Magnetic field effect as a probe of distance-dependent electron transfer in systems undergoing free diffusion

A theoretical analysis is presented of the problem of how distance-dependen t electron transfer in photoinduced forward electron transfer followed by g eminate backward electron transfer in liquid solution is reflected in the v iscosity dependence of the magnetic field effect (MFE) on the efficiency of free radical formation (phi(ce)) in such reactions. The stochastic Liouvil le equation formalism is employed to model the reaction behaviour of distan ce-distributed, triplet-born radical pairs (RPs) undergoing free diffusion, distance- and spin-dependent backward electron transfer, coherent and inco herent spin evolution in the ps time domain. In comparison with real system s the spin situation is simplified by reducing it to a two state (S, T-0) p roblem, yet it is parametrized in a way that allows sensible comparison of the results with those of recent experiments. It is predicted that the MFE on phi(ce), exhibits characteristic minima in the MFE versus viscosity curv es, and it is verified in detail that this feature is peculiar to the diffu sional model with distance-dependent electron transfer, i.e. cannot be repr oduced with the simpler ('exponential') RP model employing distance-indepen dent rate constants. Thus, the MFE versus viscosity curves are established as a genuine fingerprint of distance-dependent electron transfer. The theor etical results compare favourably with recent experimental results obtained with Ru-III complex/methylviologen RPs.