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We present a practical semiclassical method for computing the electron spindynamics of a radical in which the electron spin is hyperfine coupled to alarge number of nuclear spins. This can be used to calculate the singlet andtriplet survival probabilities and quantum yields of radical recombinationreactions in the presence of magnetic fields. Our method differs from the earlysemiclassical theory of Schulten and Wolynes [J. Chem. Phys. 68, 3292 (1978)]in allowing each individual nuclear spin to precess around the electron spin,rather than assuming that the hyperfine coupling-weighted sum of nuclear spinvectors is fixed in space. The downside of removing this assumption is that onecan no longer obtain a simple closed-form expression for the electron spincorrelation tensor: our method requires a numerical calculation. However, thecomputational effort increases only linearly with the number of nuclear spins,rather than exponentially as in an exact quantum mechanical calculation. Themethod is therefore applicable to arbitrarily large radicals. Moreover, itapproaches quantitative agreement with quantum mechanics as the number ofnuclear spins increases and the environment of the electron spin becomes morecomplex, owing to the rapid quantum decoherence in complex systems. Unlike theSchulten-Wolynes theory, the present semiclassical theory predicts the correctlong-time behaviour of the electron spin correlation tensor, and it thereforecorrectly captures the low magnetic field effect in the singlet yield of aradical recombination reaction with a slow recombination rate.

An improved semiclassical theory of radical pair recombination reactions