Recombination of radical pairs in high magnetic fields: A path integral-Monte Carlo treatment

The magnetic field dependence of photoinduced geminate hydrogen (electron) transfer processes originates from a Brownian motion of radical pairs, a hyperfine coupling, and Zeeman-induced precession of the unpaired electron spins and a spin-selective recombination. In this paper we introduce a Wiener path integral description for these processes. This approach entails an integration over all possible diffusion trajectories of two functional, one that weights the diffusion paths according to the laws of Brownian motion, and a second that accounts for the spin motion and recombination of the radical pairs. This formulation maintains a close connection with the actual physical processes and is suitable for microscopic radical reaction processes under quite general circumstances. For the path integration we employ a Monte Carlo method, and for the electron spin precession we adopt a semiclassical approximation. The theory is then applied to the magnetic field dependence of a photoinduced hydrogen transfer process involving a ketyl-hexyl radical pair recently observed with nanosecond time resolution at fields of a few kG. It is argued that the magnetic field dependence observed cannot be reconciled with a simple hyperfine-coupled Zeeman-induced spin motion. Finally, a simple analytical expression for the magnetic field dependence of geminate radical pair recombination at high magnetic fields is presented.