The generalized cumulant expansion approach to stochastic reductions in molecular collision dynamics: Applications to collisional energy transfer

A generalized cumulant expansion method is developed for applying stochastic reductions to molecular collision processes. We begin by introducing an approximate partitioning of a collision system into two subsystems Sr and Si which are assumed to be weakly correlated. Cumulant expansion methods are then used to simultaneously perform a stochastic reduction over Si, and a projection of the diagonal elements of the reduced density matrix for Sr thereby leading to a Pauli master equation describing Sr. We then apply this general equation using an impulse approximation partitioning to problems in inelastic V–T and R–T scattering. For He+H2 vibrationally inelastic collisions, the stochastic theory predicts low order moments and some probabilities in very good agreement with exact quantum results. In applications to He+H2 rigid rotor scattering, integral cross sections and opacity functions within 10%–30% of exact results are obtained at most energies.