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

Abstract

A theoretical analysis is presented of the problem of how distance-dependent electron transfer in photoinduced forward electron transfer followed by geminate backward electron transfer in liquid solution is reflected in the viscosity dependence of the magnetic field effect (MFE) on the efficiency of free radical formation (φ_ce) in such reactions. The stochastic Liouville equation formalism is employed to model the reaction behaviour of distance-distributed, triplet-born radical pairs (RPs) undergoing free diffusion, distance- and spin-dependent backward electron transfer, coherent and incoherent spin evolution in the ps time domain. In comparison with real systems the spin situation is simplified by reducing it to a two state (S, T ₀) problem, 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 φ_ce exhibits characteristic minima in the MFE versus viscosity curves, and it is verified in detail that this feature is peculiar to the diffusional model with distance-dependent electron transfer, i.e. cannot be reproduced with the simpler (‘exponential’) RP model employing distance-independent rate constants. Thus, the MFE versus viscosity curves are established as a genuine fingerprint of distance-dependent electron transfer. The theoretical results compare favourably with recent experimental results obtained with Ru^III complex/methylviologen RPs.