Diffusion-controlled reactions: A revisit of Noyes’ theory

Abstract

Noyes’ theory of diffusion-controlled reactions is revisited in great details. First, it is shown that this theory provides an interesting alternative approach to perform molecular dynamics simulations for diffusion-controlled reactions. With this approach, reaction rate can be determined from simulations of nonreactive equilibrium systems. No annihilation procedure is needed to simulate the reaction event. Provided that encounters with different reactants are strictly uncorrelated, the reaction rate can be determined more directly and accurately than by the methods that compute the survival probability. We describe in detail the method for accurately determining the key quantity in Noyes’ theory, i.e., the first recollision probability, from molecular dynamics simulations. It will also be shown that arguments similar to those in Noyes’ theory allow us to establish an exact relation (under the same assumptions of absence of correlations) between the distribution function of a reacting system at the encounter distance and that of a nonreactive equilibrium system. This relation can be used to fix the boundary condition at the reaction distance in the approaches based on a diffusion equation. New insights have been gained into the usefulness of the recollision probability. The recollision probability also provides a very useful tool for characterizing quantitatively some dynamic features of the cage effect for reactions in dense liquids. Finally, the method presented here may also be used to calculate reaction rates for diffusion-controlled reactions in systems where the dynamics cannot be described by a diffusion equation.