Comparison of three Brownian-dynamics algorithms for calculating rate constants of diffusion-influenced reactions

Abstract

A new algorithm for calculating the rate constants of diffusion-influenced reactions from Brownian-dynamics simulations is introduced and compared with two previous algorithms. It is based on the mean residence time of the pair of reactant molecules in the reactive region after the molecules are started from that region. Of the previous algorithms, one is based on the capture probability of one reactant molecule started on a spherical surface enclosing the other reactant molecule [Northrup et al., J. Chem. Phys. 80, 1517 (1984)]; the other is based on the survival probability of the pair of reactant molecules started in the reactive region [Zhou, J. Phys. Chem. 94, 8794 (1990)]. In the implementation of the residence-time based algorithm, analogy can be drawn between diffusion-influenced bimolecular reactions and diffusive energy-barrier crossing processes. When the reactive region is small, the pair of reactant molecules will be near the reactive region even after many multiples of the mean residence time have elapsed. Hence the residence time in the reactive region will not be significantly affected by the presence of an interaction potential U if the potential is smooth around the reactive region. This rationalizes an earlier analytic result k=k0〈exp(−U/kBT)〉, where k and k0 are the rate constants in the presence and absence of the potential. The three simulation algorithms are applied to the binding of a pointlike ligand to an immobile sphere with a reactive patch in the presence and absence of a Coulomb potential. The survival-probability based algorithm is always the most accurate and efficient one.