Theoretical study of memory kernel and velocity correlation function for condensed phase isomerization. I. Memory kernel

Abstract

A unified memory kernel function is proposed on the basis of molecular dynamics simulations and comparison with experimental data. A frozen-solvent-like friction arises from the near-neighbor solvent cage effect, while the interaction between the system and the disordered heat bath or ‘‘broken cage’’ gives rise to a white-noise friction. On short time scales, the apparent friction is a ‘‘series addition’’ of these two limits, each solute molecule experiencing either an intact cage or a broken cage environment. For longer time scale behavior, the solvent is able to evolve, and some system molecules can experience both types of environments during the course of their own dynamics: the effective friction for these molecules then appears as a ‘‘parallel addition’’ of the same two contributions. This leads to a memory kernel having a simple exponential behavior. As the time scale for the system dynamics becomes still longer, the cage becomes indistinguishable from the heat bath, and a purely Markoffian relaxation with delta-function memory kernel ensues. This unified memory kernel model has been found to be applicable to ultrafast chemical reaction rates and diffusion properties both in molecular dynamics simulations and laboratory experiments.