The generation, diffusion, spin motion, and recombination of radical pairs in solution in the nanosecond time domain

Abstract

Pairs of radical ions generated in polar solvents by photoinduced electron transfer either recombine within a few nanoseconds to singlet and triplet products or separate. On the basis of recent time-resolved observations of a magnetic field dependence of the pair recombination a theoretical description of this process is provided. The description, similar to the radical pair theory of CIDNP and CIDEP, is founded on a coherent spin motion superimposed on the diffusive motion of the radicals. The spin motion is induced by the hyperfine coupling between electron and nuclear spins and can be modulated by low (0–200 G) magnetic fields. The spin-selective recombination of radicals is accounted for by a Feshbach optical potential. The diffusion process described by a Smoluchowski operator depends sensitively on the solvent properties. For the case of free Brownian motion, simple analytical expressions for the time- and magnetic-field-dependent recombination yields are derived. For the Brownian motion of oppositely charged radical ions a differential–difference approximation is used to demonstrate the dependence of the recombination yields on the viscosity and polarity of the solvent medium as well as on the strength of the hyperfine coupling and on the rate of the electron back transfer.