., 2007, 129, 9616–9618. 88. A. D. Bond, N. Feeder, J. E. Redman, S. J. Teat and J. K. M. Sanders, Acta Crystallogr., Sect. E: Struct. Rep. Online, 2003, 59, M818–M820. 89. M. L. Shelby, M. W. Mara and L. X. Chen, Coord. Chem. Rev., 2014, 277, 291–299. 90. A. T. B. Gilbert, N. A. Besley and P. M. W. Gill, J. Phys. Chem. A, 2008, 112, 13164–13171. 91. E. R. Davidson, J. Chem. Phys., 1964, 41, 656. 92. B. Peng, B. E. Van Kuiken, F. Ding and X. Li, J. Chem. Theory Comput., 2013, 9, 3933–3938. 93. R. L. Martin, J. Chem. Phys., 2003, 118, 4775. 94. N. H. Damrauer, G. Cerullo, A. Yeh, T. R. Boussie, C. V. Shank and J. K. McCusker, Science, 1997, 275, 54–57. 95. J. K. McCusker, Acc. Chem. Res., 2003, 36, 876–887. 96. P. J. Reid, C. Silva, P. F. Barbara, L. Karki and J. T. Hupp, J. Phys. Chem., 1995, 99, 2609–2616. 97. A. T. Yeh, C. V. Shank and J. K. McCusker, Science, 2000, 289, 935–938. 98. S. Patchkovskii, P. M. Kozlowski and M. Z. Zgierski, J. Chem. Phys., 2004, 121, 1317–1324.

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Chapter 11

Tracking Excited State Dynamics in Photo-excited Metal Complexes with Hard X-ray Scattering and Spectroscopy Kasper S. Kjær* and Kelly J. Gaffney PULSE Institute, SLAC National Accelerator Laboratory, Stanford University, Menlo Park, California 94025, United States *E-mail: [email protected]

11.1  Introduction Optimization of photo-functional molecules hinges upon delivering the desired excited state properties for the given functionality. We presently lack the knowledge base to predict and control the most fundamental properties of electronic excited states, including their lifetime and their ability to form stable charge separated states. This knowledge gap impedes our ability to cost effectively convert and store solar energy. The experimental investigation of photoactive molecules thus aims at characterizing particular excited states, as well as identifying the mechanistic pathways through which these excited states are formed. Thorough knowledge of excited state properties   Energy and Environment Series No. 18 X-Ray Free Electron Lasers: Applications in Materials, Chemistry and Biology Edited by Uwe Bergmann, Vittal K. Yachandra and Junko Yano © The Royal Society of Chemistry 2017 Published by the Royal Society of Chemistry, www.rsc.org

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and pathways in a system, or a class of systems, provides the best possible starting point for rational targeted development. In this chapter, we describe how time-resolved X-ray free-electron laser (XFEL) measurements can address excited state dynamics of photoactive transition metal centered molecules in solution. We will focus on two time-resolved techniques: X-ray emission spectroscopy (XES) and X-ray diffuse scattering (XDS). XES monitors changes in the spectra of core-level transitions in a given atomic species, and XDS monitors changes in the coherent elastic scattering of the sample. This origin makes XES selectively sensitive to the electronic configuration of the transition metal center of the molecule under investigation, while the XDS signal is selectively sensitive to structural changes. Thus, the application of XES and XDS makes it possible to identify and isolate electronic and structural contributions to the excited state cascade. The clearly defined origin and strong selectivity of the XES and XDS measurements is particularly relevant for characterizing the dynamics of the first picoseconds following photoexcitation of a molecule in solution. On this ultrafast timescale, the excited state cascade involves a complex interplay between electronic, intramolecular structural and intermolecular solvation dynamics. More commonly used ultrafast techniques, such as transient absorption (TA) spectroscopy in the visible and near infrared (NIR) part of the electromagnetic spectrum, have joint sensitivity to both electronic and nuclear dynamics, and struggle to clearly separate these distinct dynamics. Thus, the addition of XES and XDS to the toolbox of ultrafast techniques has the potential to expand on our knowledge of the excited state cascade of molecules. The insight provided on the nature of excited states, and the dynamics with which they are formed, will help advance the development of photoactive molecules.

11.2  Experimental Techniques 11.2.1  XES The X-ray emission spectrum arises from secondary photons emitted upon repopulation of an ionized core-hole. The hard X-ray XES measurements conducted at XFEL sources to date have focused on K-emission lines of 3d transition metals in molecules and proteins.1–6 The studies have recorded either one of, or both, the Kα and Kβ emission lines arising from 2p → 1s and 3p → 1s transitions, respectively. The shape of the Kα and Kβ emission spectra are influenced by multiplet and spin orbit interactions. In 3d transition metal systems, they are highly sensitive to the oxidation state and number of unpaired electrons of the transition metal.7,8 Due to the large core-hole lifetime broadening, the Kα lines seem particularly rather unresolved. However, with careful lineshape analysis, the information content regarding charge and spin state can be extracted.9 A frequent evaluation approach applicable to the interpretation of

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photoinduced transient Kα and Kβ emission spectra is based on constructing reference difference spectra from steady-state spectra from suitable reference complexes.10–12 The reference difference spectra are constructed by subtracting a ground state reference spectrum from the spectra reference complexes with the same electronic configuration as the potential excited states. The reference difference spectra can be quantitatively compared to the recorded photoinduced difference signal. For good quality data and well-chosen reference compounds, the comparison between time-resolved data and reference spectra allows for characterization of the excited electronic state configuration and excitation fraction.13,14

11.2.2  XDS XDS provides structural information arising from the interference between X-ray photons scattered elastically from the sample. The solution state XDS measurements conducted at XFEL sources to date have focused on the structural and solvation dynamics of 3d and 5d transition metal containing systems,5,6,15–17 as well as the structural dynamics of excited state protein species.18–20 While the elastic scattering strength of an atom increases with the number of electrons, the process has no direct element specificity. The XDS measurement thus returns information of the structure of the entire sample volume probed by the X-ray pulses, and is therefore sensitive to structural changes in both the excited state molecular system, its solvent cage and any changes in the bulk solvent structure. The difference scattering signal21–23 ΔS(Q,t) can be construed as the sum of contributions arising from structural changes in the solute,24,25 the solvation cage14,26 and the bulk solvent.27,28   



ΔS(Q,t) = ΔSsolute(Q,t) + ΔSsolvation cage(Q,t) + ΔSbulk solvent(Q,t)

(11.1)

Each of these components can be further separated into different molecular structural distortions, solvation processes and bulk solvent contributions. In a common analysis approach, each contribution to the difference scattering signal is modeled, either through simulations or by reference measurements, and the sum of these contributions is fitted to the XDS data.21,23 For fits of ΔS(Q,t) for t < 100 ps, one typically5,15 fits the data with ΔSsolute(Q,t) simulated for one or two molecular distortion coordinates, ΔSsolvation cage(Q,t) simulated as a single solvation cage contribution and ΔSbulk solvent(Q,t) modelled with a reference measurement of temperature increase in bulk solvent at constant volume.

11.2.3  Combined Experimental Setup The experimental requirements of time-resolved solution phase XES and XDS measurements are very similar. Both XDS and XES are “photonhungry” X-ray techniques14 that benefit from the high pulse-intensity

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available at XFEL sources. Both techniques operate well with an X-ray energy ∼1 keV above the 1s ionization potential of 3d transition metals (6–10 keV).5,6 The detection schemes for the two techniques can be implemented in parallel, as illustrated in Figure 11.1. A dissolved sample is pumped through a nozzle generating a liquid jet, which is excited by an optical laser pulse and probed by an X-ray pulse. The XDS signal is recorded on an area detector behind the sample covering 0 to 45°. The energy of the XES signal is selected with a spectrometer placed at 90° with respect to the sample and a detector placed in Bragg conditions with respect to the sample and spectrometer. The combined setup shown in Figure 11.1 was used for recording XDS and Kα XES of Co-centered samples at the SACLA XFEL.6

11.3  Experimental Results 11.3.1  C  haracterizing the Decay of Metal-to-ligand Charge Transfer (MLCT) States in Fe-centered Molecular Systems Developing light-harvesting and photocatalytic molecules based on iron could provide a cost effective, scalable and environmentally benign path for solar energy conversion.29–31 Until very recently,32–35 development of iron-centered light-harvesters has been limited by the sub-picosecond MLCT electronic excited state lifetime. The ultrafast MLCT decay of ironbased complexes are due to spin crossover—the extremely fast intersystem crossing and internal conversion to high spin metal-centered excited states.3,36–42 A systematic characterization of spin crossover relaxation dynamics with mechanistic detail would represent an important step towards developing rational design strategies for iron-centered molecular systems with extended MLCT lifetimes. In the following, we show that XFEL

Figure 11.1  Schematic  of an experimental setup allowing for simultaneous XES and

XDS measurements of a solution state sample. Reprinted by permission from Macmillan Publishers Ltd: [Nature Communications] (ref. 6) Copyright 2015.

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measurements can be applied to provide such mechanistic insight, revealing which excited state potential energy surfaces deactivate the MLCT state of iron-centered systems.3,4 A wide array of pump-probe measurements in pseudo-octahedral polypyridyl iron coordination complexes, such as the [Fe(bpy)3]2+ (bpy = 2,2′-bipyridine) illustrated in Figure 11.2A, shows that MLCT excited states undergo internal conversion and intersystem crossing to the metal-centered high spin quintet (5MC) excited state on a sub-picosecond timescale.29,36–45 This photoexcited spin crossover involves two electronic transitions and two electronic spin flips. Recent theoretical calculations focused on the mechanism of spin crossover favor a stepwise spin crossover mechanism,46–48 with the MLCT excited state transition to the 5MC excited state proceeds through a metalcentered triplet state (3MC). Experimental investigation of this computational prediction of an ultrafast sequential spin-crossover mechanism has been challenged by the lack of element specificity in ultraviolet (UV)–visible and NIR spectroscopy, rendering the signatures from different MC states all but indistinguishable.6 Thus, while optical spectroscopies are ideally suited for identifying and tracking optically bright states, such as MLCT states in which excited electrons reside in the ligand framework, they typically struggle to address transition metal-centered states, and therefore cannot follow the mechanistic pathways of the MLCT decay. In contrast to the optical spectroscopies, XES is solely sensitive to the charge and spin-state dynamics of the atomic species under investigation.4 By tracking the X-ray fluorescence signal from the iron center, XES offers unique insight into the electronic kinetics following the decay of the MLCT state.3 The XES signal measured for photoexcitation of [Fe(bpy)3]2+ (Figure 11.2B and C) was modeled using the reference spectra for the potential excited states shown in Figure 11.2G and H.3 Analysis of the measured difference signal reveals that the sequential mechanism, where the 5MC state is populated via a 3MC state, provides a significantly better description of the data. In particular, the dynamics of the region around 7054 eV between the Kβ1,3 and the Kβ′ peak cannot be reproduced without the inclusion of a reference difference spectrum similar to that expected for a 3MC state. Recent X-ray and optical measurements,49,50 which are sensitive to the structural dynamics of the excited state, have shown that the structural dynamics are inconsistent with a 70 fs lifetime 3MC intermediate between the MLCT and 5MC states. Since there is no structural information in the XES measurement, this constraint has not been worked into the model used to fit the data presented in Figure 11.2. The simplest way to construct a model that satisfies both the clearly identified 3MC presence of XES and the observed structural dynamics would be to describe the passage through the 3MC state as a ballistic process. Within this model, the 3MC → 5MC transition happens with near unity quantum yield at the point of

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Figure 11.2  Overview  of the Kβ XES experiment on [Fe(bpy)3]2+ and [Fe(bpy)(CN)4]2−.

(A) The XES Kβ emission difference signal measured at 50 fs and 1 ps time delay for [Fe(bpy)3]2+, molecular structure shown in the inset. (B) False color plot of the XES Kβ emission difference signal. (C) The excited state population as a function of time determined from analysis of the data presented in B. (D) The XES Kβ emission difference signal measured at 50 fs and 1 ps time delay for [Fe(bpy)(CN)4]2−, molecular structure shown in the inset. (E) False color plot of the XES Kβ emission difference signal. (F) The excited state population as a function of time determined from analysis of the data presented in E. (G) Reference difference spectra for the MLCT, 3MC, 4MC and 5MC excited states constructed by subtracting the singlet model complex spectrum from the doublet, triplet, quartet and quintet model complex spectra shown in H. (H) XES Kβ emission spectra of ground state iron complexes with different spin moments matching those of the potential excited state of the Fe(bpy)3 and [Fe(bpy)(CN)4]2−. Reprinted by permission from Macmillan Publishers Ltd: [Nature Communications] (ref. 3) Copyright 2014. (I) Schematic of the difference in excited state potential energy surfaces between [Fe(bpy)3]2+ and [Fe(bpy)(CN)4]2−. Reproduced from ref. 4 with permission from the Royal Society of Chemistry and by permission from Macmillan Publishers Ltd: Nature (ref. 3), copyright (2014).

intersection between their potential energy surfaces. The slope of 5MC and 3 MC potential energy surfaces are relatively similar at the repulsive side of their intersection;48 the structural dynamics of the proposed model would thus be very similar to those of a direct MLCT → 5MC transition, while retaining the 3MC intermediate. This sequential ballistic model for the decay of the MLCT state could be readily tested through a combined XES/

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XDS experiment measuring both electronic and structural dynamics simultaneously and independently at current XFEL sources where the time resolution for solution state experiments has reached 60 fs.50 Studies indicate that spin crossover to the Fe center can be suppressed by incorporating strongly sigma-donating ligands, which increases the ligandfield splitting and thus destabilizes the MC states relative to the ground and MLCT states.32–35,51 Excited state characterization of Fe-centered molecular systems where the MLCT lifetime has been extended in this fashion has been conducted with transient optical absorption (TA) measurements.32,33,35,51 These studies all show multi-exponential decay dynamics where the component with the longest lifetime has been assigned to the MLCT decay, an interpretation that results in MLCT lifetimes in the 5–30 ps range. Extending the TA studies with XES measurements can reveal the charge and spin dynamics on the Fe centers of the systems, which would both verify MLCT lifetimes and help assign the additional decay components observed in the TA data. The simplest Fe-centered system with extended MLCT lifetime is the [Fe(bpy)(CN)4]2− shown in Figure 11.2D. Compared to [Fe(bpy)3]2+, two bipyridine ligands have been substituted by four strongly sigma-donating CN− ligands. The TA data4,33,51 shows a strong excited state absorption feature at 370 nm, which has been assigned to bpy-localized MLCT states in similar systems. In the TA data recorded for [Fe(bpy)(CN)4]2− the excited state features decay with bi-exponential dynamics of 2.4 and 19 ps. The XES difference signal following photoexcitation of [Fe(bpy)(CN)4]2− is shown in Figure 11.2E and F. The dynamics of the XES signal are very different from those observed for [Fe(bpy)3]2+. The excited state difference signal of [Fe(bpy)(CN)4]2− exhibits no changes in shape and no dynamics outside of an initial grow-in followed by a 19 ps decay. The shape of the difference signal is best described by the MLCT reference difference spectrum. This means that the 19 ps timescale observed in both XES and TA data can be robustly assigned to an MLCT state and that the short-lived decay component of the TA data can be assigned to processes that do not involve electronic state dynamics, such as vibrational cooling or solvation dynamics. Taken together, the studies on [Fe(bpy)3]2+ and [Fe(bpy)(CN)4]2− show that XES measurements allow for a detailed characterization of the electronic configuration of metal-centered excited states, and provides unique insights into the dynamics governing their interconversion. Figure 11.2I shows a sketch of the potential energy surfaces explaining the excited state dynamics of the two systems. For [Fe(bpy)3]2+, the excited MLCT state is deactivated by intersystem crossing to a 3MC potential energy surface, which decays extremely fast to a 5MC state as the Fe–N ligand system starts expanding. For [Fe(bpy)(CN)4]2−, the energy of the MC states is increased to a point where it is never populated for any significant amount of time in the excited state cascade.

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11.3.2  C  haracterizing Electron Transfer and Spin State Dynamics of Co-centered Molecular Systems Joint XES–XDS measurements have also been performed on model photocatalytic dyads. Inspired by the structural organization found within photosynthetic organisms, photocatalytic dyads combine a molecular light harvester and a molecular catalytic site with a molecular conjugated bridge to form a single photoactive molecular device.52,53 In molecular assemblies, one of the primary events associated with the functionality is the electron transfer between the light harvesting and catalytic site, with the bridge mediating directional charge transfer and, in some cases, acting as an electron relay and reservoir.54–56 For intramolecular electron transfer processes proceeding on picosecond or sub-picosecond timescales, the electron transfer happens on the same timescale as vibrational redistribution, thermalization and solvation.6 As was the case for disentangling spin-crossover pathways, the applicability of optical TA experiments is restricted to mapping states that are optically bright and the vibrational cooling observed in optical TA measurements reflect only vibrational dynamics that directly couple to optical transitions. Since the catalytically active sites of both natural and artificial molecular photocatalysts are typically based on optically dark transition metal centers, optical spectroscopies struggle to address the electronic dynamics at the active site of the system.56 In the following study, we combine the information of TA, XES and XDS to investigate electron transfer processes in the bimetallic complex presented in Figure 11.3F, consisting of a light-harvesting, ruthenium (Ru)-based chromophore linked to a cobalt (Co) electron acceptor by a bridge that mediates ultrafast electron transfer.57–60 The bimetallic ruthenium–cobalt complex [(bpy)21RuII(tpphz)1CoIII(bpy)2]5+ (bpy = bipyridine, tpphz = tetrapyrido(3,2-a: 2′3′-c:3″,2″-h::2‴,3‴-j) phenazine) is designated as Ru=Co hereafter. This molecular system exemplifies the wide class of synthetic and natural photocatalysts for which the coupled electronic and structural dynamics are only partially understood.6,56 Optical TA data reveals that selective excitation of the Ru center leads to quasi-instantaneous ( 0 and b > 0 are both considered as constants. For this potential, eqn (14.1) becomes:   

  

d2Q1 dQ   1  t  1  aQ1  4bQ13  β1 • Ea (t ). 2 dt dt

(14.9)

In the absence of an applied field Ea(t), the equilibrium values of Q1 are  a /4b . If we take  a /4b as an initial value of Q1, it is possible to imagine that an appropriately strong and impulsive electric field Ea(t) polarized in the right direction could force the system into coherent dynamics that result in a final value of Q1 in the other potential energy minimum at a /4b , and thus a domain reversal. In this case the damping factor [the second term in eqn (14.9)] can prevent a return to the left side of the double well. Alternatively, a second impulsive field arriving later could be used to “brake” the dynamics and force the system to a halt. This idea has been theoretically explored for specific application to ferro­ electric polarization switching in PbTiO3 by Qi et al., where they have showed that an appropriately timed sequence of ultrabroadband THz pulses can be used to drive a 180° reversal of the ferroelectric polarization.52 In this case, consideration of the multidimensional potential landscape offered by additional structural coordinates offered an alternate path to the switching

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that was more efficient, since the potential energy barrier between the two domains was lower using an indirect trajectory. This work predicts that electric field magnitudes in excess of 1 MV cm−1 for so-called “half cycle” pulses with a centre frequency of several THz are needed to achieve switching in this system. Experimental investigations of such dynamics are somewhat constrained by progress in delivering such large amplitude pulses to materials of interest. Some evidence for anharmonic THz pulse interaction with a strong IR active mode was, however, observed in the case of non-ferroelectric SrTiO3.53 Spin reorientation transitions can also be driven be a similar mechanism using the magnetic field component of light and may be more promising due to higher intrinsic nonlinearities. The basic idea of coherent magnon stimulation and control by THz-frequency broadband electromagnetic pulses has been demonstrated in NiO.54 There has also been some interest in extending this to achieve coherent control of ferromagnetic materials to achieve magnetization reorientation.55 In some systems, hybrid excitations of spin and vibrational modes called electromagnons (normally defined as electric dipole active spin excitations) exist and offer another possible route to coherent control. These kinds of excitations exist in several “multiferroic” materials, which exhibit a coexistence of magnetic order and ferroelectric polarization. In multiferroic TbMnO3, model calculations have suggested that a very intense single cycle THz pulse with a center frequency overlapping an electromagnon excitation near 2 THz can cause a reversal of the ferroelectric polarization on a time scale of several picoseconds.56 This work predicts that switching in such systems requires electric fields on the order of 10 MV cm−1. A first experimental validation of the coherent spin dynamics that would possibly lead to this transition was performed using magnetic resonant X-ray diffraction with femtosecond time resolution at an XFEL to measure the dynamics of spin motion involved in a THz-excited electromagnon.57 Figure 14.5 shows a representative sample of the results from this study, showing that the spin structure is modulated in response to the driving THz field. Although this experiment was only able to apply several hundred kV cm−1 to the interior of the material, and so is still far from the regime of polarization switching, the spin dynamics show behaviour consistent with the model and so argue for the general feasibility of this idea.

14.5  Prospects for Further Progress Both direct and indirect methods of light-induced control of structural transitions have limitations imposed by the nature of the desired transition and the material itself. Indirect schemes that excite dynamics in an order parameter via excitation of another degree of freedom generally suffer from problems associated with the fact that most of the energy delivered to the system resides in the auxiliary excitation and not in the dynamics of the order parameter itself. If this auxiliary excitation is also coupled to other modes there

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could be undesirable side effects, for example, a strong increase in the general temperature of the material that could compromise the reversibility of the dynamics. Direct schemes are an alternative that rely on a direct coupling of the desired order parameter to either the electric or magnetic field of a light pulse, and are thus more scalable to large-amplitude dynamics. Open questions are whether the high fields required to drive such direct dynamics are possible to couple efficiently into these materials, whether the dynamics in the strongly anharmonic regime are sufficiently underdamped, and whether these fields are sufficiently low that nonlinear electronic effects will not simply destroy the material. All these questions require further experimentation and specifically experiments where the transient structural dynamics can be quantitatively measured in response to a variety of strong stimulations. As shown in the several examples discussed in this chapter, time-resolved diffraction methods at modern fourth-generation X-ray sources offer unique opportunities in this respect.

Acknowledgements This research was supported by the NCCR MUST, funded by the Swiss National Science Foundation.

References 1. A. V. Kolobov, P. Fons, A. I. Frenkel, A. L. Ankudinov, J. Tominaga and T. Uruga, Nat. Mater., 2004, 3, 703. 2. E. Dagotto, Nanoscale Phase Separation and Colossal Magnetoresistance: The Physics of Manganites and Related Compounds, Springer, 2013. 3. M. Vojita, Adv. Phys., 2009, 58, 699. 4. O. Auciello, C. A. Paz de Araujo and J. Celinska, in Emerging Non-volatile Memories, ed. S. Hong, O. Auciello and D. Wouters, Springer, 2014, p. 3. 5. M. H. Kryder and C. S. Kim, IEEE Trans. Magn., 2009, 45, 3406. 6. H. Ishiwara, M. Okuyama and Y. Arimoto, Ferroelectric Random Access Memories: Fundamentals and Applications, Springer, 2004. 7. M. Shapiro and P. Brumer, J. Chem. Phys., 1986, 84, 4103. 8. M. Shapiro, J. W. Hepburn and P. Brumer, Chem. Phys. Lett., 1988, 149, 451. 9. K. Ohmori, Annu. Rev. Phys. Chem., 2009, 60, 487 (and references therein). 10. M. Shapiro and P. Brumer, Quantum Control of Molecular Processes, WileyVCH Verlag, 2nd edn, 2012. 11. R. W. Schoenlein, et al., Science, 2000, 287, 2237. 12. P. Beaud, et al., Phys. Rev. Lett., 2007, 99, 174801. 13. P. Emma, et al., Nat. Photonics, 2010, 4, 641. 14. T. Ishikawa, et al., Nat. Photonics, 2012, 6, 540. 15. E. Allaria, et al., Nat. Photonics, 2012, 6, 699. 16. M. Mochizuki, N. Furukawa and N. Nagaosa, Phys. Rev. Lett., 2010, 104, 177206.

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17. R. Merlin, Solid State Commun., 1997, 102, 207. 18. Y. X. Yan, E. B. Gamble and K. A. Nelson, J. Chem. Phys., 1985, 83, 5391. 19. H. J. Zeiger, et al., Phys. Rev. B, 1992, 45, 768. 20. A. M. Kalashnikova, et al., Phys. Rev. Lett., 2007, 99, 167205. 21. M. Hase, et al., Appl. Phys. Lett., 1996, 69, 2474. 22. M. F. DeCamp, et al., Phys. Rev. B, 2001, 64, 092301. 23. K. Sokolowski-Tinten, et al., Nature, 2003, 422, 287. 24. D. M. Fritz, et al., Science, 2007, 315, 633. 25. S. L. Johnson, et al., Phys. Rev. Lett., 2008, 100, 155501. 26. S. L. Johnson, et al., Phys. Rev. Lett., 2009, 103, 205501. 27. L. Rettig, et al., Phys. Rev. Lett., 2015, 114, 067402. 28. R. Yusupov, et al., Nat. Phys., 2010, 6, 681. 29. T. Huber, et al., Phys. Rev. Lett., 2014, 113, 026401. 30. T. Huber, PhD Dissertation, ETH Zurich, 2015. 31. P. Beaud, et al., Nat. Mater., 2014, 13, 923. 32. C. D. Stanciu, et al., Phys. Rev. Lett., 2007, 99, 047601. 33. I. Radu, et al., Nature, 2011, 472, 206. 34. T. A. Ostler, et al., Nat. Commun., 2012, 3, 666. 35. A. R. Khorsand, et al., Phys. Rev. Lett., 2012, 108, 127205. 36. J. H. Mentink, et al., Phys. Rev. Lett., 2012, 108, 5. 37. A. M. Kalashnikova and V. I. Kozub, Phys. Rev. B, 2016, 93, 11. 38. S. Mangin, et al., Nat. Mater., 2014, 13, 287. 39. L. Le Guyader, et al., Nat. Commun., 2015, 6, 5839. 40. A. Kirilyuk, A. V. Kimel and T. Rasing, Rep. Prog. Phys., 2013, 76, 26501. 41. C. E. Graves, et al., Nat. Mater., 2013, 12, 293. 42. A. Subedi, A. Cavalleri and A. Georges, Phys. Rev. B, 2014, 89, 220301. 43. M. Foerst, R. Mankowsky and A. Cavalleri, Acc. Chem. Res., 2015, 48, 380. 44. M. Foerst, et al., Nat. Phys., 2011, 7, 854. 45. M. Foerst, et al., Solid State Commun., 2013, 169, 24. 46. M. Rini, et al., Nature, 2007, 449, 72. 47. D. Fausti, et al., Science, 2011, 331, 189. 48. S. Kaiser, et al., Phys. Rev. B, 2014, 89, 184516. 49. W. Hu, et al., Nat. Mater., 2014, 13, 705. 50. M. Mitrano, et al., Nature, 2016, 530, 461. 51. R. Mankowsky, et al., Nature, 2014, 516, 71. 52. T. Qi, et al., Phys. Rev. Lett., 2009, 102, 247603. 53. I. Katayama, et al., Phys. Rev. Lett., 2012, 108, 097401. 54. T. Kampfrath, et al., Nat. Photon., 2011, 5, 31. 55. C. Vicario, et al., Nat. Photon., 2013, 7, 720. 56. M. Mochizuki and N. Nagaosa, Phys. Rev. Lett., 2010, 105, 147202. 57. T. Kubacka, et al., Science, 2014, 343, 1333.

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Chapter 15

Ultrafast Time Structure Imprints in Complex Chemical and Biochemical Reactions Sadia Baria,c, Rebecca Bolla,c, Krzysztof Idzika,c, Katharina Kubičeka,c, Dirk Raisera,c, Sreevidya Thekku Veedua,c, Zhong Yina,c and Simone Techert*a,b,c a

Structural Dynamics in Chemical Systems, Photon Science at DESY, Notkestrasse 85, 22607 Hamburg, Germany; bInstitute for X-ray Physics, Georg August University, Göttingen, Friedrich Hund Platz 1, 37077 Göttingen, Germany; cMax Planck Institute for Biophysical Chemistry, Am Fassberg 11, 37077 Göttingen, Germany *E-mail: [email protected]

15.1  Introduction In a chemical reaction, typical time scales of atomic or molecular motion start from femtoseconds, meaning the millionth of a billionth of a second. Life-relevant motions, however, can be as slow as seconds or even up to minute or hour time scales. The origin of these time scale differences is based on the complexity of the coordination space of a proceeding reaction.1–6 In a classical kinetic scheme, the gradients on the potential energy hypersurface define the molecular dynamics.1 Statistically population-weighted,2 they compose the kinetics of a chemical reaction. The coordinates describing the dynamics and kinetics of a chemical reaction are the reaction coordinate   Energy and Environment Series No. 18 X-Ray Free Electron Lasers: Applications in Materials, Chemistry and Biology Edited by Uwe Bergmann, Vittal K. Yachandra and Junko Yano © The Royal Society of Chemistry 2017 Published by the Royal Society of Chemistry, www.rsc.org

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and the energy. The reaction coordinate is defined as a one-dimensional projection of the reactant’s and product’s normal coordinates, which span the potential energy hypersurface of reactant and product and the potential energy hypersurfaces of their transitions (Figure 15.1).3–5 The energy gradient along a reaction coordinate is defined as reaction dynamics, and the energy gradient along the normal coordinates as molecular dynamics. Commonly, the potential energy is shown in a kinetic curve under the graph, and the axis description of the ordinate presents the sum of the potential energy of the nuclei involved in the chemical reaction and their kinetic energy (Figure 15.2). The potential and kinetic energy of molecules can be detangled through the projection of the potential energy onto the total energy axis. The activated complex or transition state (according to Eyring) includes an imaginary mode or negative eigenvalue.6 Ultrafast X-ray methods bear the potential of determining the complexity of chemical reactions during their reactions, particularly in the bulk, with techniques that utilize the specific characteristics of X-ray–matter interactions. In well-ordered systems, X-ray crystallography as a Thomson scattering process allows for element-specific determinations, such as electron densities (redox states) and high-precision spatial resolution determination of atoms in lattices from which hydrogen bonding, chemical bonding or van der Waals stacks can be derived. In less ordered and disordered systems, X-rays deliver element-specific information of the investigated molecules utilizing, for example, X-ray spectroscopy, X-ray absorption, photo-induced electron cascades, or X-ray and electron emission properties. Site-specific information is obtained by elastic and inelastic scattering processes, such as multidimensional X-ray spectroscopy, X-ray diffraction or X-ray scattering. The chemical

Figure 15.1  The  reaction coordinate (abscissa) of a chemical reaction is defined

as a one-dimensional projection of the normal coordinates spanning the reactant’s potential energy hypersurface versus the normal coordinates spanning the product’s potential energy hypersurface, and their corresponding transitions. For further reading, please see ref. 2 and 3.

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consequences of X-ray–matter interactions leading to fragmentation can be characterized by X-ray mass spectrometry. Characteristics for the X-ray photons generated in synchrotrons and free-electron lasers (FELs) are their:    (i) energy tunability (allowing for excitation-energy-sensitive methods like X-ray spectroscopy or advanced X-ray diffraction methods), (ii) pulsed structure (allowing for in-situ and time-resolved X-ray methods), (iii) defined polarization (allowing for advances in X-ray spectroscopy), (iv) coherence (allowing for X-ray imaging or correlation spectroscopy methods) and (v) high flux (allowing for high-resolution X-ray experiments in all experimental domains).    Fourth generation accelerator-based light sources (free-electron lasers, FELs) in the vacuum-ultraviolet (VUV) or X-ray regime deliver ultra-brilliant coherent radiation in very short pulses (1012–1013 photons per bunch per 10–100 fs). In order to fully exploit their unique photon capabilities, novel instrumentation is required based on single-shot (collection) schemes. Moreover, hundreds and up to trillions of fragment particles, ions, electrons or scattered photons can emerge when a single light flash impinges on matter with intensities up to 1022 W cm−2 (predicted for the X-ray FEL, XFEL). In order to meet these challenges, in the starting time of FLASH (the extreme-ultraviolet FEL in Hamburg)7a and the Linac Coherent Light Source (LCLS—a soft and hard XFEL),7b various experimental chambers and endstations have been designed.

Figure 15.2  Total  energy of a chemical system as the sum of the potential and kinetic energy of the molecules (ordinate). Inside the graph, only the contribution of the potential energy is plotted; its projection towards the ordinate allows determination of the kinetic energy. For further reading, please see ref. 4.

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Starting from basic principles, we will in the following summarize the FEL methods developed so far, including ultrafast X-ray diffraction and crystallography for condensed state chemistry studies and applications to organic electronics,8–26 and for soft condensed matter and protein applications;33–35,39,46–62 ultrafast soft X-ray spectroscopy and ultrafast twodimensional (2D) X-ray spectroscopy for bimolecular reaction studies in the liquid phase;27–32,36–38 ultrafast X-ray scattering and ultrafast X-ray emission spectroscopy (XES) for the study of photo catalysis;40–45 and ultrafast photoelectron diffraction and Coulomb explosion schemes for the study of gas-phase reactions and the fundamentals of chemical reaction dynamics.63–74

15.2  T  he Concept: Filming Chemical Reactions in Real Time Utilizing Ultrafast High-flux X-ray Sources In a proof-of-principle experiment at the white beam beamline at The European Synchrotron Research Facility (ESRF) in 2001, it was demonstrated that high-flux, pulsed X-rays—created with synchrotrons of the third generation— can act as the “photons of choice” for studying the dynamics and kinetics of small chemical systems on their complex reaction landscape.1 These studies have been used to define various expectation values for time-resolved experiments at FELs and saddling the ground for ultrafast X-ray experiments at these sources. Since then, the phrase “recording the molecular movie” has been born (Figure 15.3).7

Figure 15.3  Principle  of the “molecular movie”. After the initiation of a chemi-

cal reaction with a pulsed trigger-laser, ultrafast X-ray snapshots and photographs of the X-ray pulses are collected as a function of time (courtesy of DESY, MPIbpC and EXFEL). For further reading, please see ref. 1.

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Figure 15.3 summarizes the principles of such a “molecular movie” approach: after the initialization of a chemical reaction with a short laser pulse, ultrafast X-ray FEL snapshots take photographs of the X-ray spectroscopic or X-ray diffraction signal. By varying the time delay between laser pump and X-ray probe pulse, information about the structural changes as a function of time are collected. Time-wise, the criterion for “recording the molecular movie” is given when the time resolution of the pump and probe sources meets the time scales of the structural dynamics investigated. The resolution criterion for structural dynamics studies is fulfilled in chemistry, when the refined structure allows for determination of the electron density or the charge densities (which are equal in the redox state) around a moving atom. High-resolution X-ray crystallography studies allow for the study towards such precision.8–26

15.3  C  rystallography with Ultra-high Temporal and Ultra-high Spatial Resolution Allows Study of the Photochemical Reactions Beyond Conventional Quantum Chemical Approaches Far beyond any present laboratory technique, time-resolved synchrotron (picosecond time resolution) and FEL (femtosecond time resolution) experiments8–25 emphasize the uniqueness of the pulsed, ultrafast, high brilliance and coherent X-ray methods and metrology. For chemical bond breaking and bond formation, the criterion for spatial resolution is met in periodic systems (crystallography) when 0.01 to 0.001 Å resolution diffractograms yield high precision structural information.10–12,16,17,20 Figure 15.4 reflects the changes of X-ray synchrotron beam characteristics when evolving from synchrotrons of the second generation towards hard X-ray FELs.8,9,13–15,18,21,22 The diffractograms have been collected on a molecular crystal of the same crystal quality and with the same orientation. Utilizing broadband wiggler radiation in second generation synchrotrons (F1/DORIS), Laue diffraction patterns have been collected. Taped undulator radiation of synchrotrons of the third generation yields quasi pink Laue diffractograms (ID09/ESRF). Compared to the pink Laue beam at the X-ray pump-probe (XPP), as well as the coherent X-ray imaging (CXI) beamline of LCLS, the FEL radiation is about one to two orders of magnitude smaller in bandwidth, allowing only the investigation of a statistical number of Bragg reflections for small molecular crystals when the crystal is rotated (Figure 15.5). Compared to the nanocrystallographic approaches also explained in this book, small molecular crystallography at fourth generation synchrotrons could be utilized by the combination of traditional Laue crystallography and FEL-specific serial crystallography techniques. Small molecule crystallography in a serial-type approach is possible based on a single shot data collection strategy analogous to the time-resolved Laue diffraction.

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In contrast to conventional Laue crystallography, for normalization purposes during FEL experiments, every diffractogram is associated to an online collected X-ray spectrum. Utilizing high X-ray energies well above 15 keV (use of the third harmonic and smaller X-ray/atom cross section) with no monochromatization in the pink Laue modus reduces radiation damage so that,

Figure 15.4  Evolution  of the average brilliance of synchrotron radiation light of synchrotrons from the second generation (DORIS) through ESRF and towards the LCLS FEL, characterized at the high-resolution diffraction pattern of the same molecular crystal system with same crystal quality. For further reading, please see ref. 12, 18 and 19.

Figure 15.5  Small  molecule crystallography at LCLS, XPP and CXI beamlines (test

phase). Left top: Three circle diffractometer. Inset shows organic crystals exposed to 9 keV X-ray radiation (single shot) inducing severe radiation damage, while the right image shows 18 keV (third harmonic) radiation allowing for the collection of various quasi Laue diffractograms with the pink Laue FEL beam under different orientations. Bottom: Small molecule crystals lined up for a three-shot-serial type of crystallography experiment.

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with a monotonically running spindle and randomly changing X-ray wavelength with known X-ray spectral characteristics, various orientations under defined X-ray conditions can be collected. They are sufficient for determining the orientation matrix of small molecules and hence following the indexing of the collected diffractograms. Since the studied materials are normally compounds of small amounts, highest quality crystals could be stacked behind each other in a capillary (or other type of sample target holder) and high energy X-ray radiation utilized to minimize accumulative radiation damage. Due to the monochromaticity of FEL X-ray beams even in pink Laue mode, quasi pink Laue diffraction pattern will be recorded for various orientations, allowing a precise determination of the orientation matrix of the small molecule crystals. Additionally, on a single shot base, the Bragg peak intensities are wavelength and X-ray intensity normalized. Figure 15.6 depicts the refined result of such an experiment: the femtosecond structural dynamics or “molecular movie” of a molecular crystal, which consists of only light elements (carbon, nitrogen and oxygen). The system type21 has the most efficient optical light/electron transfer rate possible (100%), by utilizing quantum effects such as electron and structural dynamics pathways, which cannot be described through the conventional Born–Oppenheimer approximation. Comparing the effects of electron transfer of this “beyond the Born– Oppenheimer” system with the mean free path and redox properties of semiconducting plastic host materials allowed the building of fully flexible solid-type solar cells. Rationalizing energy transfer properties of the derivatives of these compounds allowed for the construction of organic light-emitting diodes with very high efficiency (Figure 15.7).

15.4  Applications in Energy Research Since the time-resolved synchrotron and FEL X-ray “molecular movie” methods allow for detangling local effects from global structural responses, desired functional actions of a device, like energy storage, can be distinguished from

Figure 15.6  Molecular  movie of a non-conventional molecular diode, which

cannot be described within the Born–Oppenheimer approximation anymore. Within femtoseconds and very shortly after optical photo-absorption, electrons (t0) are rearranged towards a conducting state (t1) on the ultrafast time scale, meanwhile the structure knocks into a tilt configuration.

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“energy-eating” processes based on non-desired heating and energy quenching processes. In Figure 15.7, the performance of an optimized all-over organic solar cell is presented. Small atomic (even not molecular) changes on the lightabsorbing chromophore unit lead to a complete switch of its functional dynamics from a light-absorbing solar cell device20–26 to a light-emitting organic diode.21,22 In another example, the understanding of the crystallization processes of organic material out of time-resolved X-ray diffraction (TRXRD) studies has influenced the optimization of the recycling process of molten PET bottles to ultra-hard polyethylene.23 Such ultra-hard plastic material is currently used in every second wind craft machine produced world-wide. Utilizing the structural dynamics and kinetics of complex perovskite systems for solar cells with new functionality have been demonstrated in ref. 25 and 26. Furthermore, the current examples emphasize that functional materials, pharmaceuticals, catalysts or energy-converting materials in the real world are not always crystalline and far from being periodically ideally arranged, as it may look when performing model-type investigations. If the intrinsic spatial resolution of the system does not allow for such detailed investigations anymore (i.e., since the phases are disordered), a combination of ultrafast X-ray spectroscopy and ultrafast X-ray diffraction or scattering as the “local to global approach” delivers configuration and charge information of the molecules studied.27–38 This approach will be described in the following section.

Figure 15.7  Once  structural relaxation processes are understood, the derived structural and dynamical properties can be utilized to improve functional dynamics performance, allowing the development of new classes of organic solar cells [see the voltage–current (I–V) curve] and organic light-emitting diodes based in plastic (see inset). For further reading please see ref. 22 and 23.

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15.5  T  he “from Local to Global” Approach: Ultrafast X-ray Spectroscopy and Ultrafast X-ray Diffraction Shake Hands and Allow the Study of Complex and Bimolecular Reactions As in optical laser sciences, X-ray laser science allows the coupling of X-ray techniques coming from entirely complementary pools of methods. Now, the “local/global” approach becomes possible by combining ultrafast X-ray diffraction (with precisions down to electron density determination) with high energy resolution X-ray spectroscopy. In ultrafast X-ray spectroscopy, site-specific and element-specific electron properties are probed (such as bonding or oxidation state changes), called the local approach. In ultrafast X-ray diffraction or scattering, the structural changes of the whole bulk are probed, and therefore called the global approach. Both methods are technically demanding on their own: ultraprecise structure determination requires the use of very hard X-ray radiation (starting from 18 keV X-ray energy) and very high angular momentum collection, while X-ray spectroscopy with ultra-high energy resolution requires the highest spectrometer grating resolution or the implementation of 2D X-ray laser spectroscopy techniques, and all this on the ultrafast time scale. The local to global approach was first postulated for FELs in early 2005, when first FLASH FEL experiments with chemical systems became possible.14–16,19,26–36 The schematic idea is presented in Figure 15.8. On the left

Figure 15.8  The  local to global approach separated into an energy triangle (bottom). Top: Ultrafast optical spectroscopy and a timeline of the experimental realization (top, left side) in comparison to ultrafast X-ray science and its timeline of experimental realization (top, right side), consisting of ultrafast multidimensional X-ray spectroscopy and ultrafast X-ray scattering. For further reading, please see ref. 4, 28 and 31.

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side, the classical setup of a time-resolved photon-in/photon-out method in the optical energy regime, also called ultrafast transient optical spectroscopy, is shown. In the X-ray regime (right side), the combination of X-ray diffraction/scattering with ultrafast spectroscopy or multidimensional X-ray spectroscopy presents a pendant to the optical methods. In order to reach the desired temporal resolution, the optical laser pump initiates the reaction and the X-ray laser pulse probes the ultrafast chemical reaction by collecting the X-ray diffraction signal and/or the X-ray spectroscopic signal in the common photon-in/photon-out type of approach. In the diffraction experiment, the photographic camera (Figure 15.3) is a detector that collects the X-ray diffraction signal.29,31 In the spectroscopy experiment, a second camera is attached that collects the energy resolved X-ray spectroscopic signal in emission. An example of a 2D X-ray spectroscopy study of water carried out by such an experimental approach is referenced in ref. 29, 32 and 33. Figure 15.9 (left) shows the technical apparatus that has been developed in this “local/global” context. The modular built-up endstation is mostly used as a benchmark for the development of pioneering new X-ray experiments investigating chemical processes with FEL sources. One example is the proof of principle experiment in which the ultrafast X-ray diffraction of a silvercontaining redox system embedded in a supramolecular organic structure has been studied (Figure 15.9, middle). The experiment demonstrated that the local/ global approach can be used to detangle ultrafast real-time atomic motions of the active chemical reaction center from the ultrafast real-time atomic motions of the non-active chemical surrounding in a time-dependent way.

Figure 15.9  Left:  The X-ray photon endstation at the FEL FLASH and DESY for ultra-

fast X-ray diffraction. This setup was also used as the liquid jet (LJ) endstation for ultrafast X-ray spectroscopy at LCLS, the SXR beamline. The LJ endstation allows the study of chemical processes according to the “local/global approach”. The modular built-up endstation is used as a benchmark for the development of pioneering new X-ray experiments for investigating chemical processes with FEL sources. Middle: Static Bragg reflection collected with a single shot FEL pulse. Right: Ultrafast changes of Bragg peak intensities and corresponding disorder processes. For further reading, please see ref. 18, 21, 22, and 28.

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By investigating the time-evolution of the Bragg reflections (Figure 15.9, right) and analyzing their time dependence, complex photo-induced transformation kinetics of partially photo-chemically induced and heatpropagation-influenced reaction kinetics have been shown. How the ultrafast transformation propagates throughout the whole material (the black areas represent the non-transformed material and the white areas show the island of transformed material) is illustrated by the red decay curve in Figure 15.9. The experiment is an experimental proof that FEL radiation can be utilized for ultrafast X-ray diffraction as the “global approach” in chemical research of importance for energy research or the “molecular view” into the dynamics of bio-physicochemical and biophysical processes. In the next experiments,28–39 the endstation was redesigned by adding time-resolved multidimensional X-ray spectroscopy (RIXS) capabilities for experiments at the FEL LCLS in Stanford. Various duplicates have very recently been built at high flux X-ray facilities (besides LCLS, also at HZB and DESYFLASH). One example illustrating the power of ultrafast, multidimensional X-ray spectroscopy for chemistry is shown by the result of RIXS using FEL X-rays, in which the real-time investigation of solvent-assisted iron pentacarbonyl dissociation in ethanol was carried out. This experiment demonstrated that it is possible to investigate complex bimolecular reactions between two reaction partners on the real-time time scale of atomic movements. The electronic imprint of the bimolecularity of the reaction is emphasized in Figure 15.10, which gives a summary of the detailed data evaluation of the ethanol­ assisted iron pentacarbonyl photo-dissociation pathways. After the optical excitation of 267 nm photons (Figure 15.10, top), iron pentacarbonyl dissociates into iron tetracarbonyl and CO under solvent assistance.36,37 Details about the femtosecond time-resolved RIXS experiment can be found in ref. 31. RIXS spectroscopy38,39 allows the determination of electronic redistribution and reorganization processes during chemical reactions that are important for molecular catalysis research.30 The typical RIXS pattern of the reaction in the liquid phase (Figure 15.10, middle) at early time points can only be reproduced when a complex between the iron penta/tetracarbonyl and ethanol is taken into account. The reaction increases in complexity due to the formation and decay of the triplet states. Figure 15.10, bottom, shows the complexity of the reaction scheme and kinetics of this reaction on the ultrafast time scale.

15.6  U  ltrafast X-ray Studies of Solution Chemical Reactions Besides pump-probe techniques, which utilize a soft X-ray probe pulse, complementary methods using a hard X-ray probe pulse have already been proposed40–42 and developed, and many have been successfully applied in studies of photoexcited states of molecules in solution.43–45 Amongst others, those pump probe techniques include femtosecond time-resolved XES, which is sensitive to the local electronic structure (spin states, etc.) at the probed

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Figure 15.10  Experimentally  acquired time-resolved resonant inelastic X-ray scatter-

ing map of iron pentacarbonyl dissociation and kinetic fit model. (A) Pumped/non-pumped difference RIXS map, (B) kinetic rate model fits (solid lines) of experimental delay scans (black circles; the error bar length is one standard deviation to each side) with three photo-products E, T and L, or (C) with four photoproducts E, S, T and L. Experimental delay scans are from the regions shown in the difference RIXS map (labeled with numbers), including the refined relative photo-product population dynamics. For further reading, please see ref. 37.

(solvated) atoms and X-ray diffuse scattering (XDS), which gives additional information about the solvent response. Using intense FEL radiation in particular, these approaches have been used to follow the femtosecond excited-state dynamics of transition metal complexes, a class of compounds that is potentially interesting for technical applications. Pioneering femtosecond time-resolved XES experiments at LCLS successfully tracked the spin crossover dynamics of [Fe(2,2′-bipyridine)3]2+ in solution after its photo-induced

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metal-to-ligand charge transfer (MLCT) excitation and showed the critical role of intermediate spin states in the crossover mechanism.43 Analogue experiments on [Fe(CN)4(bpy)]2− demonstrated how excited state levels can be manipulated through ligand substitution, allowing enhancement of the MLCT lifetimes of such systems by orders of magnitude.44

15.7  Applications in Biophysics In biophysics, the ultrafast photon-in/photon-out developments utilizing high flux X-ray sources allow investigation of the properties of bio-relevant solvents46,56,58,59 and proteins46–49,55,57,60,61 during their structural reactions.46 The literature-referenced examples include various types of small molecules up to macromolecular model systems studied with FEL radiation. Furthermore, depending on the time scale of the system studied, it is possible to merge X-ray scattering techniques, like diffuse X-ray scattering, with pressure jump, temperature jump, electric field modulations and structural freezing methods or, on the chemical modulation side, with rapid mixing or photo-switching methods.62 Beyond the contributions summarized in this book, the combination of synchrotrons or FEL radiation with other techniques, such as electrospray ionization mass spectrometry,50,53 allows entirely novel experimental techniques to be derived for the investigation of macromolecules.53,54 For example, a mass spectrometric study of gas-phase ubiquitin at FLASH has revealed a fast local structural response, leading to small fragments with yields increasing linearly with photon intensity.63

15.8  U  ltrafast Imaging of Gas-Phase Chemical Reactions The advent of X-ray FELs enabled not only novel studies in the condensed phase, as described in the first parts of this chapter, but also brought forward unprecedented possibilities to study dynamical processes in the gas phase. Gas-phase FEL experiments allow the questioning of fundamental definitions in chemistry; for example, the investigation of processes beyond the Born–Oppenheimer approximation. The very short and very intense X-ray pulses made it possible, for the first time, to probe ultrafast photo-induced molecular dynamics by electron or ion momentum spectroscopy following multiple, element-specific inner-shell absorptions. These new fourth generation light sources also called for novel, dedicated instrumentation. To this end, different endstations have been developed, initially for use at the atomic, molecular and optical physics (AMO) beamline, which was the first beamline to become operational at the LCLS in 2009. Several of the early, pioneering experiments from 2009 to 2012 were performed at the AMO beamline in the CFEL-ASG MultiPurpose (CAMP) endstation66,67 (see Figure 15.11), which was developed within the Max Planck Advanced Study Group (ASG) at the Center for Free-Electron Laser Science (CFEL) in

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Figure 15.11  Photo  of the CAMP endstation66 at the AMO beamline at the LCLS in 2012. Since 2014, CAMP is a permanent endstation at FLASH/ BL1 at DESY in Hamburg. Various experimental techniques can be employed in the instrument, including novel time-resolved X-ray studies of chemical reactions in the gas phase. On the right side, CAMP’s double-sided velocity-map-imaging spectrometer is shown.

Hamburg. Experiments in this instrument range from X-ray imaging of biomolecules and nanocrystals to (time-resolved) ion and electron spectroscopy on atoms and small gas-phase molecules.68–72 Since 2014, CAMP is a permanent user endstation at FLASH/BL1 at DESY in Hamburg,73 and its successor, LAMP, has become operational at the AMO beamline at the LCLS.74 Moreover, the high-field physics (HFP) instrument has been developed at the LCLS,75 housing an ion momentum spectrometer and several electron timeof-flight spectrometers mounted at different angles. It also offers a pulsed, supersonic molecular beam, delivering gas-phase molecules to the interaction region. The example given in the following part,76 a UV-pump, X-rayprobe study of two complementary halomethane molecules with different photochemistry, has been conducted in the HFP instrument. Gas-phase FEL studies allow for fundamental studies of photochemical reactions. As an example, a UV-pump, X-ray-probe study of two complementary halomethane molecules with different photochemistry is shown. In Figure 15.12, the schematic potential energy curves (PECs) of iodomethane (CH3I) and fluoromethane (CH3F) are displayed, illustrating that the different halogen species give rise to qualitatively different PECs. One reason for this is the considerably different electronegativity of iodine and fluorine, stabilizing the C–F bond in contrast to the C–I bond. Upon absorption of one 267 nm UV photon, CH3I dissociates into two neutral fragments, CH3 + I; whereas, in CH3F, no PEC is resonantly accessible at this photon energy. In the latter case, absorption of at least three UV photons in the same molecule populates several higher-lying ionic PECs, resulting in dissociation of the molecules. After a tunable time delay, an intense X-ray pulse (727 eV, 1 mJ, approx. 40 fs) probes the dissociating system by predominantly ionizing the iodine (3d) or the fluorine (1s) level because of their large absorption cross sections (3.3 Mb for I and 0.4 Mb for F, compared to 0.1 Mb for CH3), resulting in

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Figure 15.12  Schematic  potential energy curves for iodomethane (left) and fluoro-

methane (right). Absorption of one 267 nm photon in CH3I leads to resonant population of a repulsive neutral state, whereas multi-photon UV absorption in CH3F populates several higher-lying ionic states. After a given time delay, these states are probed by Coulomb explosion following inner-shell ionization of the respective halogen atom by one or several X-ray photons, probing the transition from a molecule to isolated atoms. For further reading, please see ref. 76.

a localized positive charge on the halogen. At these very high X-ray intensities, a single molecule can absorb many photons, such that very highly charged ions up to I21+/F4+ and C4+ are created. As the charge is initially created locally at the halogen atom, the fact that highly charged carbon ions are also detected already shows that the charge rearranges rapidly within the molecule before or during the fragmentation. In Figure 15.13, the calculated electrostatic potentials of I6+ and CH3 are plotted for three different internuclear distances between the two fragments, together with the binding energy of the highest occupied orbital. In the intact molecule (a) the electrons are delocalized, but as the fragments move apart, the potential barrier rises until a certain critical distance (b), when it reaches the electron binding energy. Therefore, for larger distances (c), the electrons can classically be regarded as localized at one of the two fragments. It is this transition from a bound molecule to isolated atoms that is probed here by time-resolved ion spectroscopy. The delay-dependent time-of-flight peaks of selected ions of iodomethane and fluoromethane are shown in Figure 15.14. It is evident that the fragmentation patterns of the two molecules are qualitatively different. For iodine charge states ≥I4+, the appearance of low-energy ions at positive delays is clearly visible [channel 3 in Figure 15.14(a)]. These ions originate from the pump-probe process as indicated for iodomethane in Figure 15.12 and can be used to extract the critical internuclear distance up to which electron transfer from methyl to iodine is classically allowed for a given charge state. Signatures of long-distance intramolecular electron transfer have been observed for both CH3I and CH3F, and the reconstructed critical distances

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Figure 15.13  Calculated  Coulomb potentials formed by an I6+ atom and a neutral

methyl radical for (a) the equilibrium distance, (b) the critical distance (see text) and (c) for isolated atoms (in a classical picture). The dashed blue line indicates the energy of the electron in the highest occupied orbital. For further reading, please see ref. 76.

(up to 15 Å for I21+) are in good agreement with a classical over-the-barrier model. Two other channels can be seen in Figure 15.14 that correspond to the Coulomb explosion of intact molecules by only the FEL pulse (1) and to ionic dissociation induced by multi-photon UV absorption (2), as illustrated for fluoromethane in Figure 15.12, which also occurs with a lower probability in CH3I. The low-energy channel is absent in the fluorine ions. The existence of ultrafast, long-distance intramolecular electron transfer has very recently been shown to also occur upon ultra-intense, hard X-ray irradiation and in larger molecules,77 which has important implications for imaging applications, in particular imaging of heavy-atom containing biomolecules or nanocrystals.

15.9  Summary During the last decades, FEL research has turned from theoretical predictions and simulations of experimental possibilities into a fourth generation light source with a broad portfolio of experimental possibilities. After ruling

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(a) iodine 4+, (b) iodine 3+, (c) fluorine 2+ and (d) fluorine 3+. Different fragmentation channels are indicated by 1, 2 or 3 (see text). Additionally, in (c) and (d), calculated delay-dependent time-of-flight curves are overlaid with the data, corresponding to an asymptotic kinetic energy of 0.4 eV. Positive delays correspond to the UV pulse arriving before the X-ray pulse. For further reading, please see ref. 76.

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Figure 15.14  Time-of-flight  spectra as a function of the pump-probe delay for selected fragments of iodomethane and fluoromethane:

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out initial skepticism, unexpected and novel X-ray methods have been and are currently being developed that utilize the unique features of FEL radiation beyond possible techniques at synchrotron sources, which can, in a first approach, be distinguished from each other by the simple fact that these sources are not X-ray synchrotrons but simply lasers.

Acknowledgements The Helmholtz Society is thanked for the Helmholtz Recruitment Grant and the Helmholtz Young Investigator Program, Grants No. VH-NG-904 and VH-NG-1104. Moreover, we thank the DESY staff for their competent help in large scale facility technical and computer support. The Max Planck Society is acknowledged for continuous financial support. The workshops and the chemical facility of the MPIbpC is thanked for their competent help in chemical synthesis, analysis and technical design of the micro apparatus and computer support. We also acknowledge the Max Planck Society for funding the development of the CAMP instrument within the ASG at CFEL. The German Science Foundation DFG (projects B03 and B10 of the SFB755 “Nanoscale Photonic Imaging”, and projects B06 and C02 of the SFB 1073 “Atomic Scale Control of Energy Conversion”), the German Academic Scholarship Foundation, the German Academic Exchange Service DAAD, the Alexander von Humboldt Foundation AvH, the Fonts of the Chemical Industry FCI, the Aventis Foundation, the Volkswagen Foundation (K. K.: Peter Paul Ewald fellowship program VW-87008) and “Niedersachsen Vorab” through the Göttingen Research Campus Laboratory “AIMS” are thanked for financial support. Over the last decade, beamline staff of the Helmholtz Center Berlin (HZB) are thanked for experimental support and hospitality. Beamline staff of the European Synchrotron Radiation Facility (ID09, ID11, ESRF), the Advanced Photon Source (ID14, APS), the Swiss Light Source (cSAXS, SLS), the Stanford Synchrotron Radiation Facility (SPEAR, SSRL) and the Advanced Light Source (ALS) are thanked for experimental support and hospitality. In particular, staff and beamline scientists of the Free-Electron Laser in Hamburg (FLASH) at DESY/Hamburg, staff and beamline scientists of the Free-Electron Laser Linac Coheren Light Source LCLS (beamlines AMO, SXR, XPP and CXI) at SLAC, and staff and beamline scientists of the Free-Electron Laser SACLA at SPRING-8/Riken are deeply acknowledged for their support and hospitality. Use of the Linac Coherent Light Source (LCLS), SLAC National Accelerator Laboratory, is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC0276SF00515.

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Section V

Sample Delivery Methods

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Sample Delivery Methods: Liquids and Gases at FELs Daniel P. DePonte SLAC National Accelerator Laboratory, LCLS Sample Environment Dept., 2575 Sand Hill Rd, Menlo Park, CA, 94061, USA *E-mail: [email protected]

16.1 Introduction Some of the defining characteristics of a free electron laser (FEL) that distinguish it from synchrotrons are also those that set the basic requirements for sample delivery. While synchrotrons are pulsed sources, the short duration between pulses does not allow enough time for physical replacement of the sample, effectively making synchrotrons continuous sources for many types of experimental methods. This is not the case for FELs with pulse repetition rates that allow for the possibility of sample replacement even at the repetition rate of 4.5 MHz currently proposed for the European X-ray FEL (XFEL). Another important difference is that the high intensity of FELs also may permit useful data collection from a single pulse. A 1 mJ pulse at 9 keV contains 1012 photons, or about the same as that for an undulator at a third generation light source over the course of 1 s. In a focused FEL beam, this results in a high enough intensity to have a measurable effect on the sample or, in many cases, completely destroy it. For these reasons and others, liquids and gases are often used for sample delivery at FELs. Fluid flows can be either the sample itself or act as sample   Energy and Environment Series No. 18 X-Ray Free Electron Lasers: Applications in Materials, Chemistry and Biology Edited by Uwe Bergmann, Vittal K. Yachandra and Junko Yano © The Royal Society of Chemistry 2017 Published by the Royal Society of Chemistry, www.rsc.org

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carriers. Examples of the latter case may be protein crystals or polymer flows in liquids or virus capsids in gas streams. The exact carrier used depends on signal to noise considerations and on sample compatibility. Highly viscous jets or extrusions can be used as slow moving targets for some crystalline samples, which can produce Bragg peaks measurable over the background. Thinner recirculating sheet and round jet systems are often used for pumpprobe experiments where the liquid itself is the sample. Yet thinner jets can be produced by accelerating liquid jets with an electric field or co-flowing fluid. In the case of single particle imaging, even the thinnest liquid jets may produce an intolerable background and gas carriers are preferred. If the gas itself should be the target, pulsed sources, cluster sources, fixed cell and recirculating flows have all been used for various applications.

16.2 Methods Overview 16.2.1 Liquid Jets Liquid jets are a straightforward way of replacing sample rapidly and with high accuracy. Any tube can be used as a liquid jet nozzle given a few  constraints. One of these constraints is a lower limit on liquid speed, or equivalently, liquid flow rate, imposed by the requirement that the Weber number (We) must be greater than some critical number.1    



v  We /  r

(16.1)



Q  π We r 3 / 

(16.2)

   

   

In eqn (16.1) and (16.2), v, Q, σ, ρ and r are, respectively, the speed, flow rate, surface tension, fluid density and jet radius. For the range of jet diameters and viscosities that are commonly used at the Linac Coherent Light Source (LCLS), the critical Weber number1 is between two and three. Table 16.1 shows a selection of calculated values for speed and flow rate. The nozzles themselves can be made by flame polishing a section of borosilicate tube to reduce the diameter to the desired size or, more commonly, they are simply a straight section of commercially available tubing. Glass, polymer or other nozzle materials can be used depending on compatibility with the sample, as well as preferred background characteristics. X-Ray scattering from Table 16.1 Calculated minimum flow rates and pressures needed to produce water jets from a 1 cm long tube.

Tube diameter (µm)

Pressure (kPa)

Minimum flow rate   (mL min−1)

Speed (m s−1)

20 50 100 500

3100 320 60 1.2

72 300 880 11 000

3.8 2.5 1.9 0.91

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glass, for example, will produce a diffuse background, whereas crystalline polyetheretherketone (PEEK) diffracts X-rays into Bragg peaks, which may be preferable depending on the experiment. For smaller nozzles, the tube outlet may be polished with 3 µm lapping paper to improve stability of the jet. The pressure necessary to produce a jet adds additional physical constraints. The minimum pressure needed for jetting can be calculated from Poiseuille’s law, if one knows the minimum flow rate, tube diameter, tube length L and the liquid viscosity µ.    



P  8 L We / r 5 

(16.3)

   

To limit pressure to within the range of commercially available pumps, small diameter tubing used as the nozzle is kept as short as possible and is fed by longer lengths of larger diameter tube. A nozzle length of 1 to 2 cm is needed to make the physical connection to high pressure fittings. While lower operating pressure is possible for converging-type nozzles due to the length of the exit section, L in eqn (16.3), straight-tube nozzles have had less problems with clogging. Larger (100 µm) diameter nozzles may be in the range of peristaltic pumps, but smaller (20 µm) nozzles require high-pressure pumps such as the solvent delivery units used with high-performance liquid chromatography (HPLC) systems. Both cylindrical jets and sheet jets are part of LCLS’s standard configuration for ambient pressure operation at hard X-ray beamlines. Cylindrical jet diameters between 20 µm and 500 µm, and sheets from 20 µm to 250 µm thickness are offered in liquid recirculating systems. The standard configuration sizes were chosen for convenience based on the availability of commercially available tube and sheet stock. Sheet nozzles are rectangular aperture nozzles made with an appropriately shaped channel in a thin film of polymer or metal clamped between two microscope slides, as shown in Figure 16.1. The thickness of the liquid sheet is approximately the thickness of the film used and the width of the sheet is given by the size of the channel cut into the film. The minimum reliable thickness for sheets and round jets produced by these simple hard-walled nozzles is about 20 µm; smaller nozzles are more prone to clogging. While these sizes are often ideal for hard X-ray spectroscopies, other uses, for example, soft X-ray studies, transmission mode experiments and scattering from suspensions, can benefit from thinner targets and so smaller jets are made by alternative methods. In order to reduce the thickness of a free liquid stream, the liquid must be accelerated. One way to do this is with an electric field. A little over a century ago, the then well-known phenomenon of liquid jet formation from a charged liquid surface was photographed2,3 and initial attempts were made to model the liquid breakup. An electric field will draw a liquid surface into a Taylor cone, named after G. I. Taylor, the first to correctly provide a mathematical description,4 and will produce a cylindrical jet or spray. These electrically driven flows, also known as electrospinning, can have jet diameters under a micron and flow rates under 1 µL min−1. By adding a cryoprotectant

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Figure 16.1 A sheet jet is made from a straight rectangular channel nozzle. The

exit aperture dimensions are 13 µm by 1.5 mm wide. The liquid sheet has approximately the same dimensions as the channel near the exit orifice then quickly collapses downstream. The nozzle is made from a patterned polyimide sheet clamped between two glass microscope slides.

to a crystal slurry, an electrospun jet has been used in vacuum for sample delivery at LCLS5 with flow rates typically at a few microliters per minute depending on the sample viscosity, feed tube diameter, accelerating voltage and reservoir pressure. Gas accelerated jets are another way to reduce jet diameter. By accelerating a liquid jet with a coaxially flowing gas stream,6 the jet diameter can be reduced to a few hundred nanometers7 and flow rates of a few hundred nanoliters per minute for water and alcohols. If the gas stream is not coaxial but rather impinges on a cylindrical jet from opposite sides, the jet flattens out into a sheet. Starting with a 20 µm cylindrical jet, we routinely produce water sheets 100 nm thick and a few hundred microns wide.8 An example is shown in Figure 16.2. Gas accelerated jets produced by nozzles known as either gas-dynamic virtual nozzles9 or flow focusing nozzles are used with both in-air and vacuum sample environments at LCLS. When operated in vacuum, the necessary distance of the breakup region from the nozzle exit determines the minimum flow. Ideally the X-ray focus should be in the continuous jet rather than further downstream in the droplet region to maximize the rate of data collection. Furthermore, if the breakup region is too close to the nozzle exit, debris

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Figure 16.2 A series of sheet jets is formed from by collision of two gas jets upon

a liquid jet. The first leaf-shaped sheet is approximately 100 nm thick and 200 µm across. The liquid flow rate is 250 µL min−1 and the mass flow rate of the accelerating gas, helium, is 0.7 g h−1. The nozzle is a glass microfluidic chip made by the common hard lithography method.

builds up on the nozzle exit, or X-ray scattering from the nozzle becomes problematic. To keep the breakup region far enough from the nozzle exit, 10 µL min−1 has proven to be a comfortable flow rate. The distance to breakup can be extended and by using an additional fluid, two coaxial liquids may be accelerated by a gas.6,10 Recent unpublished work by the Chapman group at the Center for Free-Electron Laser Science (CFEL) used an alcohol sheath around the sample in a configuration commonly known as flow focusing. When used with an X-ray focus smaller than the central sample jet, this can reduce sample consumption to approximately 1 µL min−1 without significantly reducing the data collection rate. Flow focusing can also be used for electrostatically accelerated jets and has shown similar flow rates11 as those used for gas accelerated jets. As an additional use of such jets, diffusive mixing can occur on time scales longer than the transit time of the liquid from nozzle to X-ray interaction point. For example, a jet moving at 10 m s−1 would require 10 µs to travel the 100 µm distance to the interaction region. The high speed of liquid jets allows the sample to be rapidly replaced. At the current LCLS repetition rate of 120 Hz, the sample is in fact replaced too

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rapidly, with the majority of the sample passing through the interaction region between shots. A 20 µm water jet has a minimum jetting speed of about 5 m s−1 implying approximately 10 nL of sample passes through the interaction region between shots. A few different ways have been developed to reduce sample loss; the easiest, when applicable, is simply to recirculate the sample. Recirculating jets are commonly used at the LCLS in a helium tent or ambient air. Recirculation is restricted to higher flow rate methods where evaporative loss is tolerable. A recirculating system consists of a pump, nozzle, catcher and dampener. Peristaltic or piston-type high-pressure solvent delivery units can be used depending on the pressures and flow rates needed. Both pumps have shown an unacceptable level of pulsation for some applications, thus requiring a dampening device. We use a 1 mL to 3 mL reservoir between the pump and reservoir. As the reservoir fills, the trapped air inside the reservoir acts to dampen the oscillations. The return line to the pump must be of large diameter and so another milliliter of swept volume is in the pump and lines. The amount of sample then required to operate a recirculating 20 µm jet is around 5 mL. Another method of reducing sample consumption is to increase the  viscosity of the sample, dampening out the growth rate of high frequency surface disturbances and allowing for a more slowly moving jet. The benefits of reduced sample consumption must be balanced against the X-ray scatter from the viscous material and sample compatibility. A high-viscosity, high-pressure injector will be described further in chapter 17. Yet another way to reduce sample consumption is to run the sample injector in pulsed mode. Inkjet printers operate in either the continuous mode described above or in a drop on demand (DOD) mode where single drops are ejected from a nozzle due to a pulse generated thermally or by a piezoelectric device. Droplet generation from a free liquid surface will be described in chapter 18. Drop sizes generated from a piezo-driven DOD printhead range from 20 to 140 µm diameter, with the most reliable range between 40 and 60 µm.12 A 40 µm drop has a volume of 30 pL, which implies sample usage of 200 nL min−1 when operated at 120 Hz. By comparison, a 40 µm diameter continuous jet runs at about 200 µL min−1. Droplet ejection from a printhead may drag along a thin thread of fluid behind the main drop. After detachment, this thread breaks up into smaller drops whose trajectories are not as easy to control as that of the main drop. While these fine threads are seen merely as an annoyance to the high-speed printing industry, they may serve a purpose at pulsed light sources as thin liquid targets. As with continuous jets, the X-ray path through the liquid drop may be too long for some applications, however, as the fluid behind the drop may be stretched to a few microns in thickness. Figure 16.3 shows a 7 µm diameter tail trailing behind a liquid drop containing lysozyme crystals of average size of 2 µm in water. The nozzle was operated at 120 Hz in air at the LCLS X-ray pump-probe (XPP) station. A small amount of polyethylene glycol was added to lengthen the tail. Using the tail behind the drop also made timing much easier than shooting single drops.

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It is likely that most, if not all of the previously described liquid injectors, with the possible exception of piezo-driven devices, can be mass-produced by existing microfluidic chip fabrication methods. Gas accelerated nozzles have already been produced from polydimethylsiloxane13 and hard lithography.8 Figure 16.4 shows an example of a gas accelerated jet produced from a glass microfluidic chip. Using microfluidic chips as sample injectors opens the door to all that the microfluidics community has developed: fast mixing,

Figure 16.3 A piezo-driven DOD device operating at 120 Hz with stroboscopic

illumination is shown. Lysozyme crystals of average size 2 µm can be seen flowing through the nozzle. A long thin tail of 7 µm thickness is stretched out behind the primary drop and serves as the target.

Figure 16.4 A cylindrical gas accelerated water jet can be seen exiting from a microfluidic chip. The chip seen protruding from a clamp connector is 800 µm thick and 4 mm wide. Similar versions have flow-focusing or mixing channels added to the chip.

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sorting, microencapsulation, etc. Flow focusing in microfluidic channels is now routine to the point of being commercially available from many microfluidic manufacturers, as are the addition of on-chip peristaltic pumps,  mixers, check valves and electrical contacts.

16.2.2 Gas Phase Jets Similar to liquid sample delivery, gas phase sample delivery is a rapid, reliable method of replacing sample in the interaction region between FEL pulses. Atoms and molecules can be studied in the gas phase without the scattered background or the interaction of neighbouring molecules that arise in liquid studies. As with liquids, the production of free jets of atoms, molecules and clusters is relatively straightforward and well understood. Free atomic and molecular jets can produce large speed ratios, which are useful, for example, in experiments where molecular alignment is attempted. Continuous, high-speed ratio jets have the disadvantage of high gas loads, requiring multiple differential pumping sections. Free gas jets can produce high gas density only within the immediate vicinity of the nozzle; beyond a few nozzle diameters, the gas density drops off as the inverse square distance from the nozzle. While micronozzles can produce high gas density, the trade-off to low expansion strength is the low speed ratio and low centreline intensity. As with liquid jets, pulsed gas jets can be used to reduce gas load and therefore pumping requirements to within the range of turbomolecular pumps. The Atomic, Molecular and Optical (AMO) endstation at LCLS routinely employs an Even–Lavie14 valve that can operate within the main chamber. Without the need for skimmers, the distance between the source and interaction region can be greatly reduced. When a larger number of molecules or atoms are needed in the X-ray path, gas cells can be used. Rohringer et al.15 have used a 1.4 cm long, 500 Torr gas cell, with differentially pumped entrance and exit apertures in the AMO endstation. A similar setup has been used at the coherent X-ray imaging (CXI) and XPP endstations by Minitti et al.16 In this case, the gas pressure was lower (10 Torr) due to the low vapour pressure of the samples. As a result of the lower pressures, differential pumping around the 250 µm exit apertures was not required. The continuous flow of gases, as with liquids, causes sample loss between X-ray pulses, and therefore recirculating gas jets can reduce sample consumption; introductory material can be found in the text by Pauly.17 In recent, unpublished work at LCLS by Ilchen, Moeller and others, a recirculation system was used composed of two gas reservoirs. As one reservoir is used to supply the nozzle, the other is refilled from the exhaust gas of the pumping system. By necessity, only oil free pumps are used at FELs; this has an unintended benefit to sample delivery in that gases can be recirculated from the pump exhaust without oil contamination. Larger particles, up to the size of large viruses, can also be delivered by gas flows. Single aperture converging nozzles and multiple aperture aerodynamic lens stacks18,19 have been used at FELs. These injectors can produce

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20,21

similar particle focus of about 10 µm with the lens stack providing a lower particle velocity of 10 m s−1 to 40 m s−1 for an aerodynamic lens20,22 compared to 250 m s−1 for a converging nozzle.21 The focusing of heavy, virus-sized particles by single aperture injectors is thought to be primarily due to the geometry of the converging nozzle.21 The focusing of a heavier gas by a lighter gas is also possible in binary mixtures; the focusing can be further enhanced by using a sheath gas to focus17 similar to that used in liquid accelerated jets.

16.3 Automation Unlike synchrotrons, LCLS currently runs one endstation at a time with a small but growing number of multiplexing experiments. Experiments must be run efficiently to make good use of scarce beamtime, making automation desirable for many repeated tasks.

16.3.1 Sample Handling We have constructed a sample delivery system to automate some gas and liquid sample handling tasks. The system is configurable, consisting of a master controller communicating to EPICS using Modbus TCP and EtherCAT to connect to various sample deliver components. Among these are sample selector boxes, flow meters, high-pressure pumps, peristaltic pumps, stepper motor controlled gas regulators, solenoid controlled gas regulators, sample shakers and temperature controllers. The main component of the system is a sample selector, which allows for the remote selection of up to 12 different fluids. Additional selector boxes can be added in parallel as needed. The selector box consists of two 12-port selector valves, which simultaneously select and pressurize a sample reservoir. The reservoirs have removable steel liners that seal by compression against either a commercially available frit from IDEX or with a PEEK washer. A PTFE plug separates the sample from pressurized water used to drive the sample flow. Viton O-rings were originally used in the sample reservoirs but would occasionally shed and clog the injectors. The internal volume of the selector and internal plumbing is approximately 2.4 µL depending on the port chosen, with 0.9 µL of dead volume and the rest swept. The lowest pressure rating for any component is that of the tube connectors, 28 MPa. Reservoirs are available with internal volume 1 mL, 3 mL or 5 mL with a dead volume between 9.9 and 1.3 µL depending on the frit or seal chosen. While LCLS staff are always present to operate the beamline controls, the sample delivery system was intended to be operated by the users. It has a simple graphical user interface (GUI) that depicts each component in the state configured, which has gone through several iterations, guided by user feedback. The entire sample delivery system is portable, may be deployed in any LCLS hutch and used with multiple injector types, all operated through the same GUI.

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16.3.2 Injector Automation There is a small but important set of experiments for which the injector itself must be periodically replaced during operations. The previous section described an automated sample handling system that moves the sample from the reservoir to the injector. Automation of injector replacement can also be beneficial. It is occasionally necessary to exchange injector types, exchange nozzles for other tools or exchange nonworking injectors. When operated in vacuum it is often the case that each X-ray pulse can disrupt the jet to the point where some debris can build up on the nozzle eventually causing it to malfunction. Two nozzle changers have been developed by CFEL in Hamburg for their serial femtosecond crystallography work. The first generation consists of a cartridge containing six nozzles on spring-loaded slides. A nozzle was moved into position by translational stages and then the slide was depressed to move the nozzle a suitable distance from the interaction region. Each nozzle required two feed lines, one for liquid and one for the accelerating gas—12 fluid lines in all had to be fed through the chamber wall. The cartridges were assembled ahead of time with all lines in a single flange so that the cartridge and connections could be installed as a single unit. The exchange time for a single nozzle was reduced to 3 to 4 minutes from its manual replacement time of 20 minutes. A second generation nozzle changer described elsewhere23 and also built by CFEL was constructed with an in-vacuum goniometer used to position and orient nozzles. Nozzle exchange can occur from a nozzle rack in the sample chamber or through a load-lock. Although presently only used for ambient air experiments, DOD devices are already at a fairly high level of automation. Spotting systems that dispense fluids into patterned arrays from either piezo-driven tube injectors or free liquid surfaces can be easily adapted for sample injection at an FEL. Injector changing, sample loading, nozzle decontamination and sample resuspension are presently all possible with commercially available devices. The upper limit on repetition rate, from a few kHz to perhaps 10 kHz for some fluids, limits applicability to lower repetition rate sources, but if high throughput screening of samples is desired, robotic DOD systems may become an invaluable tool.

16.4 Summary Gases and liquids are useful means of sample delivery at FELs, where the ability to rapidly and accurately replace samples is crucial. Similarities exist for both gas and liquid injection; both can be run continuously or as pulsed sources, either can be recirculated with some restrictions, either can be focused by a sheath fluid, and both can serve as either the sample or as a carrier for the sample. Despite the similarities, integration of gas phase delivery at FELs started at a much more mature stage of development than did liquid phase. Atomic and molecular beam production had for many decades been

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a productive field in itself, with some commercially available equipment predating FELs. Liquid injection required considerably more effort to adapt to the needs of FELs, with the majority of injector hardware made specifically for use at FELs and often on a case-by-case need. As the dust settles and standard techniques emerge, the move to mass-produced microfluidic devices and a high degree of automation is inevitable. This is not to imply that additional methods of sample delivery development are unneeded. For example, when acting as a sample carrier, fluid delivery of samples has, to date, suffered from inefficient use of beamtime due to the random arrival time of sample to the interaction region. To fully utilize the FEL output, additional timing or sample manipulation methods must be developed.

Acknowledgements I would like to acknowledge J. Koralek, M. Minitti and R. Sierra for useful discussions. Portions of this research were carried out at the Linac Coherent Light Source (LCLS) at the SLAC National Accelerator Laboratory. LCLS is an Office of Science User Facility operated for the US Department of Energy Office of Science by Stanford University.

References 1. S. J. Leib and M. E. Goldstein, Phys. Fluids, 1986, 29, 952–954. 2. J. Zeleny, Proc. Cambridge Philos. Soc., 1915, 18, 71–83. 3. J. Zeleny, Phys. Rev., 1917, 10, 1–6. 4. G. Taylor, Proc. R. Soc. London, Ser. A, 1964, 280, 383–397. 5. R. G. Sierra, H. Laksmono and J. Kern, et al., Acta Crystallogr., Sect. D: Biol. Crystallogr., 2012, 68, 1584–1587. 6. A. M. Gañán-Calvo, Phys. Rev. Lett., 1998, 80, 285–288. 7. D. P. Deponte, J. T. McKeown, U. Weierstall, R. B. Doak and J. C. H. Spence, Ultramicroscopy, 2011, 111, 824–827. 8. D. P. DePonte, J. D. Koralek, P. O. Mgbam and P. Bruza, Microtas 2015 Conference Proceedings, 2015, pp. 2095–2096. 9. D. P. DePonte, U. Weierstall and K. Schmidt, et al., J. Phys. D: Appl. Phys., 2008, 41, 285–288. 10. D. J. Wang, U. Weierstall, L. Pollack and J. Spence, J. Synchrotron Radiat., 2014, 21, 1364–1366. 11. R. G. Sierra, C. Gati and H. Laksmono, et al., Nat. Methods, 2016, 13, 59–62. 12. Personal Communication, Microfab Technologies Inc. and Scienion AG edn. 13. M. Trebbin, K. Kruger, D. P. DePonte, S. V. Roth, H. N. Chapman and  S. Forster, Lab Chip, 2014, 14, 1733–1745. 14. U. Even, EPJ Tech. Instrum., 2015, 2, 1–22. 15. N. Rohringer, D. Ryan and R. A. London, et al., Nature, 2012, 481, 488–491.

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16. M. P. Minitti, J. M. Budarz and A. Kirrander, et al., Phys. Rev. Lett., 2015, 114, 1–5. 17. H. Pauly, Atom, Molecule, and Cluster Beams I, Springer-Verlag, Berlin, 2000. 18. M. J. Bogan, W. H. Benner and S. Boutet, et al., Nano Lett., 2008, 8, 310–316. 19. P. Liu, P. J. Ziemann, D. B. Kittelson and P. H. McMurry, Aerosol Sci. Technol., 1995, 22, 314–324. 20. M. F. Hantke, D. Hasse and R. N. C. Maia Filipe, et al., Nat. Photonics, 2014, 8, 943–949. 21. R. A. Kirian, S. Awel and N. Eckerskorn, et al., Struct. Dyn., 2015, 2, 041717. 22. G. van der Schot, M. Svenda and F. Maia, et al., Nat. Commun., 2015, 6, 1–9. 23. L. M. G. Chavas, L. Gumprecht and H. N. Chapman, Struct. Dyn., 2015, 2, 041709.

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Chapter 17

High Viscosity Microstream Sample Delivery for Serial Femtosecond Crystallography Uwe Weierstall Arizona State University, Department of Physics, Tempe, AZ 85287, USA *E-mail: [email protected]

17.1  Introduction Serial femtosecond crystallography (SFX) has the potential to be a transformative innovation in structural biology. In SFX, micron or submicron sized protein crystals are hit by a high intensity X-ray laser pulse from an X-ray free electron laser (XFEL) and a diffraction pattern is recorded from each microcrystal. If the X-ray pulse is shorter than the relevant time scales for damage processes, then the pulse passes through the crystal before damage is caused and diffraction is recorded from a damage-free sample, even though the crystal is destroyed after the pulse. Many thousands of patterns from microcrystals with different sizes and random orientation are recorded in a serial fashion. Different data evaluation methods are now available to deal with these “still” diffraction patterns and reconstruct the structure factors. Since every crystal is destroyed by the X-ray pulse, the crystals have to be replenished with the repetition rate of the XFEL, which is 120 Hz at the Linac Coherent Light source (LCLS) and up to 1 MHz at future light sources. The requirements for an ideal SFX sample delivery method are: (1) crystals   Energy and Environment Series No. 18 X-Ray Free Electron Lasers: Applications in Materials, Chemistry and Biology Edited by Uwe Bergmann, Vittal K. Yachandra and Junko Yano © The Royal Society of Chemistry 2017 Published by the Royal Society of Chemistry, www.rsc.org

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have to be delivered at room temperature in solution with minimal background scattering from the solution, (2) crystals have to be replenished at the rate of the XFEL pulses, (3) every pulse should hit a crystal (100% hit rate), (4) delivery into vacuum for minimal background scattering or in a helium atmosphere, (5) no sample waste, every crystal should be hit, (6) no damage due to the injection process (e.g., no excessive shear forces, charging etc.), and (7) reliable operation without intervention for many hours. Most of these requirements can be fulfilled by delivering the microcrystals to the XFEL in a liquid stream.

17.2  Crystal Delivery in a Liquid Stream 17.2.1  Low Viscosity Liquid Streams A liquid pressurized through an orifice will emerge as a continuous liquid jet, which subsequently breaks up into a single file beam of droplets to minimize the free surface energy.1 The diameter of the liquid jet is equal to the orifice diameter and the droplet diameter is larger by a factor of about two.2 If a liquid jet is used for microcrystal delivery to the XFEL, it is usually positioned so that the X-ray beam intersects the liquid jet before it breaks up into droplets. The jet diameter should ideally be comparable to the X-ray beam diameter so that background scattering from the liquid is minimized and sample use is maximized. At the LCLS, the X-ray beam size at the sample is 1 µm and 100 nm at the coherent X-ray imaging (CXI) beamline, and 0.7 µm at the macromolecular femtosecond crystallography (MFX) beamline. An orifice of 1–10 µm in diameter will clog instantly if used to generate a liquid jet with protein crystal slurries. Therefore, in the first SFX experiment at the LCLS, a liquid jet was generated with a gas dynamic virtual nozzle (GDVN),3 which uses a focussing gas sheath as a “virtual” aperture, and thereby avoids clogging problems, which plague Rayleigh jet injection nozzles. A GDVN contains a fused silica capillary with a 30–100 µm inner diameter, which supplies the liquid and is tapered at the distal end. This sample capillary is axially centered inside a second larger glass capillary (Figure 17.1), which is melted at the end to provide an aperture of about 50 µm diameter, through which the coaxial gas flow exits. The sheath gas accelerates the liquid stream, and shear and pressure forces reduce the diameter of the liquid jet from initially 50 µm by a factor of about 10 and accelerate the liquid to speeds of about 10 m s−1. Melting the gas aperture to exactly the right shape and size is a difficult process, and axial alignment of the two capillaries is critical for reliable generation of a liquid jet. Therefore a micro-fabrication method has been applied for three-dimensional (3D) printing of nozzle tips, which uses a two-photon polymerization process and enables 3D printing of microstructures with a resolution well beyond other high-resolution 3D printing technologies.4 For time resolved nanocrystallography, a modified GDVN has been developed to study chemical processes, such as a substrate–enzyme interaction, or protein folding or unfolding, where the rapid mixing of two solutions initiates a reaction.5

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Figure 17.1  Left:  Bright field image of a GDVN nozzle. The nozzle has been

immersed in an index matching liquid for distortion free imaging of the round glass capillaries. The inner liquid supply line (360 µm outer diameter, 50 µm inner diameter) has a ground cone at the distal end. The outer glass tube is flame polished at the end to form a ∼50 µm diameter aperture. The liquid line is centered in the outer gas line by two laser cut Kapton spacers. Right: In operation, co-flowing gas accelerates and focusses the liquid stream and reduces its diameter by a factor of 10–15. The X-ray laser hits the liquid stream about 100 µm downstream of the nozzle end (red arrow), before the jet breaks up into droplets. The end of the nozzle has been bevelled to prevent shadowing of high angle scattering.

The sample flow rate with a GDVN is typically 10 µL min−1, which is already much reduced compared to a conventional Rayleigh jet without gas focussing, but the flow rate is not optimized for the repetition rates of currently existing XFELs (120 Hz at LCLS and 60 Hz at SACLA). Therefore, most of the sample is wasted in between pulses and, although this problem will be reduced with future high repetition rate superconducting XFELs like the European XFEL or LCLS II, strategies are needed to reduce sample waste at current XFELs. Several strategies have been explored by different groups, e.g., a concentric flow electrokinetic design,6 goniometer based sample delivery with high density sample grids7 and other fixed target approaches,8,9 and drop-on-demand sample injection systems.10 Described here is the high viscosity microstream sample delivery method, which allows for greatly reduced sample consumption.

17.2.2  High Viscosity Injector In order to reduce sample consumption when using an X-ray pulse repetition rate of 120 Hz, the speed of the liquid jet has to be reduced from 10 m s−1 to a few millimeters per second, and the jet diameter (and crystal size) has to be reduced, ideally to the size of the X-ray probe. Smaller submicron jet diameters have been achieved with great difficulty using GDVNs, but at the expense of increased jet velocity. Double focussing of the inner jet with an outer liquid and gas can, in principle, result in a reduced jet diameter without undue

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11

velocity increase. A substantial reduction in flow speed and flow rate can be achieved using a much higher viscosity carrier medium for the protein crystals, although at the cost of an increase in stream diameter. Lipidic cubic phase (LCP) is one such medium; it is a membrane-mimetic material that supports crystal growth of membrane proteins and has a dynamic viscosity of ∼48.3 Pa s.12 The high viscosity also prevents crystal settling due to gravity, which is a problem for the GDVN injector and requires an antisettling device, which slowly rotates the sample reservoir. In order to extrude LCP as a several tenths of a micrometer-sized free stream into the vacuum, a new injector was developed that can generate the necessary pressure. Figure 17.2 shows a photo and computer-aided drafting (CAD) of the injector. The injector consists of a hydraulic stage, sample reservoir and nozzle (Figure 17.2). The sample reservoir is filled with the high viscosity matrix containing the microcrystals. Different sample reservoir sizes are available with capacities of 25, 40 and 120 µL, the two larger sizes have a larger bore. When changing the reservoir from 25 to 40 µL, a larger diameter piston has to be used, whereas the 120 µL reservoir requires a change of hydraulic stage and piston, since the reservoir is longer. The piston in the hydraulic stage

Figure 17.2  Top:  LCP injector. Bottom: Cross-sectional view of the LCP injector.

At the CXI beamline at the LCLS, the injector is attached to the end of a hollow insertion rod, which allows alignment of the injector relative to the X-ray beam. The gas line (green) is connected to the nozzle assembly via a push-to-connect fitting (on the left) and is routed back into the insertion rod at the LCLS via an angled HPLC fitting at the left end of the injector. This part is not needed if the injector is operated at ambient pressure and can be removed.

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has a different diameter on both sides: on the water side, the diameter is 8 mm, whereas on the sample side, the diameter is 1.372 mm (2.134 mm for the larger reservoirs). Therefore, the pressure is amplified by the ratio of the areas, which for the small reservoir results in a pressure amplification by a factor of 34 (14 for the larger bore reservoirs). On the sample side, the piston moves a Teflon ball, which is pressed into the bore of the sample reservoir. The bore diameter is slightly smaller than the diameter of the Teflon ball, which results in a cylindrical deformation of the ball inside the bore and a tight seal against leakage at pressures of up to 10 000 psi. From the sample reservoir, the sample passes through a fused silica capillary with an inner diameter of 20–75 µm and is extruded into vacuum or ambient pressure. The capillary is kept as short as possible (about 60 mm) to reduce the pressure necessary to extrude the sample. The tapered end of the capillary is inserted into a custom-made ceramic nozzle tube. In contrast to the GDVN nozzles, however, the conical end of the sample capillary protrudes out of the ceramic nozzle tube (Figure 17.3b), which has a square inner cross section and aperture, and sheath gas can flow through the open corners. Alternatively, square glass tubing can be melted at the end and used instead (Figure 17.3a), but the ceramic nozzles have a reproducible symmetric shape, which is superior to the melted glass nozzles, and they are additionally more robust. Therefore, ceramic micro-injection molding is now used to routinely mass-produce high precision nozzles. These nozzles are similar to the ones presented by Beyerlein,13 but the inner cross section is square and ends in a four-sided pyramid, which keeps the inserted

Figure 17.3  LCP  nozzle. (a) the cone at the distal end of the sample capillary (outer

diameter: 360 µm, inner diameter: 50 µm) is inserted into a square glass tube, which is melted at the end to form an aperture. (b) Here, the melted square glass tube is replaced by a ceramic micro-injection molded outer tube. The sample capillary is sticking out of the ceramic tube. The outer diameter of the ceramic is 1.13 mm and it has a square inner cross section. The ceramic used is aluminum oxide, which is rendered translucent after thermal treatment. In both cases, sheath gas passes through the gaps between the inner capillary and the outer tube to center the sample stream. The glass melting process is not very reproducible, whereas the ceramic nozzles are all identical and less fragile. (c) CAD of a ceramic nozzle tube with fused silica capillary (yellow) inserted. The ceramic nozzle is round on the outside with a diameter of 1.13 mm and has a square inner cross section, which is slightly expanding away from the nozzle tip. The inner walls form a four-sided pyramid at the end, which centers the coned capillary and provides gaps for the sheath gas to exit.

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coned end of the sample capillary centered (Figure 17.3c). Shear forces exerted by the co-flowing gas (helium or nitrogen at 20–200 psi supply pressure) keep the LCP stream straight and on axis, but due to its high viscosity, the stream is not focussed down to a smaller size as with the GDVN. Instead, the stream diameter is identical to the capillary inner diameter and can range from 20 to 75 µm. The chosen capillary inner diameter depends on the crystal size and should be larger than the largest crystals to avoid clogging. Without the use of co-flowing gas surrounding the stream, it would curl up due to surface tension forces (Figure 17.4) and the extrusion would be unstable. The bore in the reservoir can be filled with sample via a Hamilton syringe (Figure 17.5) and for each new sample fill the Teflon ball is replaced. To achieve sufficient control over the flow of the high viscosity material, the supply pressure on the water line is controlled by a high-performance liquid chromatography (HPLC) pump in constant flow rate mode. The sample flow rate can be optimized for the chosen XFEL pulse rate, so that, between pulses, the sample stream advances only the distance needed to replenish the sample that has been damaged in the previous pulse. Figure 17.6 shows a schematic of the experimental setup for this method.

Figure 17.4  Left:  LCP extrusion through a capillary with an inner diameter of 30 µm without co-flowing sheath gas. The stream curls up into a loop and the extrusion is unstable. Right: LCP extrusion through a capillary with an inner diameter of 50 µm with co-flowing helium sheath gas from the ceramic nozzle (visible on the far left of the image) expanding into vacuum. The co-flowing gas keeps the stream stable and on axis.

Figure 17.5  The  injector reservoir can be filled with LCP from the syringe in which the protein crystals have been grown. Syringe and reservoir are coupled by an HPLC fitting.

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Figure 17.6  Experimental  setup for SFX with the high viscosity injector.

17.2.3  High Viscosity Media The initial motivation to design a high viscosity injector was the fact that many important membrane proteins, e.g., G-protein coupled receptors (GPCRs), are crystallized in LCP, which has a very high viscosity comparable to toothpaste. Crystals that grow in LCP are typically small but well-ordered, and therefore ideal for SFX. Optimization of crystallization conditions in LCP to obtain sufficiently large crystals suitable for conventional synchrotron X-ray crystallography is very time consuming. Using the high viscosity injector at an XFEL results in drastically reduced sample consumption compared to the GDVN injectors, and is therefore highly desirable for samples like GPCRs, which cannot be produced in high quantities. The reduction in sample consumption is mainly due to the drastic reduction in flow speed from 10 m s−1 to ∼2 mm s−1, which outweighs the small increase in sample needed due to the increased mismatch between stream diameter and XFEL spot size compared to GDVN jets. Whereas GPCR crystals are grown in LCP, membrane protein crystals grown in the form of a protein–detergent micelle cannot usually be mixed with LCP, since this leads to dissolution of the crystals. Therefore, other high viscosity media have been explored, e.g., a mineral oil based grease,14 petroleum jelly15 and a medium based on agarose.16 Protein crystals are embedded in these media post-crystallization. By choosing

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the appropriate high viscosity medium, many other proteins besides GPCRs can be delivered with this injector while substantially reducing the amount of required sample.

17.3  Results and Discussion In experiments at the LCLS the injector was first used with GPCR crystals grown in LCP and the structures of several GPCRs could successfully be solved, e.g., the human smoothened (SMO) receptor in complex with cyclopamine,17 the angiotensin receptor,18 the human δ-opioid receptor19 and rhodopsin bound to arrestin.20 In addition, pump probe SFX experiments, as well as native phasing measurements with protein crystals in an LCP stream are currently under way, and sulfur single-wavelength anomalous diffraction (SAD) phasing of lysozyme in a grease matrix microstream has been demonstrated recently.21 LCP can also be used as a suitable carrier medium for microcrystals of soluble proteins, thereby reducing the necessary sample amount. This has been shown with lysozyme and phycocyanin, where less than 0.1 mg of each protein led to complete data sets of 1.9 and 1.75 Å, respectively.22 The crystal size in this case was about 10 µm on average. In addition, the use of agarose as an alternative high viscosity medium showed that it can be used even for microcrystals of the largest membrane proteins photosystem I and II, which reduced the necessary amount of crystals by orders of magnitude.16 The agarose medium could also be successfully used to solve the structure of phycocyanin16 and a first attempt has been made to use Sindbis virus microcrystals23 in agarose. The protein crystals are embedded into the agarose medium post-crystallization via two coupled syringes. All these experiments have been performed at the LCLS CXI beamline in vacuum and also in an helium atmosphere. If experiments with LCP are conducted in vacuum, extra measures have to be taken to prevent a phase change of the LCP medium due to evaporative cooling and desiccation. Monoolein, the most commonly used lipid for crystallization of membrane proteins in LCP, is not ideally suited for SFX experiments in vacuum, as it undergoes a phase transition from cubic phase to a lamellar crystalline (Lc) phase below 18 °C. This leads to strong, sharp diffraction rings from the Lc phase, which are superimposed onto the Bragg reflections from the crystals and can damage the detector. Using nitrogen instead of helium as the sheath gas can sometimes prevent the formation of the lamellar phase, but the LCP stream stability suffers. It has been shown that adding a shorter chain length lipid to the LCP post crystal growth prevents formation of the Lc phase upon injection into vacuum17 without deterioration of crystal quality. Initial serial diffraction experiments with microcrystals in high viscosity streams have also been done at microfocus synchrotron beamlines, e.g., at the Advance Photon Source (APS), European Synchrotron Radiation Facility (ESRF)24 and at the Swiss Light Source.15 In this case, the exposure times were 10–50 ms24 and 100 ms,15 and the repetition rate was 10 Hz limited by the detector readout rate. These exposure times are short enough that secondary

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Figure 17.7  Image  of an LCP stream operating at the LCLS in vacuum. The stream

is hit periodically by XFEL pulses with a repetition rate of 120 Hz. The vertical lines in the left side of the stream are micro-holes drilled by individual XFEL pulses. The periodic gaps in the pattern of holes occur because every 24th electron bunch was used for an electron beam experiment at SLAC and did not produce X-ray pulses, thus leaving some larger jet regions undamaged. The jet was back-illuminated with a halogen lamp (KL 1500 LCD, Schott) and imaged with a highspeed camera (Phantom Miro M320S, Vision Research) operating at 960 frames per second with an exposure time of 1 µs.

and tertiary damage effects can be outrun.25,26 Planned future upgrades of synchrotron light sources to increase the brightness combined with fast integrating detectors will reduce measurement times in synchrotron serial crystallography and allow the use of even smaller protein crystals. The pulse energies available from present hard X-ray FELs are sufficient to generate X-ray explosions that extensively damage liquid jets used for sample delivery27 and the LCP jets can be similarly affected. In the case of LCP jets, it is possible to tune the experiments such that the sample delivery remains efficient for relatively high XFEL pulse intensities, despite a certain amount of X-ray damage. The LCP flow rate can be optimized for the 120 Hz pulse repetition rate of the LCLS so that, between X-ray pulses, the stream advances only the distance needed to expose fresh sample to the next pulse. The necessary distance depends on the X-ray beam diameter and pulse energy. Online tuning of the LCP jet and of the XFEL pulse energy can be achieved using the combination of a high-speed camera with a high-resolution optical imaging system. Figure 17.7 shows an LCP jet operating under optimal conditions during an experiment conducted at LCLS. In this experiment, the XFEL pulses (10.0 keV, 2.3 mJ pulse energy at the source) were attenuated to 3.2% of their maximum value to limit damage to the jet, while nevertheless allowing a high pulse brightness for high-resolution single-shot diffraction. As shown in the image, the probed regions were spaced at ∼15 µm along the jet to ensure that each XFEL pulse probed an undamaged part of the LCP jet, while not wasting the sample between pulses. Given the 120 Hz pulse repetition rate at LCLS, the spatial separation corresponds to a jet velocity of ∼2 mm s−1. This optimal jet velocity was determined using the off-axis high-resolution imaging system27 developed at the CXI instrument at LCLS. Compared to the GDVN injector, only a small amount of sample is wasted and flow rates of 1–300 nL min−1 have been achieved with the LCP injector by adjusting the flow rate setting on the HPLC pump. The LCP flow rate can be calculated by dividing the HPLC

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flow rate by the pressure amplification factor of 34 (14 for the large reservoirs). A typical experiment requires about 0.3 mg of protein or about 80 µL of LCP with crystals.

17.4  Conclusion Using a high viscosity microstream injector for SFX at an XFEL has been shown recently to be a viable alternative to other sample injectors and fixed targets, and is often the best solution, as in the case of some GPCR crystals grown in LCP, which will only grow to a few micrometers in size. The method reduces the amount of sample necessary for a full SFX dataset compared to GDVN use by a factor of 10–100 and the stream speed can be adjusted to the X-ray repetition rate of the XFEL. Microfocus beamlines at several synchrotrons are now starting to use this method for fast data collection from micrometer-sized crystals.

Acknowledgements Experiments were carried out at the Linac Coherent Light Source, a national user facility operated by Stanford University on behalf of the U.S. Department of Energy (DOE), Office of Basic Energy Sciences. We acknowledge support from the National Science Foundation (awards MCB 1021557 and MCB 1120997) and its BioXFEL Science and Technology Center (NSF 1231306). Special thanks to Claudiu Stan (PULSE Institute) and Sebastién Boutet (LCLS) for providing Figure 17.7 and information about the image collection technique used, and Vadim Cherezov (USC), who was the beamtime PI when the high speed images where recorded.

References 1. L. Rayleigh, Proc. London Math. Soc., 1878, 1, 4. 2. A. Frohn and N. Roth, Dynamics of Droplets, Springer Science & Business Media, 2000. 3. D. P. DePonte, U. Weierstall and K. Schmidt, et al., J. Phys. D: Appl. Phys., 2008, 41(19), 195505. 4. G. Nelson, R. A. Kirian and U. Weierstall, et al., Opt. Express, 2016, 24, 11515. 5. D. Wang, U. Weierstall, L. Pollack and J. Spence, J. Synchrotron Radiat., 2014, 21, 1364–1366. 6. R. G. Sierra, C. Gati and H. Laksmono, et al., Nat. Methods, 2015, 13, 59–62. 7. E. L. Baxter, L. Aguila and R. Alonso-Mori, et al., Acta Crystallogr., 2016, 72, 1–10. 8. C. Mueller, A. Marx and S. W. Epp, et al., Struct. Dyn., 2015, 2, 054302–054317.

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9. M. S. Hunter, B. Segelke and M. Messerschmidt, et al., Sci. Rep., 2014, 4, 6026. 10. C. G. Roessler, R. Agarwal and M. Allaire, et al., Structure, 2016, 24, 1–10. 11. A. M. Gañán-Calvo, R. González-Prieto, P. Riesco-Chueca, M. A. Herrada and M. Flores-Mosquera, Nat. Phys., 2007, 3, 737–742. 12. S. L. Perry, S. Guha and A. S. Pawate, et al., Lab Chip, 2013, 13, 3183–3187. 13. K. R. Beyerlein, L. Adriano and M. Heymann, et al., Rev. Sci. Instrum., 2015, 86, 125104–125112. 14. M. Sugahara, E. Mizohata and E. Nango, et al., Nat. Methods, 2015, 12(1), 61–63. 15. S. Botha, K. Nass and T. R. M. Barends, et al., Acta Crystallogr., Sect. D: Biol. Crystallogr., 2015, 71, 387–389. 16. C. E. Conrad, S. Basu and D. James, et al., IUCrJ, 2015, 2, 421–430. 17. U. Weierstall, D. James and C. Wang, et al., Nat. Commun., 2014, 5, 3309. 18. H. Zhang, H. Unal and C. Gati, et al., Cell, 2015, 161, 833–844. 19. G. Fenalti, N. A. Zatsepin and C. Betti, et al., Nat. Struct. Mol. Biol., 2015, 22(3), 265–268. 20. Y. Kang, X. E. Zhou and X. Gao, et al., Nature, 2015, 523, 561–567. 21. T. Nakane, C. Song and M. Suzuki, et al., Acta Crystallogr. D Biol. Crystallogr., 2015, 71, 2519–2525. 22. R. Fromme, A. Ishchenko and M. Metz, et al., IUCrJ, 2015, 2, 545–551. 23. R. M. Lawrence, C. E. Conrad and N. A. Zatsepin, et al., Struct. Dyn., 2015, 2, 041720. 24. P. Nogly, D. James and D. Wang, et al., IUCrJ, 2015, 2, 1–9. 25. R. L. Owen, D. Axford and J. E. Nettleship, et al., Acta Crystallogr., 2012, 68, 1–9. 26. M. Warkentin, J. B. Hopkins, R. Badeau, A. M. Mulichak, L. J. Keefe and R. E. Thorne, J. Synchrotron Radiat., 2012, 20, 7–13. 27. C. A. Stan, et al., Nat. Phys., 2016, 12, 966–971.

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Chapter 18

Acoustic Methods for On-demand Sample Injection into XFEL Beams Allen M. Orville Diamond Light Source Ltd, Diamond House, Harwell Science and Innovation Campus, Didcot, Oxfordshire, OX11 0DE, United Kingdom *E-mail: [email protected]

18.1  Introduction As of 04 May 2016, the Protein Data Bank (PDB) curates 118 587 atomic models, of which 105 971 are X-ray crystal structures, and 93 026 (∼88%) of these were collected at a synchrotron source from samples held at 100 K, and from an average of one large crystal (hundreds of microns or larger) per model.1 These statistics clearly demonstrate the immense value of macromolecular crystallography (MX) to the structural biology community. The methods exploited also define the “standard” MX experimental envelope for typical research activity in the field (Figure 18.1). Within these envelope borders, seven Nobel Prizes have been awarded in the past decade with a component linked to structural biology (Chemistry 2015, 2013, 2012, 2009, 2008 and 2006, and Medicine 2013). Not surprisingly then, the field is often considered mature; a concept reinforced by several decades of research and development (R&D) activity by many groups since stable photon sources at second generation synchrotrons were first commissioned in the early 1970s.   Energy and Environment Series No. 18 X-Ray Free Electron Lasers: Applications in Materials, Chemistry and Biology Edited by Uwe Bergmann, Vittal K. Yachandra and Junko Yano © The Royal Society of Chemistry 2017 Published by the Royal Society of Chemistry, www.rsc.org

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Figure 18.1  Experimental  envelopes for MX techniques as a function of X-ray expo-

sure time, crystal size and crystal quantity. Different MX techniques and science explore different regions of this three-dimensional (3D) space and exploit the characteristics of various sources in different ways. For comparison, the red shaded region shows that enzyme catalytic reactions typically take ∼1 µs to seconds (average = 60 ms); the green region highlights that photo-isomerization, photon-induced charge separation and electron transfer reactions occur in the picoseconds to milliseconds time range; the blue region illustrates that transition states, by definition, have lifetimes equivalent to one bond vibration and last only femtoseconds. Key: MX (typical, single crystal, rotation-based MX at synchrotrons); MX′ (multicrystal, rotation-based methods for MX at synchrotrons); e− MX (3D microcrystal electron diffraction with cryogenic transmission electron microscopes);55 Synch. SMX (serial, still-image-based methods for MX at synchrotrons); XFEL SFX (serial femtosecond MX at XFELs); T-R Mono (monochromatic X-ray, time-resolved serial MX, femtosecond exposure times at XFELs, longer exposure times at synchrotrons); T-R Laue (polychromatic X-ray, time-resolved MX typically at synchrotrons).

Over the past four decades, many complementary efforts have produced very reliable storage ring sources around the world; indeed, http://lightsources.org lists 47 synchrotrons in 22 nations with about 20 so-called third generation sources in operation. Many of these facilities have developed robust methods in automation that impact a range of activities from sample preparation through data collection and processing.2 As a result, there is sufficient capacity for relatively easy and frequent access to beamtime, especially for structural biologists. The improvements in automation and overall methods have penetrated the field so thoroughly that most biophysical research groups now exploit synchrotron facilities as essential tools. Furthermore, they often achieve their particular specific aims without requiring a fully dedicated crystallographic expert within their own group. Remote data collection is also supported in many facilities, which relieves the burden of travelling to the synchrotron; instead, researchers simply ship their samples for data collection under cryogenic conditions. Some facilities are now offering in situ data collection directly from crystallization trays at ambient temperature. MX beamlines

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with stable and intense micron-sized X-ray beams are also becoming more common.3 All of these developments inevitably enlarge the experimental possibilities for the entire field and enable scientists to attempt more ambitious studies. The first serial femtosecond crystallography (SFX) results were reported in 2011 by Chapman et al., with data collected at the Linac Coherent Light Source (LCLS), a hallmark for the beginning of a new era in structural biology.4 One can gauge the early impact of the new facility and the SFX methods with three search queries to the PDB: “free electron laser, femtosecond, or serial,” which return 85, 96 and 131 entries, respectively. Parsing further the 85 results from the first query term revealed that only 11 datasets were collected at 100 K and the rest were at ambient temperature (∼293 K); the other two query terms yield similar ratios. Within the “serial” pool, 70 out of 131 models were refined against data collected at a synchrotron or home source with the balance linked to an X-ray free electron laser (XFEL) source. Looking deeper reveals that most of the 70 entries are actually related to one or more SFX results from an XFEL source. Even less apparent in the XFEL entries is the fact that the vast majority of the XFEL datasets were collected from several thousands of crystals.5–7 These typically ranged in size from submicron to tens of microns in diameter and were delivered to the beam in a rapid and serial manner (Figure 18.1). This type of sample delivery method is necessary because every XFEL pulse that hits a crystal destroys the sample, an explosion that happens roughly at the speed of sound.8,9 Fortunately, the photons travel at the speed of light and encode structural information including one still diffraction pattern that emerged from a randomly orientated crystal lattice. Thus, serial crystallography approaches are most often collected at ambient temperature, from many individual crystals. Ambient temperature data collection is growing in popularity, is often synergistic with synchrotron results, and once again enlarges the experimental domain for the entire field. Indeed, one of the most important potential applications in SFX is time-resolved serial crystallography, which requires ambient temperature to allow for dynamic events to take place under physiological conditions.10–15 Several groups are working to develop strategies to bring slurries of micron-sized enzyme crystals together with reagents.16–18 The hypothesis is that microcrystals with diameters on the order of 2 µm or less should equilibrate with substrates much faster than the 60 ms average turnover time for enzyme catalysis.19,20 Thus, time-resolved SFX methods have the potential to yield atomic-resolution movies of enzymes engaged in catalysis and could become generally applicable to a very wide range of samples.

18.2  Evolution of Sample Delivery Methods at XFELs Hard X-ray FELs operating now and planned for the future have profound implications for SFX sample delivery and consumption (Table 18.1). For example, the LCLS can deliver 50 fs X-ray pulses at 120 Hz, which sums to

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Table 18.1  XFELs  producing hard X-rays in operation now or in the near future.

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Facility First beam Experiment stations Electron energy (GeV) Photon energy (keV) Photons/ pulse Peak brilliance Average brilliance Pulses/s

Detector (readout rate, Hz)

LCLS (USA)

SACLA PAL XFEL (Japan) (Korea)

European SwissFEL XFEL LCLS-II (Switzerland) (Germany) (USA)

2009 6 (7)

2011 10

2017 6

2017–18 6–15

2019 7–10

17

5.1–8.5 4–10 3.1

5.8

2.0–4.14 2.5–17

0.28–12

4–20 4–20

0.18–1.8 1.77–12.4

∼1012

2 × 1011 >1 × 1011

10.5 14.0 17.5 0.26–15 0.47–20 0.73–25 ∼1012

≥1012

∼8 × 1032

∼1033

5 × 1033

≥1032

2 × 1021

3 × 1020 1 × 1020

∼1025

≥2 × 1021

120

60

2016 5

0.28–1.2 2–20

∼1031

5 × 109–7 × 1011 1–3 × 1032 1 × 1021

60, 120 (6.5 100 keV)

CSPAD/ MPCCD MPCCD Rayonix (60) (60) (120/10)

Jungfrau (100)

0.2–1.3 1–25

27 000 120, 106 (2700 in (870 eV) in order to maximize the 1s photoionisation cross section. Figure 20.2b shows the spectral lineout of two measured single-shot spectra: while the XFEL central photon energy shifts from shot to shot, a stable emission frequency at the Kα transition at 848.6 eV and a full width of 0.53 eV (resolution limited) at half maximum was measured. For the focused XFEL beam, the achievable intensities on target are in the range of 1017–1018 W cm−2, so that the 1s ionisation rate of neon is comparable to the Auger rate, and a sizable population inversion can be built up in the medium. Both the XFEL pulse length of ∼40 fs and the core-hole lifetime are short compared to the propagation time through the sample. The population inversion is therefore transient and has a duration that is typically smaller than the XFEL pulse duration. The inversion of the medium is built up in travelling-wave geometry. The spatial and temporal evolution of the neon Kα XRL intensity and the population inversion are shown in Figure 20.3, as determined by our comprehensive theoretical model32 based on the solution of the Liouville-von

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Figure 20.3  Simulation  of the temporal evolution of the emitted XRL pulse and population inversion as a function of the propagation distance through the medium. Reprinted with permission from C. Weninger, N. Rohringer, Physical Review A, 90, 063828, 2014. Copyright (2014) by the American Physical Society.32 Shown are (a) the emitted XRL pulse intensity normalized to its maximum at a given propagation distance as a function of time, measured in the reference frame of the XFELpump pulse, and (b) the population inversion of the lasing transition. The green dotted line follows the temporal maximum of the population inversion; the black line follows the maximum of the XFEL flux. Shown are averages assuming a Gaussian XFEL pulse with a duration of 40 fs, 2 × 1012 photons and a 2 µm focal radius.

Neumann equation for the ionic density matrix that is self-consistently coupled to Maxwell’s equation in the paraxial approximation. For simplicity, we assume a temporally Gaussian pulse. Figure 20.3b shows the population inversion as a function of propagation distance through the medium and time in a moving window that propagates with the vacuum speed of light through the medium. Simulations for self-amplified spontaneous emission (SASE) pulses are presented in ref. 32, with no substantial differences to the argument that follows. The population inversion shown in Figure 20.3b, closely follows the intensity profile of the XFEL pump-radiation. The total

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absorption of the propagating XFEL pulse as a function of the propagation distance is shown in Figure 20.4a, as determined by the Liouville-von Neumann/Maxwell model. The XFEL suffers strong absorption in the optically dense medium. Initially, the medium is bleached (saturated absorption of the 1s shell), i.e., all available neutral atoms are core ionized by the rising flanks of the XFEL pulse. The leading edge of the pulse therefore depletes the 1s shell of neon with 100% probability. For the remainder of the pulse, which is tuned between the 1s ionisation edges of the neutral and singly charged neon, there is therefore no ground-state population left to be ionised and the pulse propagates quasi without absorption (only the valence electrons are absorbing, with a cross section that is roughly a factor of 10 smaller than that of the 1s absorption). Due to the saturated absorption, the temporal maximum of the XFEL intensity shifts to later and later times in the reference frame moving with the pulse, when propagating further in the medium. This is directly reflected in the temporal profile of the population inversion, shown in Figure 20.3b: the maximum of the population inversion (shown by the dashed black line) shifts to later times for a larger propagation distance. Modelling the propagation and amplification of the Kα line emission with a self-consistent model based on rate equations for the atomic and ionic populations33 and an

Figure 20.4  Evolution  of (a) the number of photons in the emission line, and (b) the spectral and temporal width of the neon Kα emission as a function of propagation distance through the target. Reprinted with permission from C. Weninger, N. Rohringer, Physical Review A, 90, 063828, 2014. Copyright (2014) by the American Physical Society.32

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equation keeping track of the X-ray flux of the XFEL and Kα radiation (as it is typically done for simulating optically driven plasma-based short-wavelength lasers and single-pass amplifiers), one would predict a temporal slippage of the population inversion with respect to the arrival of the Kα radiation pulse. Whereas this simple model correctly describes the XFEL absorption and the shift of its maximum to later times, the Kα pulse propagates with the vacuum speed of light in this model. Hence, the rate equation/flux model predicts a temporal mismatch between population inversion and the Kα XRL emission and, as a consequence, a drop of the gain cross section for longer propagation distances. In reality, better described by solving for the temporal evolution of the ionic density matrix (including populations and coherence of the upper and lower electronic states of the lasing transition) and wave equation for the electrical field (see ref. 32), the emitted Kα radiation pulse propagates with a group velocity smaller than the speed of light, which can be seen in Figure 20.3a, showing the normalized emitted Kα flux as a function of propagation distance. Similar to optical fields that are propagating resonantly on strong gain transitions,34 the X-ray pulse is slowed down. The delay of the Kα XRL emission is typically a few femtoseconds per millimeter propagation distance at the considered gain conditions. This wave effect is therefore crucial for optimal amplification conditions and constitutes a gain-guiding condition in the medium. In ref. 32, we show a comparison of the Kα XRL output between the rate equation/flux model and the more involved solution of the Liouville-von Neumann equation and Maxwell’s equation. Quick fixes that implement a gain-dependent adaption of the group velocity of the XRL emission within the rate equation/flux model still show strong differences to the Liouville-von Neumann/Maxwell approach, demonstrating that the more sophisticated method is indispensable to predict the output characteristics of the Kα XRL. For propagation distances that correspond to a few absorption lengths in the medium (∼5 mm in the considered case, corresponding to 2.5 “cold” absorption lengths), the pump flux is sufficiently attenuated, so that further attenuation proceeds according to the linear Lambert–Beer’s law (see also Figure 20.4a). The shape of the XFEL pulse is then unaltered, which is also reflected in the population inversion that no longer accrues a delay propagating deeper into the medium. The population inversion after a few absorption lengths and the achievable gain then drops considerably, and the signal amplification is less than exponential. For sufficient pump-pulse intensities, saturation of the signal amplification is achieved. This means that the rate of stimulated emission starts to become comparable to the decay rate of the upper level. In this highly saturated scheme, effects such as saturation broadening, Rabi flopping and Autler–Townes splitting of the emitted line spectrum set in. The saturation intensity is an inherent property of the lasing medium, when only lifetime decay mechanisms are considered, but can be extended to higher intensities by manipulating the lifetime of the upper state through, for example, further photoionisation (ionisation gating) or collisional processes in sufficiently dense medium. In the case of neon, collisional effects become important at

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35

the time scale of 10–100 fs, which is also reflected in the electron kinetic energy distribution. In solid-density targets, collisional effects are important at much shorter time scales, so that more sophisticated models, including collisions similar to ref. 21, 22 and 35, based on Liouville-von Neumann/ Maxwell approaches have to be developed to correctly describe the underlying physical processes and characteristics of the amplified emission. Although attempted, the experimental setup to demonstrate exponential amplification as a function of target length turned out to be difficult (see Figure 20.4a for a simulation of length-dependent emission). Instead, stimulated emission was demonstrated by varying the energy of the pump pulse. Figure 20.5 shows the experimentally measured number of photons in the Kα emission line as a function of incoming XFEL pulse energy as recorded in 2011.31 Clearly, by tripling the incoming pump-pulse energy, an increase in the emission intensity of more than three orders of magnitude is observable and the amplification starts to saturate. In the saturated lasing regime, ∼1011 photons in the Kα emission line were detected. Considering the number of ∼1012 incident XFEL photons per pulse, this strong signal demonstrates a very high conversion efficiency. Spontaneous emission in the forward direction and into the opening angle of the spectrometer setup would have resulted in

Figure 20.5  Gain  curve of the neon Kα laser, showing the number of photons in the emission line as a function of the incoming XFEL pulse energy, assuming a 20% beam-line transmission. Clear exponential gain and saturation of the signal was observed. The black points are the results of the theoretical simulations also showing the standard deviation of the emission by averaging over several XFEL SASE pulses. Reprinted with permission from C. Weninger, M. Purvis, D. Ryan, R. A. London, J. D. Bozek, C. Bostedt, A. Graf, G. Brown, J. J. Rocca, N. Rohringer, Physical Review Letters, 111, 233902, 2013. Copyright (2013) by the American Physical Society.

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∼10–100 photons for the experimental setup, showing that an amplification over nine to ten orders of magnitude, or exponential gain-length products of the order of GL ≈ 21–23 were achieved. This is in accordance with a gainlength product of GL ≈ 21 determined in the first experimental realisation.30 The evolution of the emission line width and the pulse duration as a function of target length, and hence gain amplification, is shown in Figure 20.4b. Initially, the emission has the natural lifetime width, in the case of neon, given by the Auger-decay rate. The duration of the emitted pulses initially matches the duration of the population inversion in the system and the pulses are not transform limited, i.e., longitudinally incoherent, consisting of several modes. As amplification proceeds deeper in the medium, a drop in both the line width (gain narrowing) and the pulse duration is observed and transform-limited pulses build up in the system. In this linear gain regime, the line width can be smaller than the natural lifetime width if sufficiently long pulse duration of the pump-radiation is chosen. This opens the opportunity for sharpening spectral features in stimulated emission spectroscopy. Further amplification results in stabilisation of the pulse shape despite strong exponential amplification. Once the pulses saturate, re-broadening (saturation broadening) of the emission line sets in and the build-up of Autler–Townes splitting sets in, which is a result of Rabi oscillations between the upper and lower lasing levels. Unfortunately, the spectral resolution in our neon experiments was too small to resolve the gain narrowing and saturation broadening effects. The narrowing of the emission line at the onset of the exponential gain region is particularly interesting for applying stimulated emission spectroscopy in chemical analysis, where spectral fingerprints can be sharpened and the lifetime broadening of the emission features can be overcome. In addition to the sharpening of one emission line, stimulated emission in more complex systems will favour only the strongest spectral component. This feature is discussed in the next section, discussing stimulated emission in molecular gas-phase targets, but will have a much wider impact in stimulated hard X-ray spectroscopy of liquid and solid targets.

20.3  Molecular Soft X-ray Photoionisation Lasers The extension of the photoionisation soft X-ray Kα laser to organic molecular samples in the gas phase is far from trivial. A simple “back of the envelope” calculation using atomic rate coefficients, as given in the introduction, to estimate the lasing gain is completely misleading, since rotational and vibrational degrees of freedom have to be taken into consideration in calculating the expected gain. Comprehensive theoretical studies on CO and N2 have been published.36–38 The employed theoretical model is an extension of the Liouville-von Neumann/Maxwell approach to also include the vibrational degrees of freedom on a quantum level by extending the density matrix to also include vibrational states. Rotational degrees of freedom are treated in a classical manner. Although K-shell ionisation of these diatomic molecules does not strongly depend on the molecular orientation, the emitted radiation pattern,

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filling the 1s hole by an electron from an outer valence molecular orbital typically has a strong angular dependence, i.e., the molecular dipole transition moment has a directional dependence in the molecular frame. In an isotropic gas sample without alignment, only molecules that are aligned in such a way that the transition dipole is perpendicular to the pump propagation direction are efficiently participating in the lasing process. This implies that, for transitions with dipole transition vectors parallel to the molecular axis, the molecules have to be aligned perpendicular to the propagation axis of the pump and emitted X-ray pulses; for dipole transitions perpendicular to the molecular axis, the molecules have to be aligned along the propagation direction of the X-rays. Pre-alignment by impulsive alignment with optical laser pulses of the molecular gas can therefore enhance the lasing signal by many orders of magnitude36–38 by pumping the molecular gas target at times of rotational revivals. For diatomic molecules, the alignment of the molecular axis is typically measured as the expectation value of cos2 θ(t), where θ(t) denotes the angle of the molecular axis with respect to the polarisation of the alignment laser in the picture of a classical rigid rotor. An isotropic ensemble of molecular rotors has an expectation value of cos2 θ(t) = 0.33. Rotational revivals happen at times for which cos2 θ(t) has a local maximum, and hence correspond to alignment peaks of the sample (aligned sample with cigar-shaped angular distribution of the molecular axis). These rotational revivals are typically followed by a local minimum cos2 θ(t) < 0.33 for which the molecular sample is anti-aligned (the angular distribution has a pancake-like structure, with the molecular axis aligned perpendicular to the laser polarisation direction). Typical rotational revival times are in the picosecond time range and, depending on the temperature of the sample, the revival peaks extend over a duration of 10–100 fs. Experimentally, this means that an external optical laser that enables impulsive rotational alignment has to be stabilized with respect to the arrival time of the XFEL pulses with an accuracy of ∼10–50 fs. Cooling the sample results in longer revivals and a higher degree of alignment. For the particular case of N2, we calculated that, for typical FEL parameters, a rotational temperature of 50 K results in an increase in the emission intensity of up to three orders of magnitude as compared to room temperature.38 By pumping the system at alignment peaks or minima, distinct electronic transitions can be amplified. For example, ionising the K shell in N2, the radiative decay can happen to electronic state A (2Σu+ to A2Σg+ transition), with the dipole transition moment aligned to the molecular axis, or decay to state B (2Σu+ to B2Πu transition), with the dipole transition perpendicularly aligned to the molecular axis. Figure 20.6a shows the expected number of emitted photons for transition to state A as a function of the incoming number of pump photons for different degrees of alignment. The gain involving electronic state A is strongly enhanced for an aligned sample (assuming a degree of alignment of cos2 θ = 0.62). Assuming 6 × 1012 incoming pump photons on target within a pulse of 50 fs duration—a slightly too optimistic approach for present-day sources—and a focal radius of 2 µm, this would result in ∼109 photons in the emitted lasing line, whereas for an isotropic ensemble of

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Figure 20.6  (a)  Theoretical estimates of the expected number of emitted X-ray pho-

tons in N2 as a function of the number of incoming pump photons on the transition from 2Σu+ to A2Σg+ after K-shell ionisation. The applied theoretical model is presented in detail in ref. 37 and 38. We assumed a gas density of 2.5 × 1019 molecules cm−3 and a sample length of 5 mm. For the incoming XFEL, we assumed a focal radius of 2 µm of the XFEL and a pulse duration of 50 fs at FWHM for a Gaussian pulse profile. Shown are results for different degrees of alignment, measured by the expectation value of cos2 θ quoted in the figure inset. (b) Evolution of a typical spectrum of N2 as a function of propagation distance. Figure courtesy of Victor Kimberg.

molecules, at most, ∼105 photons are expected. Probing the sample at times of anti-alignment (cos2 θ = 0.16) the emission to electronic state A is suppressed, whereas the emission involving the transition to state B is amplified (not shown), reaching ∼108 photons in the emission line. At current XFEL facilities, the number of obtainable photons on target is smaller than 1012 at the nitrogen K edge and the theory predicts only a few thousand photons in the emission line at best, which is at the onset of being measurable with the current experimental setup. CO at the oxygen K edge has slightly higher gain, and lasing to the electronic 1π−1 A2Π state was attempted in an experimental campaign in 2014 for a dynamically aligned sample, but unfortunately without success. Reasons for the failure were technical difficulties in finding the overlap of the XFEL pulse with rotational alignment revivals and XFEL photon numbers that were too low to yield considerable lasing gain. The theoretically determined evolution of the spectral characteristics of the emitted radiation is quite interesting in the molecular case;36–38 an example in Figure 20.6b shows the evolution of the normalised emission spectrum of N2 to state A as a function of propagation distance. Initially, the X-ray fluorescence is governed by the typical vibrational progression. In the exponential gain region, however, the strongest vibrational component gains weight over the others. At saturation, the emission is dominated by, typically, a single vibrational component, in strong contrast to the fluorescence spectral band. Further increasing the gain can lead to saturation of one vibrational component and the other vibrational transitions pick up and get stronger in

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weight. As in the atomic case, driving stimulated emission into saturation results in power broadening and a distortion of the spectrum. Stimulated emission spectroscopy, in contrast to mere fluorescence, hence has the possibility to enhance only the strongest vibrational component of the system. Furthermore, at the onset of the linear gain region, the emitted vibrational spectrum shows gain narrowing and the spectral features are clearer than in the lifetime-limited case of fluorescence. Stimulated emission spectroscopy is hence characterised by a sharpening of the spectral features with above lifetime-limited resolution.

20.4  Outlook and Conclusions The first realisation of the atomic XRL in neon spurred interest to realise XRLs at shorter and longer wavelengths in the solid and liquid phase. Transferring photoionisation lasers to the longer-wavelength extreme UV (XUV) and VUV spectral domains is difficult. First, the ratio of the cross sections for inner-shell and valence ionisation gets typically smaller, so that innershell ionisation is not necessarily favoured over valence ionisation, and the creation of a population inversion is more challenging. Secondly, despite the longer lifetimes of the inner-shell holes, the dipole transition matrix elements and the therewith expected gain cross sections are typically too small to result in considerable amplification of the fluorescence, so that a saturated laser output is difficult to achieve. A recent experiment in silicon showed first evidence of transient VUV lasing at 90 eV following L-edge excitation with 115 eV photons.39 These first results were, however, limited to modest gain, showing an amplification of a factor of two compared to the expected fluorescence yields, which leaves room for other explanations, such as an increased effective pump volume by the onset of bleaching of the medium. On the short-wavelength side, a hard X-ray photoionisation laser in solid copper40 was recently demonstrated at the SACLA XFEL facility in Japan, thereby demonstrating the hard XRL originally proposed in the seminal XRL paper from 1967.1 Despite the shorter core-hole lifetimes in heavier elements, which require yet higher X-ray pump intensities to build-up a population inversion, there are a few advantages. In heavier elements with 16 (sulfur) < Z < 47 (silver), Kα lasing involves a short lived, lower lasing state, with a hole in the L shell. Particularly, the lifetime of the lower lasing state for these elements is shorter than the radiative K-hole lifetime, permitting a “quasi static” inversion.41 In the recent experiment in copper, amplification over several orders of magnitude was demonstrated for the Cu Kα1 and Kα2 emission lines. Featuring variable-gap undulators, the SACLA FEL was operated in a two-colour mode for this experiment, with the main pulse being tuned above the Cu K edge and a second weaker pulse that served as a seed pulse for driving stimulated emission on the Kα1 and Kα2 transition. In this way, a particular fine-structure component of the emission spectra could be enhanced. Amplified spontaneous emission primarily enhances the stronger Kα1 emission line, similar to the molecular XRL for which weaker vibrational

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progressions are suppressed in the output spectrum. Beautifully demonstrated in this work, in the linear gain region, only the Kα1 line was present in the spectrum, whereas, at strong pump-power inducing saturation of the stimulated Kα1 emission, the Kα2 line became visible in the amplified spectrum. In addition to the appearance of the Kα2 line, the Kα1 emission shows a pronounced shoulder to the low-energy side. The spectral line shape of the emission needs further investigation and analysis. A full theoretical model that is based on a quantum mechanical description of the density matrix of the involved transitions in the solid, keeping track of collisions, inhomogeneous line broadening due to saturated core-hole production and effects due to the transient change of the band structure need to be developed to fully understand the emission spectra. A thorough computational study on the photoionisation X-ray lasing scheme in the hard X-ray region was published in 1976 by Axelrod,21 considering Kα lasing in sulfur by solving the rate equations of the pump process, also including the effect of collisional processes. As we have learned from a thorough theoretical analysis in neon, a description based on the rate equations that solely follows the occupation probabilities of the lasing states is insufficient, both on a quantitative and qualitative level. The evolution of the polarisation of the medium (off-diagonal matrix elements in the electronic density matrix), as well as wave effects, such as the slow-down of the group velocity on the gain transition and propagation effects, such as the reabsorption of the emission, need to be included in an appropriate theory. Another effect that becomes important for lasing in heavier atoms is based on multi-stage pumping concepts: in contrast to light elements, where Kα transition energies of higher charged ions are shifted several tens of electron-volts to higher energies, in heavier elements with short K-shell lifetimes the Kα energies of higher charged ions often lie within the radiative width of the singly ionized Kα line.42 As pointed out in Figure 20.1b, fast depletion of the lower Kα lasing state by rapid Auger decay can result in a K-shell ionisation event of the doubly charged ion within the pulse duration of the driving pulse.43 A specific Cu atom can hence be used more than once in the lasing process, contributing photons within the Kα line. The resulting K emission line in the triply charged ion can have a spectral overlap with the Kα emission region, leading to additional spectral intensity and a change of the emission line shape. These multi-stage pumping schemes, by a sequence of inner-shell ionisation and Auger decay events, have also been suggested for lasing in H-like boron,22 and recently revisited for He- and H-like transitions in neon33 in view of the high ionisation stages that are achievable at XFELs.44,45 Although these high charge states can be produced in optically thin samples, XFELs presently do not offer enough pulse energy and flux to prepare a sufficiently long lasing target for achieving a sizable gain-length product to strongly amplify the additional emission lines for these light elements. Preparing a pre-ionised plasma could be one way to exploit the strong gain in H- and He-like ions. In the hard X-ray region, the possibility of a spectral overlap of

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the different emission lines within the broad lifetime width of the K hole, however, changes the story, so that these effects will become important to understand the emission line shape in the saturated gain region. The study of stimulated X-ray emission based on photoionisation of inner electronic shells is interesting from both a fundamental and applied aspect. The photoionisation XRL scheme based on the transient manifestation of a population inversion in the gain medium is in stark contrast to state-ofthe-art schemes of optical and VUV lasers. Without the use of optical mirrors, the transient photoionisation XRL produces transform-limited, fully longitudinally coherent, high-intensity X-ray pulses of ultrashort duration, which are typically determined by the natural lifetime of the inner-shell hole and the inverse K-shell photoionisation rate. Although not experimentally quantified, a comprehensive simulation32 shows that, in neon, fully temporally coherent pulses with a duration ranging from ∼2–20 fs can be created, containing up to 1010–1011 photons per pulse. The recently demonstrated Cu Kα XRL is expected to have sub-femtosecond pulse duration, and therefore would beat the record of the shortest and brightest coherent hard X-ray pulse that can presently be created. However, an experimental measurement of the pulse characteristics of these XRLs remains challenging. In addition to the fundamental aspect, stimulated X-ray emission following photoionisation can potentially have a big impact on the time-resolved spectroscopic applications for chemical analysis. X-Ray emission spectra of metals in organic molecules yield electronic and structural information.46,47 The X-ray spectroscopy of transition-metal centers in biological systems has, for example, the potential to revolutionize our understanding of catalytic processes in biological systems, such as nitrogen fixation, splitting of water in photocatalytic systems, or similar processes that typically involve complex metal reaction centers. X-Ray emission spectroscopy gives information of the spin and oxidation state of the transition metals (Kα and Kβ emission), and can even resolve the ligand type, local structure and covalency if the relatively weak valence to core emission is observed. To see catalytic processes in action and determine the electronic and structural pathways of these reactions, time-resolved X-ray emission spectroscopy is therefore a powerful tool. Traditional X-ray emission spectroscopy yields X-ray emission from the sample in the full solid angle at low fluxes despite the intense XFEL pulses. Time-resolved experiments in typical laser pump/XFEL probe settings are therefore cumbersome, since an emission spectrum can typically not be recorded by a single XFEL pulse exposure and needs averaging over many shots. This bottleneck could be overcome by stimulated emission spectroscopy, forcing the emission in a narrow cone in the forward direction and coherent signal amplification, which would allow the recording of single-shot spectra. Moreover, operation at the onset of the linear gain region would result in a sharpening of the spectroscopic features and a deconvolution of congested spectra (multiplet lines) by similar arguments as the clean-up of the vibrational spectra in molecular XRLs. Moreover, stimulating valence to core emission in these systems, the typically weakest decay pathway, would

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result in the chemically most relevant information in single shots. First progress in this direction has been recently achieved by demonstrating Kα lasing of manganese salts in aqueous solution.48 The chemical shift of the Kα1 line of different Mn model compounds, characterising the different spin and oxidation states, has been demonstrated, along with amplification of the signal by more than four orders of magnitude. Stimulated hard X-ray emission spectroscopy following K-shell ionisation may therefore soon find application in time-resolved chemical analysis of catalytic reactions and open up ample opportunities in this field of research.

References 1. M. A. Duguay and P. M. Rentzepis, Appl. Phys. Lett., 1967, 10, 350. 2. H. Mimura, et al., Nat. Phys., 2010, 6, 122. 3. H. Mimura, et al., Nat. Commun., 2014, 5, 353. 4. R. C. Elton, X-Ray Lasers, Academic Press Inc, 1990. 5. G. Chapline and L. Wood, Phys. Today, 1975, 40. 6. (a) P. L. Hagelstein, 9th International Conference on Atomic Physics, Review of Short Wavelength Lasers, UCRL-92336 preprint, 1984; (b) P. L. Hagelstein, Review of Photo-pumped Short-wavelength Lasers, UCID 17629 preprint, 1977; (c) P. L. Hagelstein, Ph.D. Thesis, Physics of short wavelength laser design, UCRL-53100 preprint, 1981. 7. J. J. Rocca, Rev. Sci. Instrum., 1999, 70(10), 3799. 8. S. Suckewer and P. Jaeglé, Laser Phys. Lett., 2009, 6(6), 411. 9. D. M. Ritson, Nature, 1987, 328, 487. 10. D. W. Hafemeister, SPIE, 1984, 474, 102. 11. D. C. Eder, P. Amendt, L. B. DaSilva, T. D. Donnelly, R. W. Falcone, R. A. London, M. D. Rosen and S. C. Wilks, 4th International Colloquium on X-ray Lasers, UCRL-JC-117006 preprint, 1994. 12. C. Robinson, Aviation Week & Space Technology, February 1981, p. 25. 13. W. J. Broad, Teller’s War, The Top-secret Story behind the Star Wars Deception, Simon & Schuster, New York, 1992. 14. J. Nilsen, Quantum Electron., 2003, 33(1), 1. 15. J. Nilsen, Reminiscing about the Early Years of X-ray Laser, 2002, UCRL-JC-148426. 16. (a) N. Bloembergen, et al., Rev. Mod. Phys., 1987, 59, S1; (b) R. J. Smith, Science, 1985, 230, 646. 17. R. A. London, M. D. Rosen, M. S. Maxon, D. C. Eder and P. L. Hagelstein, J. Phys. B: At., Mol. Opt. Phys., 1989, 22, 3363. 18. D. L. Matthews, et al., Phys. Rev. Lett., 1985, 54, 110. 19. E. N. Avrorin, V. A. Lykov, P. A. Loboda and V. Yu. Politov, Laser Part. Beams, 1997, 15, 3. 20. D. C. Eder, et al., Phys. Plasmas, 1994, 1(5), 1744. 21. T. S. Axelrod, Phys. Rev. A, 1976, 13, 376. 22. T. S. Axelrod, Phys. Rev. A, 1977, 15, 1132. 23. H. C. Kapteyn, Appl. Opt., 1992, 31(24), 4931.

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24. F. N. Chukhovskii, U. Teubner, I. Uschmann and E. Förster, Laser Part. Beams, 2000, 18, 49. 25. W. T. Silfvast, J. J. Macklin and O. R. Wood II, Opt. Lett., 1983, 8, 551. 26. P. L. Csonka and B. Craseman, Phys. Rev. A, 1975, 12(2), 611. 27. K. Lan, E. E. Fill and J. Meyer-Ter-Vehn, Europhys. Lett., 2003, 64(4), 454. 28. S. Jacquemot, K. Ta Phuoc, A. Rousse and S. Sebban, X-ray Lasers 2006, Springer Proc. Phys., 2006, 115, 321. 29. L. M. Chen, et al., Sci. Rep, 2013, 3, 1912. 30. N. Rohringer, et al., Nature, 2012, 481, 488. 31. C. Weninger, et al., Phys. Rev. Lett., 2013, 111, 233902. 32. C. Weninger and N. Rohringer, Phys. Rev. A, 2014, 90, 063828. 33. N. Rohringer and R. London, Phys. Rev. A, 2009, 80, 013809. 34. L. Casperson and A. Yariv, Phys. Rev. Lett., 1971, 26, 293. 35. J. Abdallah Jr, J. Cogan and N. Rohringer, J. Phys. B: At., Mol. Opt. Phys., 2013, 46, 235004. 36. V. Kimberg and N. Rohringer, Phys. Rev. Lett., 2013, 110, 043901. 37. V. Kimberg, S. B. Zhang and N. Rohringer, J. Phys. B: At., Mol. Opt. Phys., 2013, 46, 164017. 38. V. Kimberg, S. B. Zhang and N. Rohringer, J. Phys.: Conf. Ser., 2014, 488, 012025. 39. M. Beye, et al., Nature, 2013, 501, 191. 40. H. Yoneda, et al., Nature, 2015, 524, 446. 41. F. T. Arrechi, G. P. Banfi and A. M. Malvezzi, Opt. Commun., 1974, 10(3), 214. 42. Y. L. Stankevich, Phys.-Dokl., 1970, 15, 4. 43. R. C. Elton, Appl. Opt., 1975, 14(9), 2243. 44. N. Rohringer and R. Santra, Phys. Rev. A, 2007, 76, 033416. 45. L. Young, et al., Nature, 2010, 466, 56. 46. P. Glatzel and U. Bergmann, Coord. Chem. Rev., 2005, 249, 65. 47. X-Ray Absorption and X-Ray Emission Spectroscopy, Theory and Applications, ed. J. A van Bokhoven and C. Lamberty, Wiley, 2016. 48. U. Bergmann, et al., Stimulated X-ray Emission in Transition Metal Complexes, Proposal, No. LG89, LCLS CXI Experiment, July 9-12 2015, and related manuscript under review.

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Opportunities for Structure Determination Using X-ray Free-electron Laser Pulses Henry N. Chapman a

Center for Free-Electron Laser Science, DESY, Notkestrasse 85, 22607 Hamburg, Germany; bUniversity of Hamburg, Department of Physics, Luruper Chaussee 149, 22761 Hamburg, Germany; cUniversity of Hamburg, Centre for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany *E-mail: [email protected]

21.1  Introduction X-Ray free-electron lasers (XFELs) provide two distinct advantages for the investigation of the structures of biological molecules and their complexes. One is that the duration of the pulse sets the exposure time of an image or diffraction pattern that is recorded. When precisely synchronised with an optical laser pulse that initiates a reaction in the sample, for example, a series of measurements can thereby be made with femtosecond temporal resolution. More pertinent to the discussion in this chapter is the second advantage that the pulses can outrun many of the processes of radiation damage, allowing for X-ray exposures that are many orders of magnitude larger than possible with other sources, such as synchrotron radiation facilities. The destructive nature of these pulses when focused to high intensities to obtain the   Energy and Environment Series No. 18 X-Ray Free Electron Lasers: Applications in Materials, Chemistry and Biology Edited by Uwe Bergmann, Vittal K. Yachandra and Junko Yano © The Royal Society of Chemistry 2017 Published by the Royal Society of Chemistry, www.rsc.org

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strongest possible scattering signals from small samples poses restrictions to the types of measurements that can be carried out. There are two classes of imaging experiment under such conditions: imaging of unique objects in a single flash, such as whole cells,1 organelles,2 chloroplasts3 or soot;4,5 and imaging of reproducible objects by building up information from many pulses from many individual samples.6–9 For complex biological objects, from macromolecules to whole cells, an understanding of the structure and function of those objects at fine length scales requires a three-dimensional (3D) image that is directly relatable to the structure. Any two-dimensional (2D) image of a 3D object formed by coherent scattering consists of Fourier spatial frequencies of the object’s electron density that lie on the 2D manifold in reciprocal space known as the Ewald sphere. This does provide some depth information, but the wavefields due to out-of-focus structures interfere and give rise to contrast in the image just as strong as features that are in focus, as demonstrated in Figure 21.1, which may prevent the proper interpretation of that image. If the resolution is low enough, the image is approximated by a projection through the object. But as spatial resolution is improved, the depth of focus reduces rapidly as the square of the transverse resolution length for a given wavelength. For 1 nm resolution with 8 keV photons, which would be good enough to identify macromolecules in the cell, the depth of focus is only 7 nm, and any structures outside of this depth will cause strong uninterpretable speckles in the image. Avoiding this contamination requires incoherent imaging, such as is possible in fluorescence imaging, confocal microscopy, or a complete tomographic imaging of the object. With the destructive pulses from an XFEL, we either have to collect many tomographic views of an object

Figure 21.1  The  simulated 2D coherent image of the 3D distribution of 20 nm diameter spheres (representing ribosomes in a cell) cannot generally be interpreted, due to out-of-focus information interfering to produce strong contrast that does not resemble the structure (a). This stems from the fact that only information on a 2D manifold of reciprocal space, the Ewald sphere, is obtained in such an experiment. The deficiency can be overcome by recording coherent images or diffraction in various orientations to obtain a 3D image, one slice of which is shown (b), or to carry out incoherent imaging (c). The simulations assumed a wavelength of 0.1 nm, a transverse resolution of 1 nm and a depth of focus of 10 nm.

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in a single shot (the only choice for unique objects) or acquire those views in a serial fashion from many identical objects.11 In both cases, the XFEL also brings the opportunity to freeze the motion of objects in time, hence giving the means to track those motions, and to measure a large number of objects in a short time to be able to capture rare or spontaneous events, analyse large cohorts, measure the dependence of structures on a large number of parameters or conditions, and to greatly increase the speed and ease to obtain macromolecular structures. It is therefore not only the peak brightness of the XFEL that brings new capabilities to X-ray imaging but also the average brightness. With tens of thousands of pulses delivered per second, the European XFEL and the Linac Coherent Light Source II (LCLS II) will enable dramatic new opportunities.

21.2  Outrunning Radiation Damage Imaging at atomic resolution requires radiation of angstrom wavelengths or shorter, giving X-rays or electrons as viable possibilities.12 This radiation is energetic enough to ionise matter and the very act of forming an image leads to unavoidable absorption of energy in the sample, even if the contrast of the image is formed purely by elastic scattering. In X-ray crystallography, for example, the measured signal (the diffraction pattern) is formed by elastic scattering, which has a cross section for photons of 6 keV energy (2 Å wavelength) of 5.8 × 10−16 µm2 = 5.8 × 10−8 Å2 for a carbon atom.13 Unfortunately, photoabsorption takes place with a much higher cross section of 2.2 × 10−6 Å2 per carbon atom, meaning that for every photon that contributes to the diffraction pattern, 38 photons are absorbed by other C atoms in the sample with a combined energy of 228 keV. The situation is much more favourable for imaging with electrons, where only 60 eV of energy is absorbed per elastic scattering event when using electrons of 300 keV energy, where microscopes often operate.12 The degree of structural change (i.e., damage) during the exposure depends on the amount of energy absorbed per number of atoms, termed the dose, measured in Gray (1 Gy = 1 J kg−1). This structural change evolves as various processes take place, and thus many of the consequences can be avoided using pulses that are shorter than the timescales that atoms move, as driven by those processes and dependent on the inertia of those atoms. Photoelectrons, essentially created immediately on photoabsorption, carry enough energy to collisionally ionise hundreds of other atoms in a cascade that lasts tens of femtoseconds, leading eventually to heat generation, broken bonds, mobile radicals and solvated electrons that interact with reactive components of the molecules in the sample. Auger electrons emitted by the photoionised atom also contribute to the cascade, after a delay of hundreds of attoseconds to several femtoseconds depending on the atomic species. When every atom in the sample is ionised, the Coulomb forces on atoms will cause displacements of 0.1 Å in about 10 fs, depending on the atomic species and its neighbouring atoms (see ref. 14 for a review). When using long exposures, as conventionally carried out in a crystallography

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experiment at a synchrotron facility for example, structural changes are observed at resolutions of 3 Å at doses below 100 kGy, which can be extended to about 30 MGy by cryogenic cooling of the sample.15 The cooling limits the diffusion of the products of radiolysis and similar gains in tolerance may be attainable at room temperature with nanosecond exposures.16 The tolerable dose at long exposures is similar for electrons and X-rays, since the radiolysis processes are largely the same.12 For a typical protein (of stoichiometry H50C30N9O10S1 and density 1.35 g cm−3; ref. 17), the tolerable dose of 30 MGy is reached for an incident fluence of 130 photons Å−2 at 6 keV photon energy, which, given the cross section mentioned above, provides 7 × 10−6 scattered photons into the diffraction pattern per carbon atom and about 0.08 photons per 100 kDa protein molecule. For electrons, this dose is reached with an exposure of about 10 e Å−2, or about 350 scattered electrons for a 100 kDa molecule. This comparison between electrons and X-ray scattering experiments highlights a large difference in these techniques. Cryo-electron microscopy (cryo-EM) now routinely achieves the remarkable feat of constructing images of large macromolecules at near atomic resolution from many noisy images formed from only 0.05 electrons per atom, while keeping below the maximum tolerable dose for cooled samples. Just as with X-rays, this dose limit and the sample temperature could both be raised by using a pulse that outruns the processes of damage. However, space charge may prevent achieving the required electron fluence with short pulses.18 While sub-picosecond electron pulses have been created with upwards of 106 electrons, focusing these to a spot less than 300 Å diameter (to match the cryo-EM fluence) has not been achieved. (Ultrafast electron diffraction is certainly possible using samples of larger extent.19) At the coherent X-ray imaging (CXI) instrument at the LCLS, femtosecond-duration pulses of 1013 photons can be focused to a spot size of about 0.2 µm, giving a fluence of 106 photons Å−2 and imparting a dose of 200 GGy to the sample. It is interesting that, in terms of the scattered signal, 0.05 photons per C atom (600 photons per 100 kDa molecule), this condition is essentially equivalent to that achievable by cryo-EM. This suggests that the goal of single-molecule diffractive imaging11 is indeed feasible and that the challenges in reaching this goal stem more from excessive noise in the measurement, due to scattering from more substantial objects such as mirrors and apertures in the beam-path rather than a single molecule, than due to insufficient signal. Measurements at LCLS and SACLA have demonstrated that electron densities of protein crystal structures obtained using XFEL pulses usually appear much better than counterparts elucidated using synchrotron sources, even for the same crystallographic resolution, including better definition of side chains and disulfide bridges20 without the reduction of metal centres.21 Pulse duration studies show that nuclear motion can be observed for longer-duration pulses22 and that the more highly charged states generated at heavier atoms lead to motion that does not proceed uniformly throughout the structure.23 Best results appear to be attained from pulse durations below about

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20 fs. At these timescales the concept of temperature loses its meaning, so there is no need to cryogenically cool the sample, which can therefore be measured under physiological conditions, giving access to conformational states or solvation conditions that may not be otherwise apparent. What is the physical limit of this concept of “diffraction before destruction”? Again, from the cross section of light atoms at 6 keV photon energy (e.g., 5.8 × 10−16 µm2 for C), a fluence of 1015 photons µm−2, corresponding to a dose of about 1 TGy, would be required to scatter as many photons from a protein molecule as there are non-H atoms in that molecule. However, the higher cross section for photoabsorption leads to a depletion of the number of bound electrons from which to scatter, so the total scattered counts will saturate. At these high intensities it is possible that a second photoionisation event takes place in an atom prior to Auger decay, producing a “hollow atom” whose absorption cross section is significantly reduced, frustrating further ionisation. Taking these into account, it has been predicted that incident intensities of 1015 photons µm−2 could give rise to about 0.1 scattered photons per atom, if delivered with a 1 fs pulse.24 Below fluences of 1014 photons µm−2 (100 GGy dose) and pulse durations below 100 fs, the number of scattered photons per atom is predicted to be linearly proportional to fluence.24 Although the total diffraction signal from an object scales with the total number of atoms in that object, the scattered photons are not uniformly distributed in the diffraction pattern. From well-known Guinier plots of scattering distributions of biological objects, diffraction patterns are generally much stronger at lower angles (i.e., lower resolution) due to constructive interference of waves scattering from atoms over the entire depth of the sample, with about one half of all photons (or electrons) scattered outside the central speckle scattering beyond 10 Å resolution for a large protein.12,25 Beyond this resolution, the average diffraction signal is approximately independent of scattering angle, due to atomicity of matter, until the form factors of atoms diminish the total scattering beyond about 1 Å. Periodic arrangements of multiple copies of objects lead to constructive interference in certain directions of the diffraction scattered from each object—Bragg peaks of crystals, for example. However, before discussing single-molecule diffraction and other geometrical arrangements of macromolecules that may lead to signal enhancements, and the question of how large a signal is required per diffraction pattern, we first consider other imaging modes besides those based on elastic scattering.

21.3  S  ingle Shot 3D Incoherent Imaging of Unique Objects At 6 keV photon energy, the inelastic (Compton) scattering cross section is σC = 2.2 × 10−16 µm2 = 2.2 × 10−8 Å2, which is 1% of the photoabsorption cross section (mentioned above) of σA = 2.2 × 10−14 µm2 = 2.2 × 10−6 Å2 (ref. 26). At higher photon energies, Compton scattering becomes the dominant

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−16

2

interaction. For example, at 30 keV, σC = 3.3 × 10 µm for carbon, which is three times larger than photoabsorption (a convenient plot of carbon cross sections is given in Figure 6 of ref. 27). In these incoherent scattering processes, the atom takes up energy, which is then released by ejection of an electron. This energy is either the entire photon energy E (in photoabsorption) or a fraction given by:   

  

El E 

k  1  cos2 

1  k  1  cos2 

,

(21.1)

where k = E/mc2 is the photon energy in units of the electron rest energy of 511 keV and 2θ is the scattering angle of the photon.26 The phase of the photon or electron bears no relation to the incident photon unless the emission is stimulated (an intriguing possibility not discussed here further, but see ref. 28). Forming an image by Compton scattering, X-ray fluorescence or photoelectrons therefore requires localising the origin of these interactions (and hence mapping the distribution of matter) by using a lens to form an image of the sample on a detector, in direct analogy to optical fluorescence microscopy. As in the optical case, the signal to noise of such an image benefits from the lack of a background signal (that would generate noise due to counting statistics of a large number of photons) and energy filtering of the emission could be used to discriminate incoherently emitted photons from elastically scattered photons to improve contrast. The best hard X-ray lenses have achieved about 10 nm resolution, but it appears feasible to reach 1 nm resolution or better in the near future.29 It is worth mentioning that the energy deposited into the sample per interaction is much less than for coherent scattering, since the absorption event is the interaction. A plot of the number of interactions per deposited energy is given in Figure 7 of ref. 27 and reproduced here in Figure 21.2, showing that, for soft X-rays, photo­ absorption events occur for the least deposition of energy and Compton scattering is the most “dose efficient” for photon energies above about 15 keV. Taking into account the energy imparted to the sample by inelastic scattering, the saturating dose of about 1 TGy will be reached at a 50 times higher fluence of 5 × 1016 photons µm−2 at 30 keV photon energy than for 6 keV, giving rise to over 10 inelastic scattering events per atom! Obviously, this process will also saturate, since there are not that many electrons in light atoms and a single scattered photon per atom might be achieved at a dose of 100 GGy. At 30 keV photon energy this would require a substantial pulse fluence of about 25 J µm−2 that current XFELs cannot provide (with any usable focal spot size), but it is notable that there is room to increase short-wavelength XFEL pulse energies by several orders of magnitude before the sample interaction becomes the limiting factor. Although not isotropic, the inelastically scattered photons are distributed over 4π sr, requiring optics of high collection solid angle in order to make full use of the exposure of a sample. A lens with 1 nm resolution (useful for identifying macromolecules in a living cell) at 0.5 Å wavelength has a numerical

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Figure 21.2  Number  of reactions occurring in carbon per deposited eV of energy for elastic scattering, inelastic scattering and photoabsorption. These reactions can be localised respectively by coherent diffraction or imaging, incoherent imaging, and photoemission or photoelectron imaging. For a given dose, the number of reactions per eV is proportional to the number of reactions per atom. The right–hand axis gives this for a dose of 1 TGy, assuming no saturation in the number of events that occur per atom. (Adapted with permission from ref. 27. © Inter­ national Union of Crystallography.)

aperture NA = 0.05, or a solid angle of 6 × 10−4 sr giving the opportunity to array 20 000 such lenses around the full sphere. For monochromatic illumination at this wavelength, Compton-scattered light into a given lens aperture would not vary by more than 0.4% at a scattering angle of 90°, and thus chromatic aberrations would not degrade the image (as occurs in electron microscopy, requiring energy filtering). This scheme of incoherent imaging gives the desirable capability to collect images at multiple views in a single destructive XFEL pulse, which can then be used to attain a full 3D image of a non-reproducible object. To save on the large number of detector pixels that would be needed for the 20 000 individual images, many neighbouring lenses can be combined to generate a common image, which is to say the images would be formed from larger lenses that are not diffraction limited. A schematic of this 3D single-shot Compton microscope is given in Figure 21.3. As an example, lenses with a collection solid angle of 6 × 10−2 sr and positioned at a scattering angle of 90° could collect about 3 × 10−3 of the total number of inelastic photons scattered per atom. Since for proteins there are about 2200 atoms in the 1 × 1 × 20 nm3 resolution volume of each 2D

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Figure 21.3  3D  single-shot imaging with a single FEL pulse could be achieved

using lenses to form incoherent images based on Compton scattering. Images can be combined tomographically (using long depth of focus provided by short wavelength) or by combining images at various focal planes (using short depth of focus from high NA lenses).

image, the signal and contrast of images could be large, consisting of several photons per resolution element per image per shot. It would certainly be a technical feat to array 100 or 1000 such lenses around the sample to image a common volume at different views. Given dose fractionation in tomography,30 the total signal to noise per voxel will increase in proportion to the number of images and should allow a resolution of 1 nm in all three dimensions. With the saving gained in pixels (and relying upon the inevitable future increase in detector capabilities), energy discrimination could be achieved with a detector pixel spacing in the image smaller than the resolution of the magnified image so that there are more pixels than photons in the image. Since the photon count will be less than one on average, the photon energy could be determined in each pixel from the generated charge (typically to a resolution of about 100 eV) before assembling a down-sampled image. Ideally the pixels would be small (say, 1 µm) to limit the required magnification to 2000 to achieve 1 nm resolution. A possibility to reach even higher resolution would be to apply superresolution methods of optical fluorescence microscopy, such as structured illumination.31 Here, the sample is illuminated with a fringe pattern that is of smaller period than the lens resolution, generated by interfering two waves. The lens does not resolve these fringes, but the incoherent image recorded

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by the lens is actually a Moiré pattern formed by the multiplication of the fringe pattern with the structure. Spatial frequencies of the structure are downshifted into the lens aperture, which can be interpreted accordingly. Some frequencies of the structure will be missed by this sinusoidal illumination, even when combining views from many directions. In optical structured illumination, the fringe pattern is usually varied to obtain full coverage of frequencies, but for single-pulse destructive imaging it may instead be possible to simultaneously generate multiple fringe patterns at different wavelengths. With a sufficient difference in photon energies it should be possible to distinguish the Compton scattering due to these incident colours using the same energy discrimination technique mentioned above. While high-resolution X-ray lenses are currently challenging, lenses for imaging electrons at atomic resolution are available. As such, atomicresolution imaging could be achieved by imaging the emitted electrons from the sample. Such photoelectron electron microscopy (PEEM) has not been attempted using XFEL pulses, perhaps because images may be disrupted by space charge when a significant fraction of atoms in a small sample are ionised. A more promising approach is to record structural information from the scattering of the photoelectrons from neighbouring atoms as they propagate away from their origin. Due to the large scattering cross sections for electrons, the angular distribution of the emitted photons will exhibit some variation due to interference of the secondary scattered waves with the original wave, which can be considered as a hologram.32 A measurable signal can be obtained by accumulating the photoelectron hologram from many identical molecules, which ideally are oriented in a common frame of reference such as by laser alignment.33 Due to the holographic source being located inside the structure of interest, the holographic information can be used to obtain the full 3D structure only for relatively simple molecules with limited resolution in directions away from the emitter. Multiple scattering effects limit the size too. Nevertheless, with the use of XFEL pulses synchronised to alignment and photoexcitation laser pulses, this method could offer a way to provide structural snapshots of small molecules at atomic resolution undergoing reactions.

21.4  Imaging Reproducible Objects Imaging biological materials at atomic resolution requires averaging over many copies of identical objects to attain sufficient signal. For X-ray imaging, this has been carried out very successfully by crystallography, where commonly more than 109 molecules are arrayed in a lattice, which is illuminated with sufficient coherence to give rise to constructive interference, in the directions of Bragg peaks, of the diffracted waves from each molecule. These Bragg peaks can usually be easily distinguished from the background. Finding the conditions to crystallise a particular macromolecule or complex can oftentimes be rather difficult and is recognised as one of the main bottlenecks in structure determination. With the development of XFELs came the realisation

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that it may be possible to obtain measurable diffraction signals from single uncrystallised molecules to atomic resolution11 and that the patterns could be strong enough to relate to other patterns from identical objects recorded in unknown orientations.34 Procedures for averaging single-molecule diffraction in the molecule’s frame of reference have been heavily inspired by approaches in cryo-EM. Early schemes considered classifying noisy diffraction patterns by similarity, averaging within classes and then determining the relative orientations of these classes by detecting common lines of intersecting Ewald spheres. Recently, the expansion–maximisation–compression algorithm (EMC) was developed to average all patterns into a 3D volume35 (see chapter 4). Briefly, a guess of the 3D diffraction intensity distribution is improved by extracting from it the individual 2D patterns, which would be observed, then finding the most likely match of actual measurements to these patterns. The measurements are then used to form an update of the 3D distribution based on the orientations found by matching. As this procedure is iterated, the distribution converges to one that is consistent with all measurements (and all their intersections). Experimental demonstrations have been made using noisy radiographs of an object randomly rotated about one axis to obtain a tomographic reconstruction36 and diffraction from randomly oriented crystals37,38 at signal levels of only about 200 photons per frame. The demonstrations used a weak source and a strongly scattering sample—the findings are just as valid for a strong source and a weak sample, with the only caveat that background contributions (such as fluorescence and parasitic scatter from beamline components) scale with source fluence. That the demonstration samples were crystalline and producing Bragg spots had little effect on the effectiveness of the algorithm, since the very sparse non-zero pixel values mainly consisted of single photon counts. Serial femtosecond crystallography (SFX), discussed by several authors in the Sample Delivery Methods section of this book, is one of the most-used techniques at XFELs. The experiments are usually carried out at signal levels where Bragg peaks are indeed distinguishable from noise. The method relies upon the ability to average signals from many crystals to obtain precise structure factor estimates from “still” snapshot diffraction patterns, but increasing crystal size and quality allows for a more efficient averaging over molecules in a single shot. Nevertheless, when only small crystals are available, or with large but disordered crystals (as discussed below), it should often be possible to increase the resolution of the measured diffraction beyond what is observable in a single crystal on a single shot. The strong observable Bragg peaks at low resolution can be indexed, determining lattice constants and the orientation of that lattice. From these, the locations of weaker peaks can be predicted and then these regions can be averaged with those from other patterns that were predicted to contain a peak with the same Miller index. With enough averages, the peak emerges from the noise. This approach was recently demonstrated on granulovirus particles, which consist of a viral body surrounded by a crystalline shell of the protein polyhedron.39 The volume of the crystalline part was only 0.01 µm3, less

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than 10 000 unit cells in total. Measurements at LCLS gave some observable Bragg peaks to 2.5 Å resolution, but this was improved to 2.3 Å by averaging over 80 000 crystals, giving ∼3000 averages for peaks at this resolution.39 The approach can give even more dramatic improvements in resolution for 2D crystals, such as membrane proteins.40 As crystal size diminishes, more patterns are required to obtain a total signal (proportional to the number of patterns) in excess of noise, usually dominated by the counting statistics of the background (proportional to the square root of the number of patterns). At current XFELs, with pulse rates of 120 Hz or less, it is only practical to obtain about 100 000 patterns (usually much less) in a shift and it is infeasible to spend 10 shifts in order to give three times better statistics. In such experiments it is therefore imperative to reduce background sources, since halving the background would reduce background noise by a factor 1 2 , equivalent to doubling the crystal volume. Several low-background sample delivery schemes have been used at XFEL sources, including micron-diameter liquid jets,41 single-crystal Si support structures42,43 or graphene membranes,44 and aerosol beams.45,46 As XFEL sources reach higher repetition rates, the averaging strategy becomes more effective, but then the delivery schemes must operate at high enough speeds. Assuming a 50 µm displacement between measurements and a frame rate of 100 kHz, the sample must be delivered faster than 5 m s−1, which aerosol and jet techniques can accomplish. The full 4.5 MHz rate of the European XFEL needs 100 m s−1, faster than some aerosol beams.46 Almost arbitrarily high scan speeds could be achieved by scanning the beam instead of the sample, done simply using grazing incidence reflection from a plane mirror that is tilted at a constant angular velocity (Figure 21.4). For example, a

Figure 21.4  High  throughput diffraction or crystallography experiments can be carried out using samples prepared on fixed supports and with MHz XFEL pulse rates simply by scanning a mirror with a fast enough angular velocity. The sample is advanced in the perpendicular direction (here, vertically) in between pulse trains. The method has the advantage of decreasing the dose to the beamstop.

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scan of 352 points (the buffer size of the AGIPD detector ) with 50 µm steps requires scanning the beam by 17.6 mm in 78 µs on a stationary target, or by 22 mrad s−1 if the mirror was placed 10 m away from the sample. The beam-scan method would require a detector with a slotted gap instead of the usual square hole used for SFX measurements, and each pattern in the scan would be shifted on the detector. The deflected beam would sweep out an even longer distance on a beamstop downstream of the slotted detector, but this would actually reduce dose in the beamstop by spreading out the energy of the pulse train, or a cylindrical mirror could re-image the deflection mirror onto the beamstop to reduce the beam width at the beamstop. The above discussion illustrates that serial diffraction experiments benefit from the highest possible average brightness in addition to the highest peak brightness. A higher frame rate of patterns from a constantly replenished sample completes the experiment in a shorter time with less sample consumption. The AGIPD47 at the European XFEL will record up to 3520 patterns per second, almost 30 times faster than possible at the 120 Hz LCLS. For samples similar in size to most that have been studied to date at XFELs, this speed-up of 30 times could have dramatic consequences. Many of these samples only require a few thousand patterns to obtain complete and accurate high-resolution diffraction data, which would only take seconds of measurement time, from crystal slurries of much less than 1 µL volume. Series of such measurements become possible, such as many electron density maps obtained at specific times after triggering a reaction, or structures of a target molecule associated with thousands of different molecule fragments in drug discovery. The high-energy upgrade of the LCLS-II, using a superconducting linac, will provide even greater average brightness from equally spaced pulses of up to megahertz rates, requiring detectors that can store frames at higher average rates than the AGIPD. Vetoing frames from pulses that did not hit a crystal will give effective use of these detectors. For more challenging samples, what requires a shift at 120 Hz could be completed in about 25 minutes at the European XFEL. By collecting 30 times more data, a given precision of structure factors can be reached using smaller crystals of only 20% the volume. As compared with the granulo­virus crystals measured at LCLS,39 it should be possible to obtain ∼2 Å resolution structure from crystals of about 2000 unit cells in volume (0.002 µm3), delivered in a liquid jet, with 12 hours of measurement at 3520 frames per second. High-resolution data could be aggregated from 2D crystals—these would contain a few thousand unit cells per square micrometer, the size of the focused X-ray beam. One problem with using crystals so small and invisible to an optical microscope is the lack of fast and accurate diagnostics needed to feed back to crystal screening experiments. Electron microscopy and powder diffraction at a laboratory source are two means to determine the existence of nanocrystalline material,48 but both are rather time consuming and require additional preparations not needed for XFEL diffraction experiments. Given that the most reliable way to determine if a sample yields measurable X-ray diffraction

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at an XFEL is to actually pass it through an XFEL beam, it is worth considering this as the ultimate screening method. Again, high repetition rates make this feasible, since sufficient confidence in the diffractability of a sample could probably be made in less than 10 000 frames, or 3 s, allowing 1000 conditions to be screened per hour. Such an approach only makes sense in a fully automated system, which can be envisioned using fluidic sample delivery controlled by a high-performance liquid chromatography (HPLC) system. Points in the crystallisation phase space could be accessed using microfluidic approaches, for example.49 Sample volumes in the liquid lines could be separated by immiscible oil, although some samples may require rinsing steps or be restricted to separate delivery systems. Alternatively, a robot could pipette 1000 conditions onto different locations on a small chip that is rastered through the beam (such as in Figure 21.4). Once a crystal “hit” is recorded, the preparation conditions could automatically be repeated on larger volumes and run long enough to acquire data for a structure determination. This level of automation is one of the long-term goals of the second experimental endstation at the single particles, clusters and biomolecules (SPB)/SFX beamline50 of the European XFEL. This endstation uses the spent beam from the first measuring station where the undiffracted beam passes through a hole in the diffraction detector. Rather than dumping this beam into a beamstop it will be refocused and available for measurements to be run in parallel. The feasibility of running parasitic measurements this way has been tested at the LCLS.51 Ideally each station should be confined in a separate hutch. To be useful without impacting the upstream experiment, the downstream instrument must have a high level of control from outside the common experimental hutch, since any access to the hutch would interrupt measurements at the other station. This includes the ability to change nozzles, or recover from blockages of liquid lines. The combination of high-speed screening with the ability to obtain complete diffraction data in seconds for crystals of about 1 µm3 volume (minutes or hours for significantly smaller sized crystals) could provide a pipeline for high-throughput structure determination, along the lines of the protein structure initiative or for large-scale fragment screening. The paradigm of serial crystallography enables measurements of samples covering many orders of magnitude of crystal size and quality without having to change the procedure or experimental setup, while providing structures free from the effects of radiation damage.52

21.5  Continuous Diffraction from Single Molecules Returning to the consideration of single-molecule diffraction that was discussed in Section 21.2, there has been recent progress in this quest, spurred by studies of algorithms such as EMC, which demonstrate the ability to aggregate diffraction data from randomly oriented reproducible objects with less than 200 scattered photons per pattern,37 a steady improvement of low-background particle delivery techniques, and a concerted collaborative effort at

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LCLS to overcome remaining technical challenges to the technique—obtaining enough diffraction patterns and reducing background.53 As noted above, the numbers of scattered photons are on par with the total number of electrons in a cryo-EM image, further supporting the feasibility of the approach. Besides avoiding the need for crystallisation, these efforts bring the promise of obtaining de novo 3D electron density images of macromolecules—that is, atomic-resolution images obtained from the diffraction data alone without relying upon structural models or restraints. The reason for this, detailed in chapter 4, is that the continuous diffraction pattern of a single non-periodic object carries significantly more information than diffraction of a crystal of that object. A periodic arrangement of molecules gives rise to strong constructive interference of the diffracted wavefronts from each molecule but only at discrete positions, the Bragg peaks. The information content can be compared in real space by taking the Fourier transform of the diffraction intensities, giving the autocorrelation map (or 3D pair-correlation function) of the structure. The autocorrelation map is centrosymmetric, and for a crystal has the same periodicity as the crystal itself. Thus, without further assumptions of the contents of the unit cell (such as the volume of featureless solvent), there is only half the necessary information, proportional to the volume of half a unit cell, to describe the object. This is the origin of the phase problem in crystallography. For a single isolated object, the autocorrelation map extends from the origin to a boundary set by the largest displacements of points in the object, given by its diameter. In this case, for a general convex object there is therefore four times the number of independent measurements to describe the object. Thus, the continuous diffraction from a single isolated object carries enough information to decode the diffraction phases, which are needed to synthesise an image from the diffraction amplitudes by Fourier transformation. These phases are obtained through iterative phasing algorithms54 that enforce this synthesis to yield zero density between the boundary of the object and the larger boundary of the autocorrelation function, thereby recovering a 3D image of the electron density. Crystallisation provides a huge amplification of the molecular diffraction at the cost of loss of information. However, there are other ways to design experiments that may give sufficiently sampled diffraction stronger than the faint signals obtainable from a single molecule. For example, a random, rather than periodic, arrangement of molecules will give rise to an incoherent sum of the continuous single-molecule diffraction, or an amplification equal to the number of illuminated molecules. This requires that most molecules are oriented in one or very few directions, since otherwise only an orientational average will be obtained. Alignment of molecules in the gas phase can be achieved using a laser pulse,55 as demonstrated in aligned-molecule diffraction experiments at the LCLS.8 Since the alignment axis is fixed in the laboratory frame, and a molecular beam refreshes the sample on every pulse, data can be accumulated over many pulses until the required signal level is reached, before changing the angle to obtain 3D diffraction data in a rotation series. Thus, a fast detector is not required. The feasibility of this experiment

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depends on the average brightness of the X-ray source, the laser power, the molecular density and the density of any background gas. The continuous diffraction is measurable in a gas of oriented identical rigid objects because of the lack of long-range order that otherwise gives rise to the summation of diffraction amplitudes in phase for particular but limited scattering directions. Another situation that creates this condition is a crystal with translational disorder, at least for length scales smaller than the disorder length. It is well appreciated that random displacements of rigid objects from ideal lattice positions, with a mean square displacement σ2 in each direction, will give rise to the modulation of Bragg intensities by the Debye–Waller factor exp(−4π2σ2q2), where q = 2 sin θ/λ = 1/d for a wavelength λ and scattering angle 2θ, and where d is the resolution length. That is, for high scattering angles corresponding to resolution lengths, d ≪ σ, Bragg peaks are not formed and instead the incoherent sum of the continuous diffraction pattern of the rigid units becomes visible, modulated by a factor 1 −exp(−4π2σ2q2), which is 0 at q = 0 and asymptotes to unity at high q. Macromolecular crystals often only give Bragg-peak diffraction to limited scattering angles, attributable to many kinds of disorder including such displacements of the molecules. For large macromolecules that form crystals with only tenuous intermolecular contacts and solvent filling the interstitial spaces, it is reasonable to expect that the disorder is dominated by random translations, as would be the case in the order–disorder phase transition from a crystal to a nematic liquid crystal. Recently, continuous diffraction was observed from crystals of photosystem II extending in resolution to 3.5 Å, beyond the 4.5 Å resolution of observable Bragg peaks56 (see Figure 21.5). It was found that the Fourier transform of this continuous diffraction yielded an autocorrelation map consistent with that of the photosystem II dimer complex, supporting the hypothesis of the dimer as the rigid unit in a translationally-disordered lattice. The continuous diffraction could be phased by an iterative transform algorithm, using a fixed support volume as a real-space constraint, created by blurring out an initial electron density map obtained by refining a model using the Bragg intensities. The 3D image obtained by the continuous-transform phasing showed much clearer definition of structural elements such as helices, even though the phasing algorithm had no knowledge of such structures. It is thus seen that translational disorder in a crystal not only extends diffraction resolution far beyond Bragg peaks—reducing the need to obtain highly ordered crystals—but also that the overdetermined continuous diffraction allows iterative phasing methods to be used to obtain a 3D image of the molecule, without the need for a structural model. Although the continuous diffraction is weak, as compared with Bragg peaks from an ordered crystal, it is not insignificant. Indeed, as can be seen by the conservation of energy, that beyond the Bragg peaks where the Debye–Waller factor is essentially zero, the total continuous-diffraction scattered counts within a small q range is equal to the integrated Bragg counts in the same range for a perfectly ordered crystal. The difference is that the continuous diffraction is apportioned to many more detector pixels, and thus obtaining low background is

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Figure 21.5  Weak  continuous diffraction (a) was observed in individual snapshot

diffraction patterns recorded from photosystem II crystals at the LCLS.56 (b) Merging patterns in the 3D frame of reference of the lattice increases the signal to noise of the continuous diffraction, which extends beyond the Bragg peaks. (c) The continuous diffraction could be phased using an iterative phasing algorithm to obtain a 3D image of the electron density of the photosystem II dimer. A detail of two chlorophylls of the dimer shows the improvement obtained from performing a structural refinement using the Bragg data only (to a resolution of 4.5 Å) (d) as compared with using the Bragg and continuous diffraction together (to a resolution of 3.5 Å) (e). Reprinted by permission from Macmillan Publishers Ltd: Nature (ref. 56). Copyright 2015.

key to measuring the continuous diffraction, as well as the ability to measure at high doses with short pulses. A potentially fruitful approach to crystallo­ graphy may be to develop methods to induce translational disorder in otherwise well-ordered crystals. Other methods of inducing common orientations of identical objects involve using static or pulsed electric or magnetic fields, attachment to a structured membrane or surface, or flow alignment of elongated objects in a liquid jet. Most of these methods will induce one-dimensional (1D) alignment—i.e., the object is not constrained in its rotation about the alignment axis. In terms of applying the EMC algorithm, for example, this could be considered a better situation than uniformly random orientation, and several proof-of-principle experiments show the feasibility of recovering the 3D structure factors from patterns of single 1D-aligned objects.36 Increasing signal by illuminating many such objects at once would reduce the

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measurement to a 2D fibre-diffraction pattern, which does not necessarily contain sufficient information to retrieve the 3D structure.57 However, in this case it may be possible to obtain the 3D structure factors by examining correlations between intensities measured in single patterns. Considering the orientation axis parallel to the incident X-ray beam,58 we see that diffraction intensities in two different detector pixels formed by photons that scattered from the same object will be correlated, as given by the diffraction pattern of that object, whereas scattering from different objects will not be. The intensity–intensity correlation function formed by multiplying the 2D diffraction pattern of a single object with a rotated copy of itself is independent of the in-plane orientation of the object, and thus performing this angular crosscorrelation on the measurement will provide the single-object cross-correlation map enhanced by the number of objects, added to an angle-independent background signal due to correlations between objects (proportional to the square of the number of objects).59,60 With high enough intensities to ensure multiple photons scattered per object, and with enough averages, it should be possible to extract the single-object cross-correlation function above the noise of the background. This condition, and the need to freeze any rotational motion during the exposure, requires XFEL pulses. The method can be extended to unoriented particles and experiments show much promise for determining the structures of identical objects61 or discerning local ordering in amorphous structures.62,63 A further strategy to boost the signal in a single-particle diffraction experiment is to make the object more massive, such as by joining it to a reference object. If the structure of the reference is accurately known, then the interference between the diffraction of the unknown and reference structures can be considered as a hologram. By tethering the reference far enough away from the object, so that the autocorrelation maps of the reference or object do not overlap with the cross correlation map of these objects, then the cross correlation can be isolated, from which it is possible to deconvolve the reference to obtain the unknown object.64,65 Making the reference object much larger than the object of interest boosts the overall signal, but also increases the noise in the cross term. In practice, there is a great advantage to the signal boost,65–67 perhaps because this diminishes the influence of background and detector noise. This is somewhat analogous to obtaining the structure of an amino acid by measuring the diffraction of an entire macro­ molecule. Iterative phasing using a positivity or a support constraint can improve the reconstruction, even if the initial model of the reference structure is not accurate. A suitable tether material is DNA, which can be fabricated in arbitrary structures and joined to protein molecules.68 In addition to providing the holographic reference, a DNA tether could also be used as a means to orient particles.69 One application of this holographic principle was to use the volume and boundary of a superfluid helium droplet as the reference to reconstruct internal Xe-doped vortices from snapshot coherent diffraction patterns measured at the LCLS.70,71 The approach is also used in time-resolved crystallography, where the Bragg diffraction is proportional to

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the Fourier transform of the average of the electron density of the excited and non-excited molecules.72,73 Intriguingly, a similar superposition occurs for a gas of laser-excited iodine molecules74 where the interference now occurs from individual molecules that exist in a superposition of states.

21.6  Conclusion Assuming that scattering reactions saturate at a dose of about 1 TGy in biological materials (equivalent to an absorption of about 75 keV atom−1), we see that image formation at high resolution is ultimately limited by the number of such reactions that can occur per atom. This number can be optimised by choosing the photon energy and the type of reaction; the situation for carbon is shown in Figure 21.2. There are three interactions to choose from: photoabsorption, as localised by imaging the photoelectrons or X-ray fluorescence photons with a lens; coherent scattering, as localised through interference in a diffraction experiment; and incoherent scattering, as localised with a lens, similar to fluorescence microscopy, or by intensity correlations.75 At low incident photon energies the photoabsorption reaction clearly has the benefit. Since photoelectron yields are greater at low photon energies and light elements than fluorescence, the photoelectrons would give the strongest signals, at a level exceeding an electron per atom at the saturating dose. However, space charge at such high intensities may prevent image formation, and photoelectron holography may be appropriate to image single particles at the level of one electron per molecule. For imaging unique objects, this then leaves Compton scattering as the most favourable, using photon energies of about 30 to 60 keV. With an array of lenses, a 3D image could be obtained in a single shot and with suitable lenses there would be enough signal at the saturating dose to reach 1 nm resolution. Atomic-resolution imaging requires localising more scattering events per atom than an atom can provide, so this can only be done by averaging over many identical structures. Crystallography and single-particle imaging do just that, with the latter having the desirable attribute that crystals are not needed. At the saturating dose, at an optimum photon energy of 10 to 20 keV, it should be possible to form diffraction patterns with more than 0.1 photons per atom, which is comparable to the number of electrons per atom in an image formed at the limiting dose of 30 MGy in cryo-EM. This implies that single-particle diffraction should indeed be feasible, even with some amount of background noise. More robust are diffraction experiments from aligned molecules, disordered crystals and arrangements that add reference structures to the object of interest. The power of the XFEL will not just be in the ability to form high-resolution images of biological structures at room temperature, but also from the sheer number of images that can be acquired in a short time. Sources that provide thousands to millions of pulses per second open up opportunities not possible with other instruments. Of course, handling the high repetition rate is a challenge for detectors and instrumentation (one approach is given in Figure 21.4), but once mastered these will provide a pipeline for

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high-throughput structure determination, the ability to carry out surveys of heterogeneous samples, sorting out structural elements or motifs and capturing rare events, or following the evolution of structures under a plethora of conditions or stimuli. The high rate will also be crucial for acquiring enough diffraction signal from streams of single molecules. We therefore see that the average brightness, proportional to the pulse rate, is every much as important for biological structure studies at XFELs as is the peak brightness and short wavelength.

Acknowledgements Support from the Helmholtz Association through program-oriented funds to DESY, and the DFG through the Gottfried Wilhelm Leibniz Program is acknowledged, as are helpful discussions with Kartik Ayyer, Alke Meents, Kanupriya Pande, and Saša Bajt.

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Chapter 22

Machine-learning Routes to Dynamics, Thermodynamics and Work Cycles of Biological Nanomachines Abbas Ourmazd University of Wisconsin Milwaukee, Kenwood Interdisciplinary Research Complex, 3135 N. Maryland Ave, Milwaukee, WI 53211, USA *E-mail: [email protected]

22.1  Introduction Many important biological functions are performed by Brownian nano­ machines—macromolecular assemblies, which are buffeted by and use energy from the thermal environment in their work cycles.1–6 Ideally, one would like to map the structural dynamics of such nanomachines over their free-energy landscapes, particularly the rate-limiting states far above the thermal bath (see, for example, ref. 7 and references therein). A deep understanding of the thermodynamics of biological machines and the conformational changes involved in their function will revolutionize our knowledge of key processes ranging from basic cell functions to pathological states. Unravelling the role of conformations in virulence, for example, is expected to lead to new strategies for fighting infection.   Energy and Environment Series No. 18 X-Ray Free Electron Lasers: Applications in Materials, Chemistry and Biology Edited by Uwe Bergmann, Vittal K. Yachandra and Junko Yano © The Royal Society of Chemistry 2017 Published by the Royal Society of Chemistry, www.rsc.org

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The notion that the most interesting aspects of function involve conforma­ tional change shifts the focus from a small set of discrete (often “trapped”) structures to a continuum of constantly changing ones. In essence, this notion recognizes that, in thermal equilibrium, a nanomachine assumes an abundance of conformational states, with those at higher energies occur­ ring less frequently. In fact, the number of times a conformational state is sighted yields the free energy of the state via the Boltzmann factor.8 This view naturally leads to the concept of a free-energy landscape specifying the energy associated with each conformational state. A point in this landscape is defined by the (mutually orthogonal) “reaction coordinates” governing function, with the free energy on the “vertical axis” (Figure 22.1). It is import­ ant to note that a sufficiently large number of snapshots of machines idling in equilibrium reveals the entire energy landscape, with the highest accessed energy corresponding to the conformation sighted only once in the dataset. Function is now equivalent to traversing a specific trajectory over the energy landscape. A movie of conformational changes along any trajectory over the energy landscape can be compiled without timing information. Energyefficient functions—work cycles—likely involve low-energy trajectories. Movies along highly populated low-energy, closed trajectories thus provide valuable insights into nanomachine work cycles.8 Timing information is required only when one needs to differentiate, for example, between “two steps forward, one back” and “two steps forward”, i.e., only when one needs to know the sequence of events in time. A Brownian nanomachine is constantly buffeted by the environment. This means any single trajectory of such a machine is subject to strong sto­ chastic effects, and thus irreproducible. A thermodynamically meaningful

Figure 22.1  Schematic  energy landscape. A free-energy landscape specifies the energy associated with each conformational state. A point in this land­ scape is defined by the (mutually orthogonal) “reaction coordinates” governing function, with the free energy on the “vertical axis”. In this example, the conformational state is governed by two reaction coor­ dinates, each representing a set of concerted changes in the machine conformation. A movie of the conformational changes over any trajec­ tory can be compiled.

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description requires averaging over homogeneous ensembles large enough to suppress the influence of stochastic events. Experimental datasets, in contrast, are often highly heterogeneous, com­ prising, for instance, snapshots of many individual machines, each in an unknown state and viewed in an unknown orientation. Statistically mean­ ingful analysis must therefore begin with extracting homogeneous ensem­ bles from heterogeneous data. Given the continuous nature of many types of heterogeneity, “clustering” approaches must be replaced with techniques capable of describing continuous changes in terms of orthogonal reaction coordinates. It is then possible to compile statistically meaningful averages over (nearly) homogeneous subsets, with each average pertaining to a partic­ ular state of the nanomachine. Modern experimental techniques routinely generate multi-terabyte data­ sets of snapshots. Each snapshot represents a projection, in the sense that only a subset of the governing parameters is measured. Following the preva­ lent precept that the best experiments are the most tightly controlled, much effort is devoted to constraining the number of degrees of freedom exercised by the system under observation, limiting them to those thought, for some reason, to be important. Machine-learning approaches, in contrast, extract rich information from snapshots of unconstrained systems in function, generating, for example, e-mail or Facebook postings. Machine-learning data analysis thus “follows the data”, in the sense that the vocabulary and grammar best suited to describing a system are extracted from the data, without preconceived notions or tight control of system variables. The vocabulary can consist of abstract memes,9 characteristic “empirical eigenfunctions”,10–14 or generalized principal com­ ponents.15,16 The grammar can consist of rules for handling the extracted vocabulary, e.g., through analysis on curved surfaces defined by the data.15 General means that extracting interpretable information from such analytical approaches remain elusive,17 and often heuristic. More recently, it has been shown that the injection of rather general constraints, such as the nature of possible operations on the system under observation, can provide a system­ atic route to extracting interpretable information from the analysis.18–20 The increasingly copious experimental datasets, particularly those stem­ ming from biological machines in function, are plagued by noise and/or timing uncertainty.21–24 And while the datasets can be very large, they can also be extremely sparse, because many of the important system states are rarely sighted. These factors can severely challenge machine-learning algo­ rithms,17,19,21 particularly when highly reliable information is required, as in scientific applications. The wide-ranging nature of the issues outlined above precludes an exhaus­ tive treatment here. The intention is to provide a conceptual outline of the application of graph-based geometric machine learning to biological nano­ machines, with emphasis on snapshots provided by XFEL diffraction25,26 and cryogenic electron microscopy (cryo-EM).27

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This chapter is organized as follows. Section 22.2 provides a conceptual outline of geometric machine learning. Section 22.3 addresses mapping the continuous conformations of biological nanomachines. Section 22.4 out­ lines the compilation of energy landscapes and conformational movies. Sec­ tion 22.5 shows how accurate dynamical (time-resolved) information can be extracted in the presence of substantial noise and timing uncertainty. Sec­ tion 22.6 concludes the paper with a short discussion of future prospects.

22.2  Geometric Machine Learning Here, I provide a conceptual description of the theoretical framework. More technical treatments are provided in ref. 18,19 and 28–30. The basis of the approach can be understood by considering, for example, snapshots of an object with three orientational degrees of freedom. As the object orientation is changed, the changes in the pixel intensities are a function of only three parameters. This imposes a strong correlation in the way the pixel intensities change with object orientation and can be used to determine the snapshot ori­ entations, and hence the three-dimensional (3D) structure of the object under observation.18,19,31–33 Specifically, a snapshot consisting of p pixels can be rep­ resented as a p-dimensional vector, with each component representing the intensity value at a pixel (Figure 22.2). The fact that the intensities are a func­ tion of only three parameters means that the p-dimensional vector tips all lie on a 3D hypersurface (“manifold”) in the p-dimensional space of intensities.

Figure 22.2  Manifold  as expression of correlation. A snapshot consisting of

p pixels can be represented as a p-dimensional vector, with each com­ ponent representing the intensity value at a pixel. For a collection of snapshots of the head of a person viewed from different angles, the intensities are a function of only three parameters. This means that the p-dimensional vector tips all lie on a 3D hypersurface (“mani­ fold”) in the p-dimensional space of intensities. This manifold is an expression of the correlated way in which the pixel intensities change with particle orientation, with each point on the manifold represent­ ing a snapshot at a different orientation. This approach can be easily extended to situations where more than three variables are at work, e.g., when the object can exercise conformational degrees of freedom.

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This manifold is an expression of the correlated way in which the pixel inten­ sities change with particle orientation, with each point on the manifold rep­ resenting a snapshot at a different orientation. This approach can be easily extended to situations where more than three variables are at work, e.g., when the object can exercise conformational degrees of freedom (see below). Extracting the manifold—in essence, the information content of the data—and presenting it in a suitable low-dimensional space are performed by so-called manifold embedding techniques. In brief, such approaches determine the intrinsic dimensionality of the manifold, identify the mani­ fold itself and represent it in terms of a set of orthogonal functions best able to represent the manifold. A number of powerful techniques have been devel­ oped to discover low-dimensional manifolds in high-dimensional data (see, for example, ref. 10–13 and 34–36). Each has its strengths and limitations, with the most common problem being noise sensitivity (see, for example, ref. 17 and 37). Our geometric approach incorporates three different so-called manifold embedding techniques stemming from Generative Topographic Mapping (GTM),34,38 Isomap11 and Diffusion Map.39 In each case, extensive effort was required to achieve noise-robustness. Our algorithms now oper­ ate at signal/noise ratios (SNRs) as low as −21 dB (∼1/100 on a linear scale) depending on the application.19 Once the data manifold has been determined and presented (“embedded”) in a suitable space, one must discover how to interpret the outcome. Specifi­ cally, one needs to identify the operations connecting any two points on the manifold. For example, in order to reconstruct a 3D image of a given object conformation, one must identify all points on the manifold, which can be reached by SO(3) operations (3D rotations) alone. Similarly, to map confor­ mations, all points on the manifold connected by conformational operations alone must be identified. This is tantamount to purposeful navigation on the manifold and constitutes the second important step in geometric machine learning. Manifolds are best described in differential geometric terms, with the metric—the local measure of distance—playing an important role. Using a differential geometric formulation of scattering, we have related trajectories on the data manifold to specific operations on the object and/or frame of reference.18 In non-technical terms, one would like to relate infinitesimal changes in the intensity distribution in a snapshot to the corresponding infinitesimal operations affecting the object orientation, conformation, etc. In other words, one would like to relate the metric of the data manifold to the metric of the manifold of operations. This would allow one to determine the operations connecting any pair of snapshots. Achieving this is tantamount to having a model of the object, in the sense that, given any snapshot, any other corresponding to a desired state of the object can be produced on demand. In general, however, the metric of data manifolds produced by scattering is not simply related to the metric of the manifold of operations. We have solved this problem in two steps. First, we have shown that the metric of data man­ ifolds produced by scattering onto a two-dimensional (2D) detector can be decomposed into two parts: one with high symmetry, plus an object-specific

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“residual" with low symmetry. Second, using results from general relativ­ ity and quantum mechanics,40–42 we have shown that the (Laplace–Beltrami) eigenfunctions of the high-symmetry part are directly related to those of the manifold of operations under a wide range of scattering conditions.18,19,28 This allows one, for example, to extract structural and conformational infor­ mation from the collection of snapshots.

22.3  Mapping Conformations of Nanomachines The observation of a system performing a function naturally leads to a collection of snapshots from non-identical objects. The ability to extract conformational information from large heterogeneous datasets is vital to advancing our understanding of structural variability, and its role in biology and physics. Here, I show that geometric machine learning is able to determine the structure and conformations of biological nanomachines from large ensem­ bles of heterogeneous, noisy snapshots. This capability has been demonstrated with simulated and experimental diffraction and image snapshots.8,21,43 Single-particle structure recovery methods, such as cryo-EM44 and emerg­ ing XFEL “diffract-then-destroy” approaches,26,45–49 are generally predicated on viewing a series of identical objects from different angles. The obvious method of “sorting” the data into classes, each stemming from nominally identical objects, is fraught with difficulty: the number and types of classes are often unknown, sorting must be performed at very low signal-to-noise ratios (SNR ≤ 0.1) and residual heterogeneities persist, even when the classes are small. Heterogeneity can be tackled by sorting with reference to templates, which often can only be guessed at. The dangers in this approach are well known.44 For example, the picture of Einstein or Newton can emerge from random noise, depending on whose portrait was used as a template. Approaches based on Bayesian inference and maximum likelihood are powerful (see, for example, ref. 50), but inherently favor the discovery of discrete confor­ mations. Their computational expense and scaling behavior also limit their practical application to a small number of distinct classes. It has been shown that if simulated or experimental single-particle XFEL diffraction snapshots or cryo-EM image snapshots emanate from different discrete conformations of an object, geometric machine learning can sort the snapshots into separate conformational classes and determines the structure of each conformation, with accuracies as high as 99.7% for bench­ mark datasets with SNRs as low as 0.06.21

22.4  T  hree-dimensional Conformational Movies over Energy Landscapes New analytical approaches now map the continuous conformational changes of nanomachines along their work cycle over the free-energy landscape without timing information, supervision, or templates.8 These unbiased

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approaches determine the number of degrees of freedom exercised during the observations, the energy landscape explored by the nanomachine, the trajectory corresponding to the work cycle and the continuous conforma­ tional changes associated with the work cycle. These capabilities constitute a powerful platform for quantitative study of the conformational and energy trajectories of nanomachines, including those engaged in a wide range of important biological processes. The approach has been validated with data containing ∼one million snapshots, with critical algorithmic steps extended to terabyte-datasets containing 20 million snapshots.51,52 Ideally, one would like to “see” the conformational changes of a biological nanomachine as it traverses its work-cycle trajectory over the energy land­ scape.53 This section provides a simple conceptual outline of the approach used to reach this goal. We are concerned with continuous conformational changes, which produce correlations among the points representing the snapshots. These correlations give rise to a manifold. Our approach begins with determining the orientations of the snapshots by any of a number of approaches,29 in this instance by a method well-known in electron micros­ copy.54 As shown previously,29,55 this can be achieved without taking confor­ mational heterogeneity into account, because the effects of orientational change dominate. Snapshots lying within a tight orientational aperture are then selected, and the manifold spanned by them is determined. This yields the conformational manifold (“spectrum”) in the selected viewing (projec­ tion) direction. The conformational changes are, in general, governed by more than one parameter, with the conformational manifold described by a set of orthogonal coordinates. This can be achieved by one of many wellestablished geometric machine-learning techniques, which also reveal the intrinsic dimensionality of the manifold, and hence the number of degrees of freedom exercised by the system under observation. Unfortunately, it is not possible to determine the 3D conformational changes from such a description, because the local rates of change in each projection direction are, in general, unknown10,35 and cannot be easily related to the underlying changes in the system under observation.18,56 To overcome this difficulty, one introduces an additional step, in which the cloud of points is mapped to another coordinate system, where the local rates of change are known exactly.8 This leads to a representation of the conformational changes in terms of a set of universal parameters (metrics). The density of points in this space can now be related to the energy landscape sampled by the system through the Boltzmann factor e−ΔG/kBT,57 with ΔG denoting the change in the Gibbs free energy, kB the Boltzmann constant and T the temperature. The locus of minimum energy in this landscape likely represents the trajectory traversed by the machine during its work cycle. In each viewing direction, 2D movies can be compiled to reveal the conformational changes along the path of minimum energy, or indeed any chosen trajectory. 3D movies can be com­ piled by stepping along such a trajectory and, in each step, performing a 3D reconstruction by integrating the information from many different viewing directions.

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As reported elsewhere, the implementation of this approach is, of course, more sophisticated than suggested by this simple outline. Instead of a math­ ematical treatment, the results of the analysis are demonstrated with refer­ ence to a set of about 850 000 experimental snapshots of ribosomes from yeast, obtained in the course of a study of translational initiation by a plant virus. Typical snapshots and the resulting manifold in one projection direc­ tion are shown in Figure 22.3. Figure 22.4 shows the energy landscape of the ribosome as determined by the approach outlined above, in terms of the first two eigenfunctions of the manifold. The trough of minimum free energy forms a roughly trian­ gular path (Figure 22.4B). Detailed examination of 3D movies showing the conformational changes along this trajectory reveals intersubunit rotation, head closure, head swivel and L1-stalk closing, and their reversal, all features known to be associated with the protein synthesis work cycle of the ribosome (see ref. 8 and references therein). These observations lead to the conclu­ sion that the closed minimum-energy trajectory obtained from snapshots of idling ribosomes corresponds to the protein synthesis work cycle of the ribosome. The 3D movies integrate information from a large ensemble of noisy snap­ shots, each stemming from an object viewed only once. By using manifolds to capture the properties of the entire dataset, and “nonlinear singular value

Figure 22.3  (A)  Experimental cryo-EM snapshots each showing the ribosome in an

initially unknown orientational and conformational state. The barely visible ribosomes indicate the low SNR typical of such snapshots. (B) The manifold of conformations in one projection (viewing) direction. The axes represent, in essence, degrees of freedom of the ribosome, with each point corresponding to an individual snapshot.

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Figure 22.4  (A)  Three views of a map of the 80S ribosome recovered by geometric

machine learning. Arrows indicate four key conformational changes associated with the elongation work cycle of the ribosome. (B) Energy landscape traversed by the ribosome. The color bar shows the energy scale (uncertainty: ±0.05 kcal mol−1). The roughly triangular mini­ mum-free-energy trajectory is divided into 50 conformational states. Detailed examination of 3D movies showing the conformational changes along this trajectory reveals intersubunit rotation, head clo­ sure, head swivel, and L1-stalk closing and their reversal, all features known to be associated with the protein synthesis work cycle of the ribosome (see ref. 8 and references therein). These observations lead to the conclusion that the closed minimum-energy trajectory obtained from snapshots of idling ribosomes corresponds to the protein synthe­ sis work cycle of the ribosome. Circular arrows indicate the structural changes between seven selected states, each identified by its place in the sequence of 50 conformational states.

analysis” (specifically, nonlinear Laplacian spectral analysis, NLSA) to sup­ press noise,15 the approach offers a sophisticated means for extracting the ensemble thermodynamics, i.e., the information common to a collection of objects, each viewed in an initially unknown orientational and conforma­ tional state.

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Most successful experimental studies of the conformational spectra of bio­ logical machines have been hitherto restricted to: sorting snapshots into a small number of classes,57,58 using templates in some form, relying on timing information, or a combination of these.57 In contrast, the machine-learning approach outlined above naturally yields detailed conformational trajecto­ ries and energy landscapes without a priori information or assumptions, and at moderate computational expense. The number of meaningfully distinct conformational states is governed primarily by the SNR, which determines the statistical confidence with which neighboring states can be distinguished. In this study of the ribosome, the requirement for neighboring conformational states to be separated by three standard deviations (3σ) means approximately 50 conformational states can be distinguished. This is about an order of magnitude larger than previously achieved without timing information or templates. In combination with the recent availability of large cryo-EM datasets with near-atomic resolution,59,60 this geometric machine-learning approach promises the possibility to extract 3D conformational movies of biological machines as they traverse their work cycle over the energy landscape. More generally, the approach offers a power­ ful platform for extracting accurate thermodynamic and structural informa­ tion from large collections of extremely noisy snapshots.

22.5  Dynamics Beyond Timing Uncertainty The conformational movies described above are based on similarity, not evo­ lution with time. They reveal the conformational changes associated with different trajectories over the energy landscape without any timing informa­ tion. Work cycles are inferred from highly populated low-energy paths on the landscape. Time-driven processes can involve a complex series of forward and back­ ward steps. Extracting the dynamics of such motions—the way the sequence of events unfolds with time—requires timing information with respect to a known time-zero (trigger) point. The time interval between the trigger and the time a snapshot was obtained is often highly uncertain. In biology and chemistry, for example, reaction initiation is often non-uniform. This timing uncertainty severely corrupts our knowledge of the underlying dynamics. It has recently been shown that geometric machine-learning data-analyti­ cal approaches can extract accurate dynamical information from noisy data with extreme timing uncertainty.30 This approach has been used to extract ∼1 fs information from noisy experimental X-ray free-electron laser (XFEL) spectral snapshots recorded with a timing uncertainty of ∼300 fs full width at half maximum (FWHM; ∼100 fs σ). This unprecedented capability can be applied whenever dynamical information is corrupted by timing uncertainty. The fundamental premise of the approach is simple. Even a perfect shuf­ fle leaves some remnants of the original order in a pack of cards. Thus, a series of snapshots concatenated (appended) to each other in the order of their inaccurate timestamps contains some time-evolutionary information (“a weak arrow of time”), provided the concatenation window spans a period

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comparable with, or longer than the timing uncertainty associated with each individual snapshot. This leads one to consider a series of c-fold concate­ nated snapshots, formed by moving a window c frames wide over the raw dataset ordered according to the inaccurate timestamps. The dynamics can then be extracted from the series of concatenated snapshots by powerful techniques developed to extract signal from noise, such as singular value decomposition (SVD).61 SVD determines a series of statistically significant modes, each consisting of a characteristic pattern (topogram, or “topo”) and its time evolution (chronogram, or “chrono”). A topo can, for example, be a characteristic image, or spectrum, with the corresponding chrono showing its change with time. For each mode, a singular value specifies the power contained in that mode.61 Consider snapshots, such as images or spectra, which can be represented as vectors by using the pixel values of each snapshot as the components of a vector x. The snapshots then form a cloud of points in multidimensional space. Like principal component analysis, SVD is a linear-algebraic approach, efficiently applicable only when the data cloud defines a flat hypersurface. Unfortunately, many systems of interest cannot be adequately treated within the framework of linear-algebraic methods, such as SVD. Geometrically, this is tantamount to the data lying on an intrinsically curved hypersurface (man­ ifold). Fundamental to our approach, therefore, is NLSA,15 which performs the same analysis as SVD, but on curved manifolds. For a dataset consisting of a series of Ns time-ordered snapshots, the analysis begins with a “time-lagged embedding”14,62,63 to form c-fold con­ catenated “superframes” (or “supervectors”) from the dataset consisting of vectors x. A typical supervector Xt = (xt,xt−δt,…,xt−(c−1)δt) is obtained by append­ ing the column vectors xt−iδt, (0 ≤ i ≤ c − 1) to each other, with xt−iδt repre­ senting the ith snapshot in the sequence of c snapshots ordered according to timestamps. The timestamp assigned to each of the resulting (Ns − c) supervectors is defined as the mean of the timestamps of its constituent vectors. Unlike averaging, concatenation retains the information content of the dataset.15 Next, one uses graph-based analysis—specifically the diffusion map algo­ rithm10—to identify the nonlinear data manifold formed by the collection of supervectors. The matrix of supervectors Xt is then projected onto the mani­ fold to obtain matrix A:   



A = XµΦ,

(22.1)

  

with X representing the matrix of supervectors Xt, µ the Riemannian measure of the manifold and Φ the empirical orthogonal eigenfunctions (EOFs)—a truncated set of the eigenfunctions of the Laplace–Beltrami operator on the manifold. This Euclidean description of the nonlinear manifold allows us to analyze matrix A using standard SVD. The chronograms obtained using SVD are projected from the space defined by Φ back to the time domain and the topograms corresponding to the superframes are “unwrapped” to obtain

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individual frames. This approach is able to deal naturally with complex nonlinear dynamics15,64 and to extract conformational information from ultralow-signal snapshots of molecular machines.8 Now consider the effect of stochastic timing uncertainty. Recall that data matrix X is affected by timing uncertainty in two ways: first, the sequence of superframes can differ from the correct, jitter-free case; and, second, the time intervals within the members of a superframe, and those between the superframes themselves, can vary stochastically about a mean. It can be shown that the SVD step in NLSA is immune to jitter-induced changes in the superframe sequence, which are, in any case, unlikely for large concatena­ tion parameters. As for non-uniformity in time sampling, it can be shown analytically and by simulation that, with a sufficient number of snapshots, the outcome of SVD corresponds to time samples that are uniformly spaced to within small oscillations about the mean.30 The results of SVD analysis of matrix A must be projected back into the time domain in order to reconstruct the dynamics. This involves “undo­ ing” the effect of the projection described in eqn (22.1) by computing AΦT. Because the EOFs represented by Φ are evaluated with our imperfect knowl­ edge of timing, this back-projection re-injects jitter into the results.15 But it has been shown that, in the limit of large concatenation parameters, the manifold geometry and hence the EOFs are biased toward the most stable component of the dynamics,65 as supported by the reduction in the number of significant eigenvalues from five (in the manifold of raw data) to one (after concatenation). One may, therefore, regard the timing jitter as a form of sto­ chastic forcing, which has been extensively studied.66 The effect of re-injecting jitter is substantially alleviated by the use of super­ frames, as follows. The timestamp associated with each superframe corre­ sponds to the mean of the timestamps of the constituent single frames.67 Neighboring superframes share all but one frame, with the number of shared frames decreasing as the interval between two superframes increases. Con­ sider two superframes, each formed by concatenating c frames, n of which are not shared between the two superframes. With Gaussian jitter σ wide, the distribution of uncertainty in the time interval between the superframes has a width  2n  c . This must be compared with the average time interval between these two superframes n〈Δt〉, with 〈Δt〉 being the mean sampling interval. Reliable dynamical information emerges on timescales exceeding the timing uncertainty between two superframes with n unlike frames, i.e. when   



nt  

 n c

2

,

   i.e., n    .  c t  

(22.2)

  

For the experimental dataset used to validate this approach (see below), the above expression leads one to expect reliable dynamical information on the ∼1 fs timescale. This conclusion is supported by the analysis of a series of simulated trial input data.30

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Figure 22.5  (A)  Experimental time-of-flight movie of the Coulomb explosion of N2.

The individual time-of-flight spectra were recorded with 300 fs timing uncertainty and substantial Poisson noise in pixel intensities. Inaccu­ rate timing information often degrades our ability to extract accurate dynamical information. In XFELs, for example, the timing uncertainty can exceed the length of an X-ray pulse by up to two orders of magni­ tude. (B) Movie extracted from the same data by geometric machine learning. The fundamental premise behind the approach is simple. A sufficiently long series of snapshots ordered according to their inac­ curate timestamps still contains some time-evolutionary information (“a weak arrow of time”). The course of events can thus be accurately reconstructed by graph-based mathematical techniques able to extract signal, in this case the arrow of time, from noise. The algorithmically extracted movie has a time resolution a factor ∼300 better than the timing uncertainty with which the data were recorded.

This capability has been validated in the context of noisy experimental time-of-flight spectral data recorded with substantial timing uncertainty stemming from the stochastic nature of the process used to generate ultra­ short X-ray pulses in FELs68 (Figure 22.5). The measured pump-probe timing jitter in this experiment was characterized by a FWHM value of 300 fs. The data were collected in a pump-probe experiment, in which an infra-red (IR) pulse was used to induce impulsive orientational alignment in a gas of N2 molecules, with the pulse either preceding or succeeding an ultrashort (∼6 fs envelope) X-ray pulse.24 This approach was able to map the shape of the IR pulse with ∼1 fs accuracy and recover all known vibrational modes of N2 molecules with periods as short as 15 fs.30 Combined with the recent near-atomic resolution of cryo-EM and increas­ ing resolution of XFEL-based imaging techniques, the possibility to extract accurate dynamical information from noisy data recorded with extreme timing uncertainty provides access to the dynamics, i.e., the time-ordered sequence of molecular motions at near-atomic level.

22.6  Conclusions and Future Prospects The primary conclusions of this paper are as follows. First, geometric machine-learning approaches can extract rich and detailed information from noisy data without the need for careful control of system variables. These approaches determine the intrinsic degrees of freedom at work, and provide

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a data-driven vocabulary and grammar for describing the system of interest. Second, such approaches offer experimental access to the energy landscapes of biological nanomachines and allow the compilation of conformational movies over any trajectory over the landscape, without the need for timing information. Third, accurate dynamical movies showing the time-ordered sequence of events can be extracted from noisy data recorded with extreme timing uncertainty. This capability has important implications, particularly for XFELs, whose otherwise exquisite short-pulse performance is marred by timing jitter due to the underlying stochastic nature of the processes they use to produce radiation. In the future, the availability of increasingly large datasets will drive algo­ rithms to enhance their “big data” capabilities. These capabilities concern not only the size, but also the sparse nature of big data, because many states of interest are rarely sighted. As an example, the European XFEL is expected to produce ∼108 useful snapshots per five-shift experiment. In principle, one can then glimpse rare, but rate-limiting states up to 18kBT above the thermal bath. However, this presents the algorithmic challenge of identifying important, but rarely sighted states in an ocean of data from lower energies. Similarly, in dynamical experiments, each (2D) snapshot often stems from a poorly known time point. But one would like to reconstruct a reliable 3D reconstruction at a series of accurately known time points. This requires the ability to deal intelli­ gently with the consequences of extreme sparsity in big data. Despite or perhaps because of these exciting challenges, it seems certain that machine-learning approaches will provide deep insights into the vital functions of biological nanomachines underlying life.

Acknowledgements The results included in this paper were obtained in collaboration with many colleagues cited in the references, especially A. Dashti, J. Frank, R. Fung, A. Hosseinizadeh, R. Santra, and P. Schwander, to whom I am deeply indebted. The research was supported by the US Department of Energy, Office of Sci­ ence, Basic Energy Sciences under award DE-SC0002164 (algorithm design and development, and data analysis), and by the US National Science Foun­ dation under awards STC 1231306 (numerical trial models) and 1551489 (underlying analytical models).

References 1. R. P. Feynman, R. B. Leighton and M. Sands, The Feynman Lectures on Physics, Addison Wesley, 2006, vol. I. 2. A. S. Spirin and A. V. Finkelstein, in Molecular Machines in Biology: Workshop of the Cell, ed. J. Frank, Cambridge University Press, 2011. 3. P. B. Moore, Annu. Rev. Biophys., 2012, 41, 1–19. 4. H. Linke, Appl. Phys. A, 2002, 75, 167. 5. A. van Oudenaarden and S. G. Boxer, Science, 1999, 285, 1046–1048. 6. T. Motegi, H. Nabika and K. Murakoshi, Langmuir, 2012, 28, 6656–6661.

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7. J. Noel, J. Chahine, V. Leite and P. Whiteford, Biophys. J., 2014, 107, 2872–2881. 8. A. Dashti, et al., Proc. Natl. Acad. Sci. U. S. A., 2014, 111, 17492–17497. 9. Y. LeCun, Y. Bengio and G. Hinton, Nature, 2015, 521, 436–444. 10. R. R. Coifman, et al., Proc. Natl. Acad. Sci. U. S. A., 2005, 102, 7426–7431. 11. J. B. Tenenbaum, V. de Silva and J. C. Langford, Science, 2000, 290, 2319–2323. 12. D. L. Donoho and C. Grimes, Proc. Natl. Acad. Sci. U. S. A., 2003, 100, 5591–5596. 13. S. T. Roweis and L. K. Saul, Science, 2000, 290, 2323–2326. 14. T. Sauer, J. A. Yorke and M. Casdagli, J. Stat. Phys., 1991, 65, 579–616. 15. D. Giannakis and A. J. Majda, Proc. Natl. Acad. Sci. U. S. A., 2012, 109, 2222–2227. 16. T. Berry, J. R. Cressman, Z. Gregurić-Ferenček and T. Sauer, SIAM J. Appl. Dyn. Syst., 2013, 12, 618–649. 17. R. R. Coifman, Y. Shkolnisky, F. J. Sigworth and A. Singer, IEEE Trans. Image Process., 2008, 17, 1891–1899. 18. D. Giannakis, P. Schwander and A. Ourmazd, Opt. Express, 2012, 20, 12799–12826. 19. P. Schwander, D. Giannakis, C. H. Yoon and A. Ourmazd, Opt. Express, 2012, 20, 12827–12849. 20. A. Hosseinizadeh, et al., Philos. Trans. R. Soc., B, 2014, 369, 20130326. 21. P. Schwander, R. Fung and A. Ourmazd, Philos. Trans. R. Soc., B, 2014, 369, 20130567. 22. A. Ourmazd, Struct. Dyn., 2015, 2, 041501. 23. A. Hosseinizadeh, A. Dashti, P. Schwander, R. Fung and A. Ourmazd, Struct. Dyn., 2015, 2, 041601. 24. J. M. Glownia, et al., Opt. Express, 2010, 18, 17620–17630. 25. R. Neutze, R. Wouts, D. van der Spoel, E. Weckert and J. Hajdu, Nature, 2000, 406, 752–757. 26. K. J. Gaffney and H. N. Chapman, Science, 2007, 316, 1444–1448. 27. J. Frank, Annu. Rev. Biophys. Biomol. Struct., 2002, 31, 303–319. 28. A. Hosseinizadeh, et al., Philos. Trans. R. Soc., B, 2014, 369, 20130326. 29. P. Schwander, R. Fung and A. Ourmazd, Philos. Trans. R. Soc., B, 2014, 369, 20130567. 30. R. Fung, et al., Nature, 2016, 532, 471–475. 31. R. Fung, V. Shneerson, D. K. Saldin and A. Ourmazd, Nat. Phys., 2009, 5, 64–67. 32. N. T. Loh and V. Elser, Phys. Rev. E., 2009, 80, 026705. 33. B. Moths and A. Ourmazd, Acta Crystallogr., 2011, A67, 481–486. 34. C. M. Bishop, in Learning in Graphical Models, ed. M. I. Jordan, 1999, pp. 371–403. 35. M. Belkin and P. Niyogi, Neural Comput., 2003, 15, 1373–1396. 36. T. Lin, H. B. Zha and S. U. Lee, Lect. Notes Comput. Sci. Eng., 2006, 3951, 44–55. 37. M. Balasubramanian and E. L. Schwartz, Science, 2002, 295, 7a.

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38. C. M. Bishop, Neural Networks for Pattern Recognition, Oxford University Press, 1995. 39. R. Coifman and S. Lafon, Appl. Comput. Harmon. Anal., 2006, 21, 5–30. 40. B. L. Hu, Phys. Rev. D, 1973, 8, 1048–1060. 41. B. L. Hu, Phys Rev D, 1974, 9, 3263–3281. 42. D. A. Varshalovich, A. N. Moskalev and V. K. Khersonskii, Quantum Theory of Angular Momentum, World Scientific, 2008. 43. C. H. Yoon, et al., Opt. Express, 2011, 19, 16542–16549. 44. J. Frank, Three-dimensional Electron Microscopy of Macromolecular Assemblies, Oxford University Press, 2nd edn, 2006. 45. J. C. Solem and G. C. Baldwin, Science, 1982, 218, 229–235. 46. R. Neutze, G. Huldt, J. Hajdu and D. van der Spoel, Radiat. Phys. Chem., 2004, 71, 905–916. 47. H. N. Chapman, et al., Nat. Phys., 2006, 2, 839–843. 48. M. M. Seibert, et al., Nature, 2011, 470, 78–81. 49. A. Aquila, et al., Struct. Dyn., 2015, 2, 041701. 50. S. H. Scheres, et al., Nat. Methods, 2007, 4, 27–29. 51. A. Dashti, I. Komarov and R. M. D. D'Souza, PLoS One, 2013, 8, e74113. 52. I. Komarov, A. Dashti and R. M. D. D'Souza, PLoS One, 2014, 9, e92409. 53. H. Frauenfelder, S. G. Sligar and P. G. Wolynes, Science, 1991, 254, 1598–1603. 54. P. A. Penczek, R. A. Grassucci and J. Frank, Ultramicroscopy, 1994, 53, 251–270. 55. J. Fu, H. Gao and J. Frank, J. Struct. Biol., 2007, 157, 226–239. 56. R. R. Coifman, Y. Shkolnisky, F. J. Sigworth and A. Singer, Appl. Comput. Harmon. Anal., 2010, 28, 296–312. 57. N. Fischer, A. L. Konevega, W. Wintermeyer, M. V. Rodnina and H. Stark, Nature, 2010, 466, 329–333. 58. X. Agirrezabala, et al., Proc. Natl. Acad. Sci. U. S. A., 2012, 109, 6094–6099. 59. A. Amunts, et al., Science, 2014, 343, 1485–1489. 60. M. Liao, E. Cao, D. Julius and Y. Cheng, Nature, 2013, 504, 107–112. 61. N. Aubry, R. Guyonnet and R. Lima, J. Stat. Phys., 1991, 64, 683–739. 62. N. Packard, J. Crutchfield, J. Farmer and R. Shaw, Phys. Rev. Lett., 1980, 45, 712–716. 63. F. Takens, Dynamical Systems and Turbulence, Warwick 1980, Lecture Notes in Mathematics, Springer, 1981, vol. 898, pp. 366–381. 64. D. Giannakis and A. J. Majda, Geophys. Res. Lett., 2012, 39, L10710. 65. T. Berry, R. Cressman, Z. Greguric-Ferencek and T. Sauer, SIAM J. Appl. Math., 2013, 12, 618–649. 66. J. Stark, D. S. Broomhead, M. E. Davies and J. Huke, J. Nonlinear Sci., 2003, 13, 519–577. 67. D. Giannakis and A. J. Majda, Geophys. Res. Lett., 2011, 39, L10710. 68. C. Pellegrini and J. Stohr, Nucl. Instrum. Methods Phys. Res. A, 2003, 500, 33–40.

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New Science Opportunities and Experimental Approaches Enabled by High Repetition Rate Soft X-ray Lasers Robert W. Schoenlein*, Andy Aquila, Daniele   Cocco, Georgi L. Dakovski, David M. Fritz, Jerome B.   Hastings, Philip A. Heimann, Michael P. MINITTI, Timor Osipov and William F. Schlotter Linac Coherent Light Source, SLAC National Accelerator Laboratory,   2575 Sand Hill Rd, Menlo Park, CA 94025, USA *E-mail: [email protected]

23.1  Introduction We are in a golden age for X-ray light sources, with thousands of scientists routinely using X-ray beams at modern synchrotron facilities to answer fundamental questions in chemistry, physics, materials science, and biology. The recent development of X-ray lasers has initiated a new era in X-ray science by providing coherent ultrafast X-ray pulses with unprecedented peak brightness. The first generation of these facilities [e.g., the FLASH facility at DESY Hamburg,1 and the Linac Coherent Light Source (LCLS) facility at SLAC2] have already had tremendous scientific impact, and numerous similar facilities are now in operation or are under construction around the world.3     Energy and Environment Series No. 18 X-Ray Free Electron Lasers: Applications in Materials, Chemistry and Biology Edited by Uwe Bergmann, Vittal K. Yachandra and Junko Yano © The Royal Society of Chemistry 2017 Published by the Royal Society of Chemistry, www.rsc.org

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However, despite their enormous peak brightness, the average X-ray brightness from these facilities is quite modest, comparable to or lower than that available from existing storage rings. This restricts their application in many important areas of science. This results from the fact that first-generation X-ray free-  electron lasers (XFELs) are based almost exclusively on pulsed-radio frequency (RF) accelerator technology, which limits the achievable repetition rate. A new generation of XFELs is now under development that will overcome this restriction by exploiting continuous-wave RF superconducting accelerator technology (CW-SCRF) to provide ultrafast X-ray pulses at high repetition rate (∼MHz) in a uniform or programmable time structure. This development is driven by important new science opportunities that have been identified and advanced over the past decade through scientific workshops, both in the U.S. and around the world. Most recently, a series of science workshops held at SLAC National Accelerator Laboratory in February 2015 focused on the new science opportunities4 that will be enabled by the LCLS upgrade project (LCLS-II), which will provide ultrafast X-rays in the 0.25–5 keV range at repetition rates up to 1 MHz with two independent XFELs based on adjustable-gap undulators: the 0.25–1.25 keV soft X-ray undulator (SXU) and the 1–5 keV hard X-ray undulator (HXU).5 This chapter highlights a few of the important, new science opportunities enabled by such a facility in the areas of: (1) fundamental charge and energy flow in molecular complexes, (2) photo-catalysis and coordination chemistry, (3) quantum materials, and (4) coherent imaging at the nanoscale. The examples in this chapter represent just a few of the many science opportunities where high repetition rate is particularly enabling, and is not intended to be comprehensive of the broad range of science to be done at such facilities. Some key new experimental methods enabled by high repetition rate are also described, and initial concepts and capabilities of new instrumentation being planned for the LCLS upgrade are outlined.

23.2  F  undamental Dynamics of Energy and Charge in Atoms and Molecules Charge migration, redistribution, and localization, even in simple molecules, are not well understood at the quantum level. These fundamental phenomena are central to complex processes such as photosynthesis, catalysis, and bond formation/dissolution that govern all chemical reactions. Charge migration and localization in molecules is a coordinated process of both electronic and atomic motion, and indirect evidence points to the importance of quantum coherences and coupled evolution of electronic and nuclear wave functions in many molecular systems. However, we have not been able to directly observe these processes to date, and they are beyond the description of conventional chemistry models. Ultrafast soft X-rays at high repetition rate from advanced XFELs will enable new dynamic molecular reaction microscope techniques that will directly map charge distributions and reaction dynamics in the molecular frame.

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23.2.1  Dynamic Molecular Reaction Microscope Ultrafast soft X-rays at high repetition rate from advanced XFELs will provide qualitatively new probes of excited-state energy and charge flow, and how they work in simple and complex molecular systems. The high repetition rate will enable sophisticated coincidence measurement schemes for kinematically complete experiments at each time step of an evolving reaction. This experimental approach, known as a “molecular reaction microscope”,6,7 measures simultaneously the momenta (energy and direction) of all the constituent components of a molecular complex, typically via pulsed ionization and spectroscopy of the charged fragments using position-sensitive time-offlight (TOF) techniques with multiple detection channels for electrons and ions, or charged fragments (as illustrated in Figure 23.1). Photoelectrons emitted from localized inner shell levels are powerful probes for “illuminating molecules from within”.6,8 A photoelectron wave originating from a specific site in the molecule is scattered by the instantaneous molecular structure at the moment of photo-absorption. Recording such photoelectron scattering patterns in coincidence with the momenta of the fragment ions enables the reconstruction of the molecule at a fixed

Figure 23.1  Artist  view of a molecular reaction microscope (also known as cold-  target recoil ion momentum spectroscopy, COLTRIMS). Only one molecule is in the X-ray beam on each pulse (i.e., less than one  ionization event per pulse). The ion and electron momenta are fully characterized in coincidence via position-sensitive TOF detectors (graphic courtesy of R. Dörner, Goethe U. Frankfurt).

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orientation in space (and time). Figure 23.2 shows a recent example of the structure of a methane molecule in the stationary electronic ground state measured via coincidence techniques at a synchrotron source. Photoelectrons emitted from the C-1s shell clearly reflect the positions of the H atoms in the molecular reference frame. The promise of high-repetition-rate XFELs is to advance these techniques to the time domain to follow molecular dynamics in the excited-state on fundamental time scales, using coincidence techniques to identify molecules with a fixed orientation in space. In these applications, specific dynamics are initiated via tailored transient excitations such as: charge transfer, vibrational excitation,

Figure 23.2  Methane  (stationary electronic ground state) imaged in the molec-

ular frame via the K-shell photoelectron angular distribution. Top: Calculated photoelectron angular distribution integrated over all polarization directions. Bottom: The experimental photoelectron angular distribution obtained from the (H+, H+, CH+2) decay pathway. Reprinted with permission from J. B. Williams et al., Physical Review Letters, 108, 233002, 2012. Copyright 2012 by the American Physical Society.9

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creation of a valence hole via ionization, creation of non-equilibrium Rydberg wavepackets, strong dressing fields, etc. Recent XFEL experiments point toward promising opportunities for dynamic reaction microscope studies.10–13 For example, studies of charge-transfer dynamics in gas-phase iodomethane14 identified three dissociative channels based on the time-dependent kinetic energy distributions of the charged fragments and comparison with model calculations. Dynamic reaction microscope studies at high repetition rate will enable the complete spatial reconstruction of the excited-state charge transfer and subsequent dissociation at each time step for a fixed-in-space molecular orientation. This is a potentially powerful approach for visualizing a broad range of excited-state molecular dynamics from dissociation of simple diatomic molecules, to charge-transfer processes, to isomerization and ring–opening reactions,15 to non-Born–Oppenheimer relaxation processes,16 to quantum symmetry breaking processes that mediate the emergence of chirality.17 Some of the key instrumentation requirements to exploit high-repetition-rate X-ray pulses for dynamic molecular reaction microscope studies include the following capabilities:     (a) Tuning range: 0.25 to 1.2 keV. This spans the K-edges of critical light elements, C (284 eV), N (410 eV), and O (543 eV), through the L-edges of the 3d transition metals. (b) Beam focus: ∼300 nm diameter. Reaction microscopes operate with only one molecule in the X-ray beam per pulse. A small focus (short Rayleigh range) enables the use of higher density gas jet targets, thus providing a well-defined spatial origin of the charged fragments to facilitate the spatial reconstruction of the reaction. (c) Vacuum: Ultra-high vacuum (UHV) ∼10−11 Torr. This is essential to ensure that electrons and charged fragments originate only from molecules in the focal region by minimizing contributions from background gas along the X-ray beam path. (d) Electron spectrometer: Electric and magnetic fields collect electrons and ions over a 4π solid angle and project them to high-speed detectors (combination of micro-channel plates and delay-line) providing both position and time information (TOF), ideally with multi-hit capability at rates >100 kHz. (e) Lasers: Provisions for tailored excitation spanning a broad spectral range from ultraviolet (UV) to visible to terahertz at peak intensities of >1012 W cm−2, with synchronization to X-ray pulses at the and |f2> are created and probed via resonant Raman processes at specific atoms. This approach creates a local valence excitation, and enables element-specific probing of charge flow.

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Figure 23.4  Excitation  energy transfer simulation in Zn/Ni porphyrin heterodimer.

The X-ray pump pulse is resonant with the Zn L3-edge, and creates a localized valence excitation (wavepacket) via SXRS. Evolution of electron and hole densities (isosurfaces) are calculated from the nonstationary valence superposition states prepared via SXRS (adapted with permission from PNAS 2013, 110 (39) 15597–15601, ref. 19).

in resonance with a second atom can then follow the time evolution of the wavepacket and the flow of valence charge between different atomic sites via various probe interaction mechanisms, for example, X-ray absorption spectroscopy, photoelectron spectroscopy, or via a second SXRS process (as illustrated in Figure 23.3). The potential impact of SXRS is illustrated in Figure 23.4, which shows recent SXRS simulations of ultrafast energy transfer dynamics in a Zn/Ni porphyrin heterodimer, which is of interest as a model component in artificial light harvesting and photosynthetic complexes.19 In the simplest pump-probe implementation, a nonstationary valence electronic wavepacket (in the vicinity of an atom of interest) is created by two interactions with the field of a pump pulse resonant with a core transition. The delayed probe pulse (e.g., resonant with a core transition from a different atom) interacts with this wavepacket via a second Raman process, and the change in absorption reports on the dynamics of the wavepacket. Importantly, since the final state (from either the pump or probe pulse) is not core-excited, but only valence-excited, this approach accesses time scales that are much longer than the core-hole lifetime. A complement to SXRS is X-ray core-hole correlation spectroscopy (XCCS) as illustrated in Figure 23.5.20–22 This approach is essentially the equivalent of two-dimensional (2D) electronic spectroscopy22–24 but in the X-ray regime.

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Figure 23.5  Illustration  of core-hole correlation spectroscopy in which resonant

core-level excitation of two atoms is used to probe the coupling between their respective valence states f1 and f2. Reprinted with permission from I. V. Schweigert and S. Mukamel, Physical Review Letters, 99, 163001, 2007. Copyright 2007 by the American Physical Society.20

It exploits nonlinear interactions with coherent X-ray pulses to probe correlation effects between pairs of valence electrons excited at different atomic sites in a molecule. Figure 23.6 presents an example in which core-hole correlation spectroscopy probes the quantum coupling between nitrogen- and oxygen-associated valence states in different isomers of aminophenol. Here, two pulses probe the aminophenol molecule, one centered at 400 eV (ωN) and the other at 535 eV (ωO), in resonance with the N-1s and O-1s core excitations, respectively. In a coherent four-wave mixing implementation, the initial excitation is created by a pulse pair, and a third pulse (in a phase-matched geometry) reads out the scattered Raman signal. Thus, XCCS measures a third-order, χ(3), four-wave mixing process, whereby a sequence of three incident pulses (three fields), En(kn,ωn)|n = 1, 2, 3, generate a stimulated signal, e.g., Esig(−ω1 + ω2 + ω3), in the momentum-matched direction, ksig = −k1 + k2 + k3. The Fourier transform of the signal with respect to the time delays of the pulses creates a 2D spectral map of the valence electronic structure. Off-diagonal features in this 2D map are present only when there is correlation between the two excited valence electrons on the N and O atoms; no signal should be seen in the Hartree–Fock limit of independent orbitals. Calculations show that the extent of this correlation depends not only on molecular structure (i.e., it differs in ortho- and para-aminophenol), but also on the nature of the molecular orbitals excited within the energy envelopes (∼10 eV) of ωN and ωO.20,21 An important criterion for core-level correlation spectroscopy is that the X-ray pulse durations must be faster than the Auger decay time (∼5 fs25), since Auger decay suppresses the correlation signal of interest. A rough estimate for the photon densities required for SXRS, XCCS, and related nonlinear X-ray science is based on typical absorptions cross-sections in the soft X-ray range, ∼10−18 cm2, which suggests that a fluence of >1017 ph cm−2  

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Figure 23.6  Valence  and core-excited states of the para and ortho isomers of amino­

phenol, and the predicted corresponding 2D X-ray core-hole correlation maps. The off-diagonal cross-peaks (right map) indicate the quantum mixing between nitrogen- and oxygen-associated valence states [mixing of the N-1s and O-1s X-ray absorption near edge structure (XANES) spectra]. Such quantum effects are absent in the para isomer due to the separation of the O and N atoms. Reprinted with permission from I. V. Schweigert and S. Mukamel, Physical Review Letters, 99, 163001, 2007. Copyright 2007 by the American Physical Society.20

is required. In the case of XCCS, the pulse duration must be comparable to (or less than) the order of the core-hole lifetime (∼5 fs for X-ray transitions25). This corresponds to >109 photons pulse−1 in a 1 µm focus (>1015 W cm−2 at 500 eV). Estimates based on X-ray nonlinear susceptibilities lead to similar conclusions for the required X-ray peak power density.18,20 Note that modern nonlinear optical spectroscopy experiments typically operate in the perturbative regime, ∼0.1 photons per cross-section, in order to avoid distortion of the spectral signal of interest from saturation, and other undesirable effects. In the case of SXRS, a coherent bandwidth of ∼3 to 5 eV is required to couple to a manifold of valence states in order to create a localized wavepacket. This corresponds to a pulse duration of 0.36 to 0.6 fs at the Fourier transform limit, although SXRS may be tolerant to some degree of pulse chirp.

23.2.3  LCLS Instrument NEH 1.1 A new LCLS instrument, NEH 1.1,26 is now under development to support the following areas of science: (1) fundamental dynamics of energy and charge as described above, as well as (2) quantum systems in strong fields, and

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(3) nanoscale structure and dynamics in matter via soft X-ray coherent imaging and scattering. The tuning range of NEH 1.1 will span from 0.25 to 2.5 keV covering the K-edges of critical light elements, C (284 eV), N (410 eV), and O (543 eV), through the L-edges of the 3d transition metals, and extending into the tender X-ray range where an optimum balance is predicted between resolution and scattering cross-sections for coherent X-ray imaging applications.27 The instrument will operate without a monochromator to support sub-femtosecond and two-color operating modes of LCLS.28,29 Instrument NEH 1.1 will support two endstations: the Dynamic REAction Microscope (DREAM) and LAMP (named after the original LCLS-ASG-Michigan project). The new DREAM endstation will be optimized for dynamic reaction microscope studies with extreme vacuum, sub-micron X-ray focus, and will target purity requirements dictated by pump-probe and coincidence detection at repetition rates in excess of 100 kHz. The projected X-ray fluence from the SXU source is ∼1021 photons cm−2 (e.g., at 700 eV) with the new CW-SCRF linac at high repetition rate, and ∼1022 photons cm−2 with the existing copper (Cu-RF) linac at 120 Hz.30 LAMP is a highly flexible and modular endstation optimized for coherent forward scattering, small and wide angle scattering, diffraction, and imaging. It will accommodate a variety of gas, liquid, and solid samples, and will support a suite of established spectrometers including high resolution ion and electron TOF (iTOF, eTOF) spectrometers, magnetic bottle, hemispherical analyzer, velocity-map imaging (VMI), etc., in addition to the suite of LCLS X-ray imaging detectors. The projected X-ray fluence is ∼1021 photons cm−2 (e.g., at 700 eV) with the CW-SCRF linac, and ∼1022 photons cm−2 with the Cu-RF linac.30

23.3  Photo-catalysis and Coordination Chemistry Understanding the fundamental processes of photo-chemistry is essential for the directed design of photo-catalytic systems for chemical transformation and solar energy conversion that are efficient, chemically selective, robust, and based on earth-abundant elements. The central events of excited state chemistry critically influence the performance of photo-catalysts since stable charge separation, transport, and localization are mediated by internal conversion, intersystem crossing, and conformational changes on the ultrafast time scale. Understanding charge dynamics in molecular systems with strong interactions between the electronic and nuclear structure, particularly for systems far from equilibrium, remains a significant challenge as these processes cannot be readily observed or calculated with standard experimental or theoretical methods. Conventional chemistry models assume disparate time scales for the evolution of electronic and atomic structures (Born–Oppenheimer approximation), but evidence points to the importance of coupled electronic/atomic structures (non-Born–Oppenheimer) in many systems. In materials and molecules with strong coupling between charge and vibrational modes, carriers trap in self-induced local distortions (conformational changes) and defects.

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Figure 23.7  Non-equilibrium  electron-transfer across the photoexcited

( 1RuII= 1CoIII) model photo-catalyst. The fundamental time scales are indicated, as obtained from transient optical absorption spectroscopy (TOAS), X-ray emission spectroscopy (XES), and X-ray diffuse scattering (XDS). Reprinted by permission from Macmillan Publishers Ltd: Nature Communications,32 copyright (2015).

The energetics and dynamics of these processes are critical to the photo-  catalyst performance, but we lack the requisite tools to reliably disentangle the coupled motion of electrons and nuclei in many energy-critical materials. New tools that enable direct observation of these central events will qualitatively advance our understanding of chemical dynamics in photo-catalytic systems, and advance the development of design principles for directing molecular and materials synthesis. The transition metal based Ru–Co donor–bridge–acceptor complex (shown in Figure 23.7) illustrates these ideas that impact on the performance of a diverse range of molecules and materials.31 In this model photo-catalyst, metal-to-ligand-charge transfer (MLCT) excitations of the coordinated Ru cation efficiently harvest visible light. This initiates a series of ultrafast changes in electronic and nuclear structure (spanning tens of femtoseconds to several picoseconds) including: electron transfer, solvation between the distinct ligands coordinating the Ru and Co cations, and conversion of the optically dark Co site from low-spin CoIII to high-spin CoII. In principle, the oxidized RuIII site and the reduced CoII site can catalyze oxidation and reduction reactions. While the processes that follow photoexcitation have been identified, the sequence of events remains unclear, and we lack effective design rules for how to manipulate these processes through intra- and inter-molecular modifications.

23.3.1  Excited-state Charge Dynamics via RIXS Ultrafast soft X-rays at high repetition rate from advanced XFELs will enable powerful new methods for understanding and ultimately controlling the physics and chemistry of photo-catalysis. Charge separation, charge transport,

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Figure 23.8  Left:  RIXS. Right: Time-resolved Fe L3-RIXS maps (energy transfer vs.

incident photon energy) of the Fe(CO)5 ground state (top), and difference intensities for the time intervals 0–700 fs (middle) and 0.7–3.5 ps (bottom). Reprinted by permission from Macmillan Publishers Ltd; Nature (ref. 32), Copyright (2015).

and catalysis are local phenomena. X-Ray techniques can disentangle the coupled motion of electrons and nuclear dynamics with atomic resolution and chemical specificity, making them uniquely powerful for studying chemical dynamics. The new capabilities of LCLS-II will complement and significantly enhance the present attributes of LCLS, particularly for X-ray spectroscopy such as RIXS, as shown in Figure 23.8. RIXS measures the energy distribution of occupied and unoccupied molecular orbitals, thus providing sensitivity to the local chemistry of a metal center with high resolution. Time-resolved RIXS at the femtosecond scale has recently been demonstrated at the LCLS where solution-phase studies of Fe(CO)5 were combined with quantum chemical calculations to provide the first detailed mechanistic picture of frontier-orbital changes associated with the ligand photo-dissociation process (Figure 23.8).32 These studies of large structural changes on model molecular systems at high concentrations (∼1 M) demonstrate the potential of time-resolved RIXS to correlate orbital symmetry with spin multiplicity and reactivity in short-lived reaction intermediates. However, the RIXS technique is currently still limited in data quality and not feasible for many interesting systems at lower concentration. With the dramatic increase in average brightness provided by high-repetition-rate XFELs, RIXS with high

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spectral resolution and femtosecond time resolution will enable complete time-sequenced mapping of frontier orbital energies and subtle conformational changes that drive charge separation and transfer in complex functioning systems where the active sites are often in dilute concentrations.

23.3.2  LCLS Instrument NEH 2.2 A new LCLS instrument, NEH 2.2,26 is now under development to support the following areas of science: (1) photo-catalysis and coordination chemistry as described above, (2) heterogeneous catalysis and interfacial chemistry, (3) nonequilibrium spin and magnetism at fundamental time scales, and (4) nanoscale electronic structure dynamics, heterogeneity, and fluctuations in materials. The tuning range of NEH 2.2 will span from 0.25 to 1.6 keV covering the K-edges of critical light elements, C (284 eV), N (410 eV), and O (543 eV), through the L-edges of the 3d transition metals, and extending into the lanthanide M4,5-edges. The instrument will be served by the SXU source followed by a monochromator with adjustable resolving power from R = 10 000 to 50 000 at close to the Fourier transform limit. For example, ΔEFWHM = 100 meV ⇔ ΔtFWHM = 18 fs (R = 10 000 at 1 keV) or ΔE = 20 meV ⇔ Δt = 90 fs  (R = 50 000 at 1 keV). NEH 2.2 will provide an adjustable focus from ∼1 µm (horiz.) × 4 µm (vert.), compatible with high spectrometer resolution and micron-scale liquid jets, up to ∼1 mm diameter for moderate spectrometer resolution, high throughput, and low incident fluence (ph cm−2) as maybe required for delicate samples. Instrument NEH 2.2 will incorporate a kinematic mounting scheme for accommodation of a wide range of specialized endstations supporting the following experimental capabilities:     (a) Resonant coherent X-ray imaging and small angle X-ray scattering for studies of non-periodic materials, nano-structures, and domain dynamics (e.g., magnetization imaging and dynamics). This endstation will provide moderate vacuum (∼10−7 Torr) and will incorporate a forward scattering area detector with adjustable q-range suitable to access nanometer to micrometer length scales, and in-situ magnetic field capabilities. (b) Low-resolution spectroscopy (XAS, XES, and RIXS) for studies of the excited-state dynamics of condensed-phase molecules (predominantly solution environment): photo-catalysts, metallo-enzymes, and other bio-molecules. This endstation will accommodate both liquid jets and solid samples. A moderate resolution spectrometer (