Fokker–Planck–Kramers equation treatment of dynamics of diffusion-controlled reactions using continuous velocity distribution in three dimensions

Abstract

A theory has been developed for the short-time dynamics of diffusion-controlled reactions based on the Fokker–Planck–Kramers equation (FPKE) in three dimensions. A continuous velocity distribution function has been proposed to solve the FPKE approximately. The present theory agrees better with the Langevin dynamics results than the earlier theory using a discontinuous velocity distribution. This indicates the validity of the present theory in three dimensions, because the Langevin dynamics results can be assumed to be the exact solutions to the FPKE. The theory is compared with molecular dynamics (MD) simulations in Lennard-Jones fluids to examine the applicability for realistic systems. The present theory predicts a somewhat smaller rate constant than the MD simulation in the time range of a few picoseconds. The discrepancies can be explained qualitatively in terms of the non-Markovian effect on the molecular motions.