On the calculation of diffusive reaction rates using Brownian dynamics simulations

An analytical derivation is presented of the expression of Northrup et al. [J. Chem. Phys. 80, 1517 (1984)] for extracting diffusive reaction rates from Brownian dynamics simulations. By working with the Smoluchowski equation governing the distribution function of the reactants, we obtain two identities that directly lead to this expression. This derivation provides a rigorous theoretical basis for this important expression.