A rigorous foundation of the diffusion-influenced bimolecular reaction kinetics

We formulate a general theory of the diffusion-influenced kinetics of irreversible bimolecular reactions occurring in the low concentration limit. Starting from the classical Liouville equation for the reactants and explicit solvent molecules, a formally exact expression for the bimolecular reaction rate coefficient is derived; the structures of reactant molecules and the sink functions may be arbitrarily complicated. The present theoretical formulation shows clearly how the well-known Noyes and Wilemski-Fixman rate theories are related and can be improved in a systematic manner. The general properties of the rate coefficient such as the long-time behavior and the upper and the lower bounds are analyzed. When the reaction can occur at a range of distance, the non-Markovianity of repeated encounter events between a reactant pair becomes significant and either the Noyes theory or the Wilemski-Fixman theory fails. The present theory provides a practical method for calculating the rate expression for such reactions, which improves significantly on the Wilemski-Fixman theory.