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Register a new userFloquet theory of radical pairs in radiofrequency magnetic fields
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We present a new method for calculating the product yield of a radical pair recombination reaction in the presence of a weak time-dependent magnetic field. This method successfully circumvents the computational difficulties presented by a direct solution of the Liouville-von Neumann equation for a long-lived radical pair containing many hyperfine-coupled nuclear spins. Using a modified formulation of Floquet theory, treating the time-dependent magnetic field as a perturbation, and exploiting the slow radical pair recombination, we show that one can obtain a good approximation to the product yield by considering only nearly-degenerate sub-spaces of the Floquet space. Within a significant parameter range, the resulting method is found to give product yields in good agreement with exact quantum mechanical results for a variety of simple model radical pairs. Moreover it is considerably more efficient than the exact calculation, and it can be applied to radical pairs containing significantly more nuclear spins. This promises to open the door to realistic theoretical investigations of the effect of radiofrequency electromagnetic radiation on the photochemically induced radical pair recombination reactions in the avian retina which are believed to be responsible for the magnetic compass sense of migratory birds.
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Radical pair recombination reactions are known to be sensitive to the application of both low and high magnetic fields. The application of a weak magnetic field reduces the singlet yield of a singlet-born radical pair, whereas the application of a strong magnetic field increases the singlet yield. The high field effect arises from energy conservation: when the magnetic field is stronger than the sum of the hyperfine fields in the two radicals, ${rm S}to {rm T}_{pm}$ transitions become energetically forbidden, thereby reducing the number of pathways for singlet to triplet interconversion. The low field effect arises from symmetry breaking: the application of a weak magnetic field lifts degeneracies among the zero field eigenstates and increases the number of pathways for singlet to triplet interconversion. However, the details of this effect are more subtle, and have not previously been properly explained. Here we present a complete analysis of the low field effect in a radical pair containing a single proton, and in a radical pair in which one of the radicals contains a large number of hyperfine-coupled nuclear spins. We find that the new transitions that occur when the field is switched on are between ${rm S}$ and ${rm T}_0$ in both cases, and not between ${rm S}$ and ${rm T}_{pm}$ as has previously been claimed. We then illustrate this result by using it in conjunction with semiclassical spin dynamics simulations to account for the observation of a biphasic--triphasic--biphasic transition with increasing magnetic field strength in the magnetic field effect on the time-dependent survival probability of a photoexcited carotenoid-porphyrin-fullerene radical pair.
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