Diffusion, spin and reaction control in geminate reverse electron transfer

Kinetic analyses of geminate radical escape yields in terms of a simple (“exponential”) reaction scheme with first-order rate constants of separation and geminate recombination have been widely used in the literature, e.g. to evaluate rate constants of reverse electron transfer (k−et). Here we demonstrate the limited value of such rate constants by formally analysing, in terms of the exponential model, the diffusion coefficient (iz. viscosity) dependence of the radical escape yield as theoretically calculated in the framework of diffusion-dependent electron transfer theory (unified treatment of non-contact photoinduced forward and geminate reverse electron transfer). It is shown that, while the true electron transfer rate constant is kept constant, the apparent rate constant k−et from the exponential model undergoes a wide variation as a function of diffusion coefficient and the rate of spin conversion. Nevertheless, the function k−et(D) represented in a double log plot for various rates of spin conversion provides a useful map suitable to assign characteristic regions of diffusional, spin and reaction control of the geminate process. As an application to real systems the experimental example of the [Ru(bpy)3]2+/methylviologen system is reconsidered. Here a magnetic field effect on the k−et(D) dependence is useful to corroborate the non-contact formation of the radical pair in the photochemical forward electron transfer reaction.