Nonequilibrium distribution function formalism for diffusion-influenced bimolecular reactions: Beyond the superposition approximation

We introduce an improved and systematic procedure for solving the diffusion-influenced reaction kinetics problem based on a hierarchical set of kinetic equations for many-particle distribution functions. As a representative example, we apply the formalism to the reversible association kinetics problem. The new method gives an approximate analytic solution which is in almost perfect agreement with the Brownian dynamics simulation results for the whole time range. It is shown that results of previous nonequilibrium distribution function theories are reproduced as lower order solutions in the present formalism.