Stochastic model for the kinetic rate constants of bimolecular exchange reactions

Elementary exchange chemical reactions in stirred solutions (e.g., SN2 reactions) arise from the interplay between the reactive quantum-mechanical event and the roto-translational diffusion of the reaction partners in the medium. We develop a basic stochastic model capable of providing an interpretation of the macroscopic bimolecular rate constants that enter the mass-action kinetic law of bimolecular exchange reactions. The model is based on a simple, yet effective, reaction-diffusion scheme in which the mass transport is described as a diffusive process and the quantum-mechanical reactive events are treated as instantaneous jumps. The two processes are considered kinetically coupled but, as a first approximation, "orthogonal" to each other at the mechanistic level. The methodology is illustrated for the simple reaction of halide nucleophilic substitution to halomethane in aqueous solution, taking bromide and chloride as halides.