Boundary conditions and reversibility in diffusion controlled reactions

Two simple models are explored in which a newly formed reaction product relaxes by internal radiationless transitions between its bound states and by redissociation and diffusion of the reactants back into the solvent. The boundary condition linking the diffusion and reaction processes is found to be of the radiation–convolution form, first derived by Northrup and Hynes. However, the kernel or memory function of the convolution is found to consist of a set of N relaxation modes for the first model (N is the number of bound states) and an infinite denumerable set in the second model which presupposes the Smoluchowski equation in the reaction zone and in the body of the solvent. The two level model is discussed in detail and is found to lead to the usual irreversible form of the boundary condition at intermediate times and to a somewhat unexpected form close to equilibrium.