Quasiclassical approximation, nonadiabatic dynamics

The mapping approach outlined above has been designed to furnish a well-defined classical limit of nonadiabatic quantum dynamics. The formalism applies in the same way at the quantum-mechanical, semiclassical (see Sec. 7), and quasiclassical level, respectively. Most important, no additional assumptions but the standard semiclassical and quasiclassical approximations are needed to get from one level to another. Most of the established mixed quantum-classical methods such as the mean-field-trajectory method or the surface-hopping approach do invoke additional assumptions. The comparison of the mapping approach to these formulations may therefore... 

All approaches for the description of nonadiabatic dynamics discussed so far invoke simple quasiclassical approximations to treat the dynamics of the nuclear degrees of freedom. As a consequence, these methods are in general not able to describe 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 as well as the conservation of zero-point energy. In contrast to purely classical approximations, semiclassical methods are in principle capable of describing quantum effects. 

In contrast to the quasiclassical approaches discussed in the previous sections of this review, Eq. (77) represents a description of nonadiabatic dynamics which is semiclassically exact in the sense that it requires only the basic semiclassical Van Vleck-Gutzwiller approximation to the quantum propagator. Therefore, it allows the description of electronic and nuclear quantum effects. 

Quantum mechanical effects—tunneling and interference, resonances, and electronic nonadiabaticity— play important roles in many chemical reactions. Rigorous quantum dynamics studies, that is, numerically accurate solutions of either the time-independent or time-dependent Schrodinger equations, provide the most correct and detailed description of a chemical reaction. While hmited to relatively small numbers of atoms by the standards of ordinary chemistry, numerically accurate quantum dynamics provides not only detailed insight into the nature of specific reactions, but benchmark results on which to base more approximate approaches, such as transition state theory and quasiclassical trajectories, which can be applied to larger systems. 

---