Time-dependent importance sampling in semi-classical initial value representation calculations for time correlation functions. III. A state-resolved implementation to electronically non-adiabatic dynamics

Abstract

The recently developed time-dependent (TD) Monte Carlo (MC) importance sampling method [Tao and Miller; JCP 135, 024104 (2011)] provides an efficient implementation of the semi-classical (SC) initial value representation (IVR) methodology for the evaluation of time correlation functions. The key idea in this TD-SC-IVR method is to perform importance sampling of trajectories for the MC averages in the SC calculations with a sampling function that includes information about the final (time-evolved) values of the coordinates and momenta of trajectories in addition to (the usual) information of their initial values. This paper shows how this approach deals with electronically non-adiabatic dynamics, i.e. dynamics that involves coupled multiple electronic states. We suggest that a state-resolved sampling function may facilitate the efficient implementation of TD-SC-IVR for such processes. This is illustrated by application to the calculation of the nuclear momentum distribution function (i.e. the nuclear energy-loss spectrum) for a benchmark non-adiabatic scattering problem.