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.