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We describe how the semiclassical theory of radical pair recombinationreactions recently introduced by two of us [D. E. Manolopoulos and P. J. Hore,J. Chem. Phys. 139, 124106 (2013)] can be generalised to allow for differentsinglet and triplet recombination rates. This is a non-trivial generalisationbecause when the recombination rates are different the recombination process isdynamically coupled to the coherent electron spin dynamics of the radical pair.Furthermore, because the recombination operator is a two-electron operator, itis no longer sufficient simply to consider the two electrons as classicalvectors: one has to consider the complete set of 16 two-electron spin operatorsas independent classical variables. The resulting semiclassical theory is firstvalidated by comparison with exact quantum mechanical results for a modelradical pair containing 12 nuclear spins. It is then used to shed light on thespin dynamics of a carotenoid-porphyrin-fullerene (CPF) triad containingconsiderably more nuclear spins which has recently been used to establish a'proof of principle' for the operation of a chemical compass [K. Maeda et al.,Nature 453, 387 (2008)]. We find in particular that the intriguing biphasicbehaviour that has been observed in the effect of an Earth-strength magneticfield on the time-dependent survival probability of the photo-excited C+PF-radical pair arises from a delicate balance between its asymmetricrecombination and the relaxation of the electron spin in the carotenoidradical.

Asymmetric recombination and electron spin relaxation in the semiclassical theory of radical pair reactions