Nonadiabatic processes tunneling effects

Below we will use Eq. (16), which, in certain models in the Born-Oppenheimer approximation, enables us to take into account both the dependence of the proton tunneling between fixed vibrational states on the coordinates of other nuclei and the contribution to the transition probability arising from the excited vibrational states of the proton. Taking into account that the proton is the easiest nucleus and that proton transfer reactions occur often between heavy donor and acceptor molecules we will not consider here the effects of the inertia, nonadiabaticity, and mixing of the normal coordinates. These effects will be considered in Section V in the discussion of the processes of the transfer of heavier atoms. 

All approaches for the description of nonadiabatic dynamics discussed so far have used the simple quasi-classical approximation (16) to describe the dynamics of the nuclear degrees of freedom. As a consequence, these methods are in general not able to account for processes or observables for which quantum effects of the nuclear degrees of freedom are important. Such processes include nuclear tunneling, interference effects in wave-packet dynamics, and the conservation of zero-point energy. In contrast to quasi-classical approximations, semiclassical methods take into account the phase exp iSi/h) of a classical trajectory and are therefore capable—at least in principle—of describing quantum effects. 

Most of the discussion in this chapter is based on a classical mechanics description of chemical reactions. Such classical pictures are relevant to many condensed phase reactions at and above room temperature and, as we shall see, can be generalized when needed to take into account the discrete nature of molecular states. In some situations quantum effects dominate and need to be treated explicitly. This is the case, for example, when tunneling is a rate determining process. Another important class is nonadiabatic reactions, where the rate detennining process is hopping (curve crossing) between two electronic states. Such reactions are discussed in Chapter 16 (see also Section 14.3.5). 

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