Real-time path-integral simulation of vibrational transition probabilities of small molecules in clusters: Theory and application to Br2 in Ar

Abstract

A discretized real-time Feynman path integral is applied to a system containing a diatomic in a small cluster of solvent molecules. The system considered consists of Br2 in Ar. An adiabatic separation of variables is assumed. The solvent as well as the Br2 center of mass are gathered into a vector called bath or solvent coordinates. The forced oscillator approximation is used to analytically obtain the vibrational contribution to the transition amplitude. The discretized real-time propagators (bath dependent only, since the vibrational part is carried out analytically) are highly oscillatory and, therefore, not suitable for Monte Carlo calculations. The coarse-graining technique introduced by Filinov and developed by Freeman and Doll, and Miller is employed to make the integrals more suitable for Monte Carlo calculations. The computations are carried out for five different times. For each time, we study the convergence of the technique for a range of Gaussian widths used as conditioning functions. We also examine the convergence as a function of the number of points in the discretized description of the solvent path.