Analysis of Short-Time Transient Dynamics of a Diffusion-Controlled Reaction in a Hard-Sphere Fluid Based on Fokker–Planck–Kramers Equation

Abstract

Abstract Molecular dynamics (MD) simulations are performed for a simple diffusion-controlled reaction in a hard-sphere fluid. The short-time transient rate constants are compared with the Markovian Langevin dynamics (LD), two theories based on the Fokker–Planck–Kramers equation (FPKE), and the Smoluchowski–Collins–Kimball (SCK) theory based on the diffusion equation. At n* = 0.7856, where n* is the total number density reduced by the diameter of the molecules, molecular motions are diffusive and Markovian, and the MD results agree well with the LD results. At n* = 0.9428, the MD results are much larger than the LD ones at short times, and the discrepancy can be explained by non-Markovian effects. Also at n* = 0.2000, where inertia effects are important, the time profile of the MD rate constant is satisfactorily explained by LD, while the MD rate constant shows a smaller decay than at higher densities. FPKE theory with a continuous velocity distribution reproduces the LD results under all conditions indicating that the theory is valid over a wide density range. FPKE theory with a discontinuous velocity distribution cannot explain the simulation results at the lowest density despite taking into account inertia effects. Although SCK theory is expected to be valid only at high densities, the predicted rate constant is close to that from the simulation even at the lowest density, if the intrinsic rate constant is chosen to reproduce the exact value of the initial rate constant.