Spin Dynamics in Radical Pairs

Abstract

The coherent spin dynamics of radical pairs play a crucial role in their reactions, which consequently cannot be described by a simple kinetic scheme. Instead, simulations of the spin dynamics are required in order to predict the rate and outcome of radical pair reactions, and especially their response to the application of a magnetic field. Unfortunately, the number of spin states of the radical pair increases exponentially with the number of nuclear spins, making deterministic quantum mechanical simulations of realistic radical pairs difficult. To overcome this difficulty, this thesis begins by presenting an efficient stochastic quantum mechanical method capable of describing a radical pair with as many as 20 nuclear spins, which we use to analyse spin-dependent charge recombination rates along molecular wires. This enables us to identify the mechanism of charge recombination of both the singlet and triplet states of the wire by determining their relative contributions to the overall recombination rate. We then derive an approximate semiclassical theory which allows to treat the spin dynamics of much larger radical pairs, since the time required for a semiclassical calculation scales linearly with the number of nuclear spins, rather than exponentially. Using this method, we reproduce the results of the first experiments to show that the outcome of a radical pair reaction may be in uenced by an Earthstrength magnetic field, and calculate the anisotropy in the singlet recombination yield of the radical pair thought to be responsible for avian magnetoreception. We show that our semiclassical theory reduces to the earlier Schulten-Wolynes theory under two additional approximations, and use this simpler theory to reveal that singlet-triplet dephasing plays an important role in the spin dynamics of polaron pairs in the semiconducting polymer layer of organic light emitting diodes. We derive a new expression which relates the magnetic field dependence of the electroluminescence and conductance observed in these materials to the singlet yield of the radical pair recombination reaction, which we confirm produces better agreement with experimental data than the relationships used previously.