Chapter 6: Nonadiabatic Electron Wavepacket Dynamics in Path-branching Representation

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.