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Chemists have long been enthused by the elusive goal of being able to “steer” chemical reactions to a predicted conclusion. That goal seems nearer now using electronic control via excited state chemistry. However, to effect real progress, experimentalists and theorists need to work in tighter knit harmony than has been conventionally the case. Excited state theoretical chemistry is becoming an essential partner in experimental investigations, not only for the interpretation of the results but also to suggest new experiments. Indeed theory may soon reach the point where we can simulate experiment. The target audience of this book is theorists and experimentalists who may want to work together in this ambitious and sometimes challenging way.

The aim here is to develop the theoretical chemistry of the excited state that incorporates the integration of electronic structure methods and nuclear/electronic dynamics as well as mechanistic concepts based upon the shapes of excited state potential surfaces using cartoons constructed from valence bond (VB) theory. In recent decades, experimental excited state chemistry has reached the point where time resolution is short enough to resolve nuclear dynamics, so-called “femtochemistry” and we are just entering the even faster attosecond era where we can resolve electronic motion as well. This is a significant advance that motivates us to develop the new field of “attochemistry” and to consider electronic control to “steer” chemistry by creating a superposition of electronic states using an attosecond laser pulse. Designing an appropriate laser pulse is one example of the need for joint theorist/experimentalist effort.

The chemistry of the excited state needs more sophisticated (multi-state) electronic structure methods because it involves nonadiabatic events (surface crossings) where the Born–Oppenheimer concept of a potential surface breaks down. Thus an integrated approach involving electronic structure computations and nonadiabatic dynamics is required. In attochemistry, the electronic and nuclear motion may even be asynchronous.

Most chemists learn synthetic chemistry in a conceptual way. Molecular orbital theory, resonance theory and VB theory provide the basis for the rationalisation of most ground state structure and reactivity. The judicious use of “curved arrows”, which focuses on the migration of electron-pairs, provides an approach through which the synthetic chemist can interpolate between experiments and predict the course of chemical reactivity. Multi-bond reactions, where the electrons rearrange (e.g. pericyclic reactions) are rationalised through the use of the Woodward–Hoffman approach.1  Such approaches enable the rationalisation of much of ground state (thermal) synthetic organic chemistry.

The mechanisms of excited state reactivity are not as well developed. There are few mechanistic ideas based upon simple bonding considerations that enable the prediction or rationalisation of electronic excited state reactivity. The reason for this is that an electronic excited state reaction begins with the absorption of light, which promotes the system to an excited state. However, the bonding in this excited state must be different from the bonding in the ground state and there is very little qualitative theory that predicts excited state bonding patterns. The molecule in the excited state will thus be subjected to forces that arise as a result of the new bonding pattern. Accordingly, the excited state molecule will evolve and change its geometry along a reaction path. Upon return to the ground state, the system will again evolve along a reaction path where the forces are characteristic of the ground state bonding situation rather than the excited state bonding situation.

It is clear that in order to understand excited state chemistry from a conceptual point of view, we must understand how the bonding in an excited state differs from that in the ground state, since this determines the forces that govern the initial reaction path on an excited state. Further, we must understand the mechanism of radiationless decay. This means predicting the shape of the potential surface in the region where the electronically excited system must return to the ground state by changing from the excited state potential surface to the ground state potential surface. Physically, radiationless decay occurs as a result of nonadiabatic coupling, where nuclear and electronic motion become coupled. It is only recently that theoretical calculations have given some insight into the nature of this nonadiabatic event. At the point of radiationless decay, the bonding in both the excited state and the ground state balance each other.

The preceding paragraphs identify some key conceptual problems of excited state chemistry. The information needed to understand these concepts must come from both theory and experiment. Thus the study of theoretical aspects of excited state chemistry requires a three-pronged attack: the development of the conceptual/mechanistic aspects just discussed, the use of theoretical electronic structure computations coupled with nuclear dynamics and, of course, complementary experiments using time resolved spectroscopy. This book will attempt to discuss the first two aspects making connections with the third aspect via case studies. In our discussions of theoretical computations, we will try to focus on the conceptual aspects rather than particular algorithms or computer software. Thus our aim is more to enlighten the end user of the conceptual aspects of the various computational methods so that they can choose methods that are appropriate for the particular problem being addressed. The most important conceptual idea is that excited state chemistry involves at least two electronic states simultaneously. The methods for electronic structure and dynamics (i.e. reactivity) used must reflect this idea.

The relationship between the bonding pattern and the gradients, which drive nuclear motion, can be understood using VB theory. In general, there are two types of electronic excited state: states that involve charge transfer to create a zwitterionic state (typically a HOMO–LUMO excitation) or states where the pattern of single and double bonds changes (for example single double bond inversion in the dark excited state of a polyene). These conceptual changes are most easily described using VB theory and this is the approach that we will exploit, for discussing concepts, in this book. VB theory describes electronic structure explicitly in terms of paired electrons and zwitterionic structures. We will exploit these VB ideas in this book to develop some analytical models that can be used to generalise the results of theoretical computations. In addition these ideas can be extracted from general electronic structure computations.2,3 

Radiationless decay, where the electronically excited system returns to the ground state without emitting light is central to excited state reactivity. This occurs when nonadiabatic coupling (coupling between nuclear and electronic motion) is large. Nonadiabatic coupling is intense around molecular geometries where two electronic states are degenerate. This was first pointed out by Teller4  in 1937, who extended the seminal work of Zener5  in 1932 on nonadiabatic transition probabilities. Teller also demonstrated the possible existence of what he called “conical crossings” between potential energy surfaces in polyatomic molecules. This is in contrast with the non-crossing rule for diatomic molecules, first recognised by Hund6  in 1927 and demonstrated by Wigner and von Neumann7  in 1929. These non-avoided crossings or “funnels” are called conical intersections because of the local shape of the two potential energy surfaces around the degeneracy point. Zimmerman8  and Michl9  were the first to suggest, independently, that non-radiative decay (internal conversion) occurring at a conical intersection was the key feature to understand certain photochemical mechanisms. In the last few decades the subject has grown rapidly. Conical intersections are now discussed in textbooks of photochemistry.10,11  There are also numerous more specialized reviews.12–20 

Excited state computations involve both electronic structure methods and nonadiabatic dynamics. Electronic structure methods used must treat several states in a balanced way. This ultimately requires a balanced treatment of electron correlation. Our discussions of electronic structure methods will focus on this aspect so that the reader may make informed choices about the most appropriate methods to use in applications. The study of excited state chemical reactivity ultimately involves dynamics.21  Again, independent of whether one uses semi-classical or quantum dynamics for nuclear motion, at least two electronically excited states are always involved.14  We will develop this topic in a manner that is integrated with the various electronic structure methods.

This book is aimed at the advanced undergraduate or beginning postgraduate who will have had some exposure to excited state theoretical chemistry. We will assume an understanding of excited state chemistry that might be found in standard texts10,22–24  or the recent encyclopaedic text of Turro.11  This book might even be thought of as a sequel to the book of Michl,22  which was one of the first to treat excited state theoretical chemistry in the tradition we will follow in this book. In addition, we shall assume that the reader has some basic knowledge of quantum chemistry,25  but we will review the most important points as we need them.

This book collects the ideas developed in collaboration with former co-workers over many years. Our work on photochemistry was started in collaboration with Massimo Olivucci and the late Fernando Bernardi. Much of the work discussed in this book has involved current and former collaborators (Luis Blancafort, Mike Bearpark, Marco Garavelli, Graham Worth, Martial Boggio-Pasqua, Benjamin Lasorne, Martin Paterson Fabrizio Sicilia, Stefano Vanni, Morgane Vacher, Andrew Jenkins and Iakov Polak).

There are many figures in the book. They are mostly reproduced from original papers. So they are do not follow a coherent/consistent style. The captions are fairly detailed, so that the reader should be able to understand any figure without reference to the text.

Lastly, my thanks go to Dr Alex Simperler who edited the first complete draft and made many helpful suggestions and to my patient wife who spotted many typographical errors without understanding a single word of the text.

The figures in the text are in black and white. Full colour versions are available as ESI at http://dx.doi.org/10.1039/9781788013642.

Michael A. Robb

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