A Generalized Fokker–Planck Equation Treatment of Inertia and Non-Markovian Effects on the Short-Time Dynamics of a Collision-Induced Reaction

Abstract

Abstract The inertia and non-Markovian effects on the short-time dynamics of a diffusion-controlled reaction were studied using a generalized Fokker–Planck equation with a boundary condition suitable for a collision-induced reaction. The approximation of half-range Maxwellian velocity distributions was employed to calculate the time-dependent rate constant. At time zero, the rate constant obtained analytically exhibits a limiting value which is independent of the friction kernels, and is smaller than that of the Smoluchowski–Collins–Kimball (SCK) theory. At finite times, the rate constant is obtained numerically, and its initial decay is slower than that of the SCK theory even when only the inertia effect is taken into account. When a non-Markovian effect is also taken into account, the initial slow decay becomes more pronounced. We have also found that the theoretical rate constant is sensitive to the boundary condition for the velocity distribution at the reaction radius. In order to test the results, we carried out a computer simulation of an encounter reaction between a test particle and hard-sphere reactants in a hard-sphere fluid, and obtained the survival probabilities of the test particle. Our results agree excellently with the simulation results.