  We describe how the semiclassical theory of radical pair recombination
reactions 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 different
singlet and triplet recombination rates. This is a non-trivial generalisation
because when the recombination rates are different the recombination process is
dynamically coupled to the coherent electron spin dynamics of the radical pair.
Furthermore, because the recombination operator is a two-electron operator, it
is no longer sufficient simply to consider the two electrons as classical
vectors: one has to consider the complete set of 16 two-electron spin operators
as independent classical variables. The resulting semiclassical theory is first
validated by comparison with exact quantum mechanical results for a model
radical pair containing 12 nuclear spins. It is then used to shed light on the
spin dynamics of a carotenoid-porphyrin-fullerene (CPF) triad containing
considerably 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 biphasic
behaviour that has been observed in the effect of an Earth-strength magnetic
field on the time-dependent survival probability of the photo-excited C+PF-
radical pair arises from a delicate balance between its asymmetric
recombination and the relaxation of the electron spin in the carotenoid
radical.
