Classical mapping approaches for nonadiabatic dynamics: Short time analysis

A systematic approach to improve the short time dynamics for classical mapp ing treatments of nonadiabatic dynamics is developed. This approach is base d on the Taylor expansion of time-dependent observables around t=0. By samp ling initial conditions in a manner that renders accurate static moments of the electronic population, it is shown that the short time electronic popu lation dynamics described by classical mapping approaches for nonadiabatic dynamics can be greatly improved. The approach is illustrated on the exampl e of the spin-boson model. For this problem, the analysis of the expansion coefficients reveals why classical mapping approaches to nonadiabatic dynam ics often perform much worse for energetically biased reactions than they d o for reactions with zero bias. The analysis presented here not only allows for the improvement of short time (and often long time) behavior, but also points to a systematic way of accessing how accurate a given classical map ping approach should be for a given problem. (C) 2001 American Institute of Physics.