Floquet theory of radical pairs in radiofrequency magnetic fields.
Journal of Chemical Physics
© 2017 AIP Publishing
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.
We gratefully acknowledge funding from the European Research Council under the European Union’s 7th Framework Programme, FP7/2007-2013/ERC Grant Agreement No. 340451, and from the US Air Force (USAF) Office of Scientific Research under the Air Force Materiel Command, USAF Award No. FA9550-14-1-0095.
This is the final version of the article. Available from AIP Publishing via the DOI in this record.
Journal of Chemical Physics, 2016, Vol. 145, 124117
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