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

TL;DR

This paper extends the semiclassical theory of radical pair reactions to account for asymmetric recombination rates, enabling better modeling of spin dynamics in complex radical systems relevant to chemical magnetoreception.

Contribution

The authors generalize the semiclassical theory to include different singlet and triplet recombination rates and validate it against quantum results for complex radical pairs.

Findings

The extended theory accurately reproduces quantum results for a 12-nuclear-spin radical pair.

It explains the biphasic magnetic field effects observed in carotenoid-porphyrin-fullerene systems.

Asymmetric recombination influences the electron spin relaxation and radical pair survival probabilities.

Abstract

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.