Chemical Theory beyond the Born-Oppenheimer Paradigm

The following sections are included:

• Contents
• Preface
• Acknowledgments

The following sections are included:

• Potential energy surfaces and nonadiabatic transitions
  • Electronic state theory
  • Nonadiabatic transitions—A brief overview
• Necessity of nonadiabatic dynamical electron theory
  • Progress in laser chemistry
  • Chemistry without potential energy surfaces: Highly quasi-degenerate electronic states
  • General theory of mixed quantum and classical dynamics
• Structure of this book

The following sections are included:

• Born–Huang expansion
• Born–Oppenheimer approximation
  • Bound states and notion of potential energy surface
  • Stationary-state scattering theory for electrons by molecules
• Validity of the BO approximation
• Generalization of the adiabatic electronic states

On the very affirmative basis about the accuracy of the adiabatic potential energy surfaces as shown above, one can study the dynamics of nuclear motions on those potential surfaces to explore the dynamical aspects of chemical reactions like rate process and product distribution, which are not determined by the energetics within quantum chemistry. In this class of dynamics, everything begins from Eq. (2.10), which declares that an adiabatic potential energy surface arising from the electronic energy serves as a potential energy function for the nuclei involved…

Although this book attempts to guide readers to modern nonadiabatic electron wavepacket theory (both in the presence and absence of external laser fields), we should first review the traditional theories, which have led the study of nonadiabatic transitions for a long time. Our motive for reviewing time-honored theories is not a historical interest but to help readers to understand fundamental ideas in the nonadiabatic dynamics, and therefore the list of the theories presented here is far from perfect. More complete reviews are already available in Refs. [28, 84, 85, 117, 178, 198, 291, 295].

The Born–Oppenheimer (BO) approximation based on an infinitesimal limit of electron mass against nuclear one provides a solid notion as well as powerful theoretical tools for a description of molecular static properties. However, there exist many situations where this picture breaks down when a nuclear kinematic coupling magnitude sufficiently exceeds an adiabatic BO energy gap. Because the energy gaps in excited state manifold tend to become small compared to that against the ground electronic state, the BO break down is usual in an excited state dynamics in molecule. The typical examples are the photochemical reaction dynamics accompanied with the crossing of different electronic characters and electron fluctuation induced by structural deformation in electronically unstable system. This BO breakdown assists many important chemical phenomena involved with an electronic quantum nature, for instance, a long range energy transfer in an excited state manifold, flexible chemical bond deformation, and so on. The molecular model should be constructed according to the characteristics of its constituents in as possible as natural manner. Otherwise, the theory would not work on prediction of molecular properties. In this chapter, we look at its physical origin and overview the several theoretical formalisms intended for describing this non-BO chemistry.

In this chapter we introduce a theory of electron dynamics involved with nonadiabatic path branching of nuclear motions. We have already emphasized in Chapter 1 an importance of the studies on real-time dynamics of electron wavepackets, which may undergo nonadiabatic transitions in the presence or absence of optical fields. The theory presented below can be regarded as one of the most general theories for dynamics in mixed quantum and classical representation. It will also give a complete theoretical foundation of the semiclassical Ehrenfest theory, which was derive rather intuitively without a rigorously theoretical basis. This section also serves as a preparation of the (nonadiabatic) electron wavepacket dynamics of molecules placed in intense and/or extremely short pulse lasers, which will be discussed in Chap. 8. Even without lasers, the electron wavepacket theory offers a promising method to analyze very fast chemical reactions, in which the dynamics of electrons are supposed to dominate chemical changes.

In the preceding section we have studied the rather formal theory for adiabatic electron wavepacket dynamics and its technical aspects. Electronic theory of organic chemistry had been initiated even before wave (quantum) mechanics and was brought to be the final form by Robinson and Ingold. It still constitutes the very basic heart of the theoretical understanding of chemical reactivity. The valence bond theory, resonance theory, the notion of electron negativity by Pauling and the so-called π-electron theories by Coulson and many other authors are the first monumental works of quantum mechanical reaction theory. Then, after the progress of molecular orbital theory based on the Hartree–Fock method by Mulliken et al., the frontier orbital theory by Fukui and the Woodward–Hoffmann rule have established the idea on how critical the role of quantum phases is to comprehend and even predict chemical reactions. Yamaguchi and Fueno have developed a theory of non-concerted chemical reactions (the Woodward– Hoffmann forbidden reaction), in which biradicals (even in totally spin singlet case) are generated in the course of reactions mainly by nonadiabatic interactions. Recent progress in chemical reaction theory relies more on accurate energetics such as the relative relations of the transition states with respect to the initial molecular arrangement, and so on. All these theories are based on the Born–Oppenheimer approximation, and therefore no chemical or physical situation beyond it is considered, such as time-fluctuation of electronic states due to the breakdown of the BO approximation, which becomes prominent for dynamics in the manifold of highly quasi-degenerate electronic states…

In Chapter 5, we have studied some of the effects of laser fields on chemical dynamics. In particular, we have investigated how time-resolved photoelectron spectroscopy can be used as a very good means to monitor the femtosecond-scale nuclear dynamics such as the passage across nonadiabatic regions. The modulation of nonadiabatic interactions (both avoided crossing and conical intersection) is also among the main subjects from the view point of control of chemical reaction. Chapter 7, on the other hand, has treated nonadiabatic electron wavepacket dynamics relevant to chemical reactions. Here in this chapter, we therefore rise to the theory of electron dynamics in laser fields mainly associated with chemical dynamics…

The following sections are included:

• Epilogue
• Bibliography
• Index