Effect of potential of mean force on short-time dynamics of a diffusion-controlled reaction in a hard-sphere fluid

Abstract

We calculated the time-dependent rate constant of a diffusion-controlled reaction between hard-spheres in a hard-sphere fluid at short times starting from the Fokker–Planck–Kramers equation combined with the approximation of half-range Maxwellian velocity distributions. For the potential function, we employed the potential of mean force (PMF) obtained from the equilibrium radial distribution function. The rate constant at short times was much larger than that neglecting the PMF effect, though the steady state rate constant did not sensitively depend on the PMF effect. This indicates that the effect of the initial distribution of the reactants is important in determining the rate constant at short times. The results were compared with a computer simulation. The dependences of the survival probability of a target on the time, the transmission coefficient, and the reactant concentration were examined, and satisfactory agreements between the calculation and the simulation were obtained at a relatively low density. At a high density, the non-Markovian effect should be taken into account to explain the simulation result.