Attosecond Molecular Dynamics

Marc J J Vrakking, Franck Lepine

• Publisher: Royal Society of Chemistry
• Year: 2018
• Print ISBN: 9781782629955
• eBook ISBN: 9781788015134
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Chemistry
• Index: Chemistry

Attosecond science is a new and rapidly developing research area in which molecular dynamics are studied at the timescale of a few attoseconds.

Within the past decade, attosecond pump–probe spectroscopy has emerged as a powerful experimental technique that permits electron dynamics to be followed on their natural timescales. With the development of this technology, physical chemists have been able to observe and control molecular dynamics on attosecond timescales. From these observations it has been suggested that attosecond to few-femtosecond timescale charge migration may induce what has been called "post-Born-Oppenheimer dynamics", where the nuclei respond to rapidly time-dependent force fields resulting from transient localization of the electrons. These real-time observations have spurred exciting new advances in the theoretical work to both explain and predict these novel dynamics.

This book presents an overview of current theoretical work relevant to attosecond science written by theoreticians who are presently at the forefront of its development. It is a valuable reference work for anyone working in the field of attosecond science as well as those studying the subject.

CHAPTER 1

Introduction

Marc J. J. Vrakking^a and Franck Lepine^b

^aMax Born Institute, 2A Max-Born Strasse, Berlin 12489, Germany

^bInstitut Lumière Matière, Université Lyon/CNRS, 10 Rue Ada Byron, Villeurbanne Cedex 69622, France
^*E-mail: [email protected]; [email protected]

In this introductory chapter, the rationale for the publication of this book is briefly explained: it aims to create a resource for both experimentalists and theoreticians that captures the current state-of-the-art in theoretical studies of attosecond molecular dynamics. We moreover present an overview of the current state-of-the-art of experimental studies of attosecond chemistry and molecular physics and present a short overview of the contents of the subsequent chapters, pointing out links between the material that is presented in the individual chapters.

1.1Introduction

The development of methods for the generation of attosecond pulses, as well as their use in time-resolved pump–probe experiments with attosecond time resolution, creates tremendous novel opportunities in atomic, molecular and condensed phase physics.¹ The attosecond timescale is the natural timescale for electronic motion, and is the fastest timescale that is relevant for investigations of the fundamental phenomena underlying many of the technologies that drive today’s information age. Attosecond spectroscopy got underway shortly after the turn of the century,^2,3 and initially focused on the development of necessary techniques and first applications of attosecond pump–probe spectroscopy in atomic physics. However, in the last few years, the scope of the applications of attosecond techniques has significantly broadened.

At the time that the first attosecond pulses were demonstrated, ideas for their use in molecular systems were soon suggested.^4,5 The use of time-domain methods in chemistry received a major impetus with the development of the field of femtochemistry towards the end of the last century.⁶ In femtochemistry experiments it is possible to “observe” the atomic motion underlying structural changes in molecules by performing pump–probe experiments, where a first femtosecond laser (the pump) excites a molecule, which is then allowed to evolve for a chosen period of time, before a second laser (the probe) further interacts with the molecule or its reaction products, leading to an observable that is measured as a function of pump–probe time delay.

The time-domain observation of chemical processes in a pump–probe experiment is based on the fact that the pump laser excites a coherent superposition of states, which, after the pump laser interaction has ceased, evolve with a phase factor that is proportional to their energy. The shorter the duration of the pump laser, and accordingly, the larger its energy bandwidth, the larger the energy bandwidth of the excited wave packet and the faster the dynamics that can be observed in the experiment will be. Femtochemistry experiments are almost exclusively based on the excitation of coherent superposition states that span a range of rotational and vibrational states, while maintaining well-defined electronic character. In other words, in a typical femtochemistry experiment a single electronic state is initially excited. The experiment may then reveal the relaxation of this excited state, through processes such as dissociation, internal conversion (IC) or intersystem crossing (ISC). The latter two processes occur when multiple electronic states become degenerate at a particular molecular geometry, the most important example of such a situation being a conical intersection.

The development of attosecond pulses created the opportunity to go beyond this paradigm. Attosecond pulses are so short^† that their bandwidth typically spans a range of electronic states. This means that, in addition to being sensitive to the rotational and vibrational coherence that is imposed on the molecule by the pump laser interaction, electronic coherences can be excited and probed. As a consequence the excitation (or ionization) of a molecule by an attosecond laser pulse is expected to lead to an electronic (or hole) motion on extremely short timescales, reaching down into the attosecond or few-femtosecond domain, i.e. a timescale that is short compared to the timescale that is commonly associated with vibrational or rotational motion.^‡ As a result, scenarios have been proposed where excitation or ionization of molecules by attosecond laser pulses creates the conditions for a so-called “charge-directed reactivity”,.⁷i.e. a time-evolution of the structural dynamics of the molecule driven by the electron (or hole) dynamics initiated by the attosecond laser pulse. To distinguish the purely electronic rearrangement preceding nuclear motion that one might be able to initiate using an attosecond pulse from the electronic rearrangement encountered in electron transfer processes, the term “charge migration” was coined to refer to electronic rearrangement processes resulting from the excitation of electronic coherent superpositions of states.⁸

It is important to point out that the dynamics initiated by an extreme ultraviolet (XUV) attosecond pulse is no different from the XUV-initiated dynamics that is encountered when another source of XUV radiation is used, such as a synchrotron. At a synchrotron, narrow bandwidth XUV radiation is available, and, following XUV single photon absorption, the observables that can be measured as a result of the photo-absorption are determined by the photon energy that has been selected. Similarly, when in an attosecond experiment a molecule absorbs an XUV photon without further interaction with any lasers, its fate (and the observables that can be measured as a result of this absorption process) is determined by the energy of the photon that it has selected out of the large available bandwidth of the attosecond pulse. The uniqueness of attosecond experiments derives from the fact that they are, by definition, pump–probe experiments. At some delay with respect to the pump laser interaction, the molecule has a further interaction with a probe laser, and this interaction can lead to an interference between multiple pathways that can be initiated by XUV photons with different energies, all lying within the bandwidth of the attosecond pulse, and with all pathways bringing the molecule to the same final state. This interference is a handle that can be used towards control of the outcome of the experiment, and it is in this way that the attosecond experiment can be used to control the outcome of the chemical process.

Two comments need to be made at this point, which together provide the motivation for the current book. Firstly, the short history of the field of attosecond science has already clearly shown that successful attosecond science requires a close interplay between experimental and theoretical research. The reason for this is relatively easy to understand. The enormous energy bandwidth of attosecond pulses creates a situation where, depending on their use as the pump or the probe laser in the experiment, the attosecond pulse will pump or probe many electronic, vibrational and rotational states at the same time, implying that many distinct dynamical processes are activated or probed at the same time. This situation is further reinforced by the fact that many current implementations of attosecond pump–probe spectroscopy use a two-color XUV+NIR pump–probe arrangement, where the XUV represents the attosecond pulse,^§ and NIR is a near-infrared driver laser that is furthermore used for the generation of the attosecond pulse (see below). In these experiments, attosecond time resolution is achieved by using the optical cycle of the NIR laser (which lasts 2.7 fs in the case of commonly used Ti : sapphire lasers with a central wavelength near 800 nm) as a clock with attosecond time resolution.^¶ While in most attosecond pump–probe experiments only a single attosecond XUV photon is absorbed, it is often not possible to ensure that only a single NIR photon is used in the pump–probe sequence, further increasing the number of processes that may occur in parallel in a given experiment, and increasing the challenge of interpreting the experiment. Theory plays an invaluable role in this process. Using theoretical and numerical methods, the range of states involved in an attosecond pump–probe experiment, as well as their possible signatures in the experimental observables, can be modeled, greatly facilitating the interpretation and the correct assignment of the observed phenomena.

Secondly, the excitation of electronic coherences in attosecond pump–probe experiments takes molecular dynamics outside the realm of femtochemistry experiments, implying that the theoretical and numerical methods that are commonly used to interpret femtochemistry experiments are no longer sufficient. When a single electronic state is excited in a pump–probe experiment, then this allows the use of numerical techniques that are based on the Born–Oppenheimer approximation. This approximation exploits the fact that the mass of electrons is smaller by several orders of magnitude than the mass of even the lightest of atoms. Accordingly, the Schrödinger equation can be separated into an equation that describes the electronic properties of a molecule under conditions where the molecular geometry is fixed, and an equation that describes the time-dependent changes of the molecular geometry. In the latter equation, the electronic energy takes on the role of potential energy, leading to the common description of dynamics in molecules in terms of ro-vibrational wave packets moving on a potential energy surface. Of course, in such a description, points on the potential energy surface where the Born–Oppenheimer approximation breaks down, i.e. geometries where two potential energy surfaces corresponding to two distinct electronic states approach each other (so that the electronic timescale, given by the inverse of the energy spacing between the two surfaces, becomes comparable to the ro-vibrational timescale), need to be given special attention, since they will give rise to ro-vibrational dynamics that is non-adiabatic, i.e. including transitions between the two potential energy surfaces. The excitation of electronic coherences in an attosecond experiment takes the molecular dynamics outside the realm of the Born–Oppenheimer approximation from the outset, and into a “post-Born–Oppenheimer” regime.⁹ where the electronic dynamics and the nuclear dynamics have to be treated in a fully correlated manner. Moreover, this dynamics often cannot be described in a single active electron picture, but is strongly influenced by electron correlation, which assumes increasing importance when molecules are excited by high energy photons that address inner valence and core levels.^|| Based on this argumentation we conclude that theoretical treatment of the molecular dynamics that is encountered in attosecond experiments requires the development of novel computational approaches that take electron correlation and electronic coherence into account in ways that have not previously been necessary or available.

This then leads us to the motivation of this book. In this book we have collected contributions from a number of leading theoreticians, who—each in their own way—have made important contributions to the development of the numerical approaches that are required for simulations of the chemistry and molecular physics that manifests themselves in the new experiments that have become possible, using a time-resolution in the attosecond domain. We have asked these authors to prepare a chapter, fulfilling a three-fold goal.

1. The book should serve as a resource for experimental researchers that would like to understand the theoretical methods appropriate for use in attosecond theoretical chemistry research. The strengths and limitations of particular techniques, the approximations that are inherent, and the conditions under which these approximations are justified should be described, leading to a better appreciation of how experimental and theoretical results can be compared with each other. This will facilitate the further development of the important (see above) connection between experimental and theoretical attosecond science.
2. The book should serve as a resource for new students and researchers that are joining the emerging field of attosecond theoretical chemistry. Accordingly, descriptions are needed of how a certain theoretical method is formulated, how the method is implemented, and what the particular numerical challenges are in its implementation.
3. The book should serve as a platform to showcase the current status of the attosecond theoretical chemistry field, by presenting selected results that have been achieved in recent years.

We hope that the readers of this book will find the material that is discussed in this book of significant interest, on the basis of one or more of the criteria defined above. In the remaining part of this introduction, we will present an overview of the current state-of-the-art in experimental studies of attosecond chemistry and molecular physics, and we will present a short overview of the contents of the subsequent chapters, pointing out links between the material that is presented in the individual chapters.

1.2State-of-the-art of Molecular Attosecond Experiments

The generation of attosecond laser pulses relies on the availability of techniques that are able to generate coherent light over a large energy bandwidth spanning multiple electron-Volts (eV).^** This implies that the occurrence of attosecond pulses is linked t...

Table of contents

• Cover
• Half Title
• Series editors
• Title
• Copyright
• Contents
• Chapter 1 Introduction
• Chapter 2 Low-dimensional Models for Simulating Attosecond Processes in Atoms and Molecules
• Chapter 3 First-principles Many-electron Dynamics Using the B-spline Algebraic Diagrammatic Construction Approach
• Chapter 4 Ultrafast Electron Dynamics as a Route to Explore Chemical Processes
• Chapter 5 Time-dependent Multiconfigurational Theories of Electronic and Nuclear Dynamics of Molecules in Intense Laser Fields
• Chapter 6 Light-induced Conical Intersections
• Chapter 7 Theoretical Methods for Attosecond Coupled Electron-nuclear Dynamics In Molecular Photoionization
• Chapter 8 How Nuclear Motion Affects Coherent Electron Dynamics in Molecules
• Chapter 9 Attophotochemistry: Coherent Electronic Dynamics and Nuclear Motion
• Chapter 10 General Trajectory Surface Hopping Method for Ultrafast Nonadiabatic Dynamics
• Chapter 11 Time-dependent Restricted-active-space Self-consistent-field Theory for Electron Dynamics on the Attosecond Timescale
• Chapter 12 Real-time and Real-space Time-dependent Density-functional Theory Approach to Attosecond Dynamics
• Chapter 13 Elements of Structure Retrieval in Ultrafast Electron and Laser-induced Electron Diffraction from Aligned Polyatomic Molecules
• Subject Index