Magnetic field effect on the hyperfine-induced electron spin motion in radicals undergoing diamagnetic-paramagnetic exchange

A semiclassical description of the hyperfine-induced spin motion of radical pairs suggested recently [K. Schulten and P. G. Wolynes, J. Chem. Phys. 68, 3292 (1978)] has been generalized to arbitrary magnetic field situations. Analytical expressions for the elements of the electron spin correlation tensor 〈S(o) S(t)〉 averaged over all nuclear spin configurations are derived and applied to calculate the time evolution of the electron spin state of radical pairs initially prepared in a singlet state. The treatment includes the possibility that the radicals undergo a diamagnetic-paramagnetic exchange reaction. The effect of such exchange on the magnetic field dependence of the radical pair (triplet) recombination is predicted.