Magnetic ® eld e ect as a probe of distance - dependent electron transfer in systems undergoing free di usion

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 re ̄ ected in the viscosity dependence of the magnetic ® eld e€ ect (MFE) on the e ciency of free radical formation u 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 di€ usion, distanceand spin-dependent backward electron transfer, coherent and incoherent spin evolution in the ps time domain. In comparison with real systems the spin situation is simpli® ed 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 u ce exhibits characteristic minima in the MFE versus viscosity curves, and it is veri® ed in detail that this feature is peculiar to the di€ usional 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 ® ngerprint of distance-dependent electron transfer. The theoretical results compare favourably with recent experimental results obtained with Ru complex/methylviologen RPs.