Bimolecular kinetics according to a stochastic analysis of reactant dynamics

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Abstract
A stochastic representation of the reversible bimolecular process A+B⇌AB is introduced on the basis of the nearest-neighbor distribution. It leads to a description of the reactant pair dynamics under the action of its interaction potential, without introducing any boundary condition or sink function. In this way it becomes evident that reaction processes are particular manifestations of the molecular dynamics. The analysis of the eigenvalues of the time evolution operator allows one to identify the conditions for a well-defined time scale separation between the slow kinetic processes and the fast equilibration of the unbound pair. Correspondingly the rate equations for the reversible bimolecular kinetics are recovered from the long time behavior of the nearest-neighbor distribution. By means of asymptotic methods, analytical approximations are derived for the rate coefficients and their concentration dependence. This allows a simple rationalization of the effects of the interaction potential between the reagents.

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