Optimization of Brownian dynamics methods for diffusion-influenced rate constant calculations

Abstract

One-dimensional Brownian dynamics algorithms for reaction and reflection recently developed by Lamm and Schulten are adapted into the special boundary topology necessary to compute diffusion-influenced rate constants of arbitrarily complicated bimolecular reactions in three dimensions. Performance of these relative to the primitive free diffusion algorithm commonly employed is discussed. Remaining sources of error arising from boundaries are (1) boundary curvature effects and (2) reactive discontinuity effects in cases where orientational criteria for reaction exist. The magnitudes of these errors are calculated as a function of simulation time step size. In addition, a special statistical sampling procedure is developed which allows the simultaneous treatment of a large class of reactive boundary problems in one simulation. This procedure is illustrated by the treatment of reactive patch size effects on the rate constant in the model of Solc and Stockmayer.