Magnetoreception is the ability of some animals to use the weak magnetic field of the Earth for navigation over long-distance migrations. It is a well-known phenomenon, but its underlying biophysical mechanisms remain poorly understood. One proposal involves light-induced, magnetically sensitive chemical reactions occurring within cryptochrome proteins, rationalised via the radical pair mechanism (Chapter 1). The absence of evidence in support of this hypothesis is in part due to the lack of sufficiently sensitive techniques to measure magnetic field effects (MFEs) in biological samples. Cavity-enhanced detection, most commonly in the form of cavity ring-down spectroscopy (CRDS) or cavity-enhanced absorption spectroscopy (CEAS), is widely used in the gas phase to provide significant sensitivity gains over traditional single-pass measurements (Chapter 2). However, successful studies in the condensed phase are less prevalent due to the additional background losses inherent to the sample. This thesis reports on the application of broadband (i.e. monitoring > 100nm) variants of CRDS and CEAS to the study of MFEs on the radical recombination reactions of flavin-based systems in solution. The broadband CRDS (BBCRDS) instrument employed in Chapter 4 is able to monitor the spectral changes induced by magnetic fields with submicrosecond time resolution. However, the need to scan both the probe wavelength and time delay to construct time-resolved spectra leads to prohibitively long acquisition times, and hence exposure of sensitive samples to high numbers of photons. The broadband CEAS (BBCEAS) studies reported in Chapter 5 combine the high irradiance and spectral coverage of a supercontinuum radiation (SCR) source with a CCD detector to simultaneously acquire absorption spectra across the visible region (480–700nm). The CW nature of this technique precludes the possibility of following radical pair kinetics in real time. In an effort to combine the respective advantages of these two instruments, which individually have represented powerful advances in capability, a new cavity-enhanced technique is reported for the first time (Chapter 6). The result, optical cavity-enhanced transient absorption spectroscopy (OCTAS), is able to simultaneously monitor spectral evolution and associated MFEs on the microsecond timescale, with comparable sensitivity to the existing techniques. Magnetic responses in animal cryptochrome proteins have successfully been recorded using all three techniques, lending considerable weight to the hypothesis that these molecules are at the heart of the magnetic sense in animals.

<strong>Chapter 1</strong> introduces the concept of spin, how spins interact, and how the spin state in a radical pair can affect the outcome of a chemical reaction between the unpaired electrons. The computational methodology for simulating such radical pairs is also discussed. <strong>Chapter 2</strong> discusses anisotropy in the singlet recombination yield of a radical pair in a carotenoid-porphyrin-fullerene triad, containing many hyperfine couplings. The singlet yield was calculated as a function of the direction of an applied magnetic field, using symmetry in the molecule to reduce the size of the problem. The symmetry reduction was partially successful, however it was not possible to include all the hyperfine couplings in the molecule. <strong>Chapter 3</strong> introduces a radical pair located on a flavin ligand and a tryptophan residue in the protein cryptochrome, and discusses the spin-relaxation mechanism of singlet-triplet dephasing. Magnetic field effect curves, describing the formation of a secondary radical pair as a function of applied magnetic field, were found to be broader in longer-lived radical pairs, due to dephasing caused by spin-selective recombination to the singlet ground state. Additional singlet-triplet dephasing may occur due to hopping of one of the unpaired electrons, between a zone of strong exchange interaction and a zone of negligible exchange interaction, although this is an incomplete description of the spin-relaxation. <strong>Chapter 4</strong> discusses the effect of rotational tumbling on spin-relaxation in the flavin-tryptophan radical pair in cryptochrome. Simulations indicated that the resulting modulation of anisotropic hyperfine couplings contributed modestly to spinrelaxation during transient absorption measurements, but was insufficient to explain the lack of an experimental low-field effect, or to explain the width of the experimental magnetic field effect curves as a function of magnetic field strength. <strong>Chapter 5</strong> discusses magnetic field effects on the mutual annihilation of a pair of triplet excitons in tetracene and anthracene crystals. The experimental singlet recombination yield was found, for the first time, to be modulated as a function of the direction of a applied magnetic field as weak as 2 mT. Simulations indicated that this anisotropy arose due to the zero field splitting of the electronic state in each triplet exciton. The direction of the external magnetic field altered the singlet component of the eigenstates of the Hamiltonian, and therefore altered the timeaverage of the singlet probability of a triplet exciton pair. This is different to the already established mechanism under a strong magnetic field, where the anisotropy arises from level crossings of eigenstates.

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The outcome of chemical reactions proceeding via radical pair (RP) intermediates can be influenced by the magnitude and direction of applied magnetic fields, even for interaction strengths far smaller than the thermal energy. Sensitivity to Earth-strength magnetic fields has been suggested as a biophysical mechanism of animal magnetoreception and this thesis is concerned with simulations of the effects of such weak magnetic fields on RP reaction yields. State-space restriction techniques previously used in the simulation of NMR spectra are here applied to RPs. Methods for improving the efficiency of Liouville-space spin dynamics calculations are presented along with a procedure to form operators directly into a reduced state-space. These are implemented in the spin dynamics software Spinach. Entanglement is shown to be a crucial ingredient for the observation of a low field effect on RP reaction yields in some cases. It is also observed that many chemically plausible initial states possess an inherent directionality which may be a useful source of anisotropy in RP reactions. The nature of the radical species involved in magnetoreception is investigated theoretically. It has been shown that European Robins are disorientated by weak radio-frequency (RF) fields at the frequency corresponding to the Zeeman splitting of a free electron. The potential role of superoxide and dioxygen is investigated and the anisotropic reaction yield in the presence of a RF-field, without a static field, is calculated. Magnetic field effect data for Escherichia coli photolyase and Arabidopsis thaliana cryptochrome 1, both expected to be magnetically sensitive, are satisfactorily modelled only when singlet-triplet dephasing is included. With a view to increasing the reaction yield anisotropy of a RP magnetoreceptor, a brief study of the amplification of the magnetic field experienced by a RP from nearby magnetite particles is presented. Finally in a digression from RPs, Spinach is used to determine the states expected to be immune from relaxation and therefore long-lived in NMR experiments on multi-spin systems.