Multistate quantum Fokker–Planck approach to nonadiabatic wave packet dynamics in pump–probe spectroscopy

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Abstract
The quantum Fokker–Planck equation of Caldeira and Leggett is generalized to a multistate system with anharmonic potentials and a coordinate dependent nonadiabatic coupling. A rigorous procedure for calculating the dynamics of nonadiabatic transitions in condensed phases and their monitoring by femtosecond pump–probe spectroscopy is developed using this equation. Model calculations for a harmonic system with various nonadiabatic coupling strengths and damping rates are presented. Nuclear wave packets in phase space related to electronic coherence are shown to provide an insight into the mechanism of nonadiabatic transitions. The Green’s function expression for these wave packets is used to explore possible algorithms for incorporating electronic dephasing in molecular dynamics simulations of curve crossing processes.