It is a remarkable fact that the interactions between electron and nuclear spins, and their interactions with a magnetic field, can have a profound effect on chemical reactivity, despite the fact that the characteristic interaction energies are orders of magnitude smaller than thermal energy. These observations are explained by the existence of long-lived quantum coherences between spins in certain molecular species (in particular radical pairs), and the study of these spin effects constitutes the field of spin chemistry, a field which spans a wide range of systems, from biochemical reactions to device physics. Because spin chemistry involves subtle quantum effects, many intuitive models used by Physical Chemists, in particular classical kinetic equations, cannot be universally applied. On the other hand, complete first principles modelling of reactions involving spin effects comes at an impossibly high computational cost in complex systems, and often offers little physical insight. In order to address the shortcomings of these approaches, quantum master equations (QMEs) are employed to describe spin chemical phenomena. These are equations that describe a reduced set of degrees of freedom quantum mechanically, accounting for the effects of remaining degrees freedom implicitly. In this thesis I explore the use of QME techniques to resolve a range of problems in spin chemistry. These techniques can be used to obtain the correct radical pair spin QME, resolving questions about the role of quantum measurement in these systems. As well as aiding the development of the theory of spin chemistry, QMEs provide a practical tool for modelling radical pair reactions including spin relaxation effects, as I also demonstrate. As a final study of QME techniques in spin chemistry, I use these methods to show when the classical kinetic description of radical pair reactions is and is not valid.
It is a remarkable fact that the interactions between electron and nuclear spins, and their interactions with a magnetic field, can have a profound effect on chemical reactivity, despite the fact that the characteristic interaction energies are orders of magnitude smaller than thermal energy. These observations are explained by the existence of long-lived quantum coherences between spins in certain molecular species (in particular radical pairs), and the study of these spin effects constitutes the field of spin chemistry, a field which spans a wide range of systems, from biochemical reactions to device physics. Because spin chemistry involves subtle quantum effects, many intuitive models used by Physical Chemists, in particular classical kinetic equations, cannot be universally applied. On the other hand, complete first principles modelling of reactions involving spin effects comes at an impossibly high computational cost in complex systems, and often offers little physical insight. In order to address the shortcomings of these approaches, quantum master equations (QMEs) are employed to describe spin chemical phenomena. These are equations that describe a reduced set of degrees of freedom quantum mechanically, accounting for the effects of remaining degrees freedom implicitly. In this thesis I explore the use of QME techniques to resolve a range of problems in spin chemistry. These techniques can be used to obtain the correct radical pair spin QME, resolving questions about the role of quantum measurement in these systems. As well as aiding the development of the theory of spin chemistry, QMEs provide a practical tool for modelling radical pair reactions including spin relaxation effects, as I also demonstrate. As a final study of QME techniques in spin chemistry, I use these methods to show when the classical kinetic description of radical pair reactions is and is not valid.
The development of the radical pair mechanism has allowed for theoretical explanation of the fact that magnetic fields are observed to have an effect on chemical reactions. The mechanism describes how an external magnetic field can alter chemical yields by interacting with the spin state of a pair of radicals. In the field of quantum biology, there has been some interest in the application of the mechanism to biological systems. This paper takes an open quantum systems approach to a model of the radical pair mechanism in order to derive a master equation in the Born-Markov approximation for the case of two electrons, each interacting with an environment of nuclear spins as well as the external magnetic field, then placed in a dissipative bosonic bath. This model is used to investigate two different cases relating to radical pair dynamics. The first uses a collective coupling approach to simplify calculations for larger numbers of nuclei interacting with the radical pair. The second looks at the effects of different hyperfine configurations of the radical pair model, for instance the case in which one of the electrons interact with two nuclei with different hyperfine coupling constants. The results of these investigations are analysed to see if they offer any insights into the biological application of the radical pair mechanism in avian magnetoreception.
Radical pairs are short-lived, spin-correlated intermediates that underpin processes in chemistry, biology, and emerging quantum technologies. Their behavior is governed by coupled electron-nuclear spin dynamics and is sensitive to weak magnetic fields, but full quantum treatments have been obstructed by the extreme computational cost of modeling many interacting spins. Here, this barrier is removed, demonstrating that open-system radical-pair dynamics can be resolved at nuclear-spin scales previously intractable, explicitly reaching regimes with tens of coupled nuclei and validated up to 60 spins. In biologically relevant flavin-tryptophan radical pairs, electron-transfer pathways and magnetic-field anisotropy are found to reshape spin evolution and, in turn, spin-selective reaction yields. The resulting directional responses expose a strong mechanistic link between the nuclear environment, magnetic geometry, and chemical outcome-a relationship central to hypotheses of avian magnetoreception and other magnetic-field effects in biology. This establishes a widely applicable simulation framework that removes a long-standing barrier in spin chemistry, quantum biology, and spin-based device science.
The dynamics of many chemical systems can be influenced significantly by interactions with their environment (bath). An exact treatment of this is often infeasible due to the exponential scaling of Hilbert space with the number of degrees of freedom. In this thesis, dynamical methods, which overcome this difficulty, are considered for spin systems coupled to spin baths as well as systems coupled to harmonic oscillator baths. The thesis begins by considering recombination reactions of radical pairs, in which two electron spins interact with baths of nuclear spins. Motivated by inaccuracies observed in semiclassical treatments of the dynamics of a series of cryptochrome-based radical pairs, a new approach capable of treating the quantum dynamics of spin systems coupled to large baths of spins is presented. This method is validated for a series of central spin models, and is found to correctly describe the quantum dynamics of spin systems containing up to 1000 spins. Following this, the validity of the conventional treatment of radical pair recombination reactions is explored by considering the coupled electronic, nuclear and spin dynamics of a model radical ion pair. The dynamics of this model is treated using the hierarchical equations of motion (HEOM) formalism, and the results obtained are used to validate a recently proposed series of master equations. The HEOM formalism exactly captures the quantum dynamics of systems that are coupled to harmonic baths. However, due to the scaling of its computational cost with the strength of the coupling, it often becomes impractical. To overcome this difficulty, an efficient tree tensor network-based approach is presented and valided by treating a series of simple models. Following this, it is applied to the calculation of electron transfer rates for a series of models spanning a wide range of physical regimes in order to validate a recently proposed interpolation formula for the calculation of electron transfer rates.
The Radical Pair Mechanism, a process by which magnetic fields modulate the kinetics of chemical reactions by influencing spin dynamics, is thought to underlie a variety of biological mechanisms and is inherently both quantum and noisy. Model simulations with limited electron-nuclear interactions have been conducted on classical devices resulting in experimentally verified final state results, however these simulations become too complex to simulate as the systems scale in size. This motivates us to propound the simulation of the relevant spin dynamics in a noisy quantum device to probe the currently unexplored open quantum systems aspects of the radical pair mechanism and to provide a novel theoretical tool for us to be able to tackle bottlenecks in simulating larger and more physically relevant biological spin systems. We employ a hybrid quantum machine learning approach where we evaluate a parametrized quantum circuit representing the evolution of the system on the quantum device and then update the parameters according to our objective cost function on a classical computer using a gradient optimizer and a noisy gradient free (SPSA) optimizer. We show that a 3 qubit circuit with a series of parametrized rotation gates representing the Hyperfine and Zeeman interactions can be optimized, resulting in a circuit that evolves a singlet state under different magnetic field angles. Moreover, we show that the noisy gradient free optimizer is better suited for optimizing on a noisy quantum device. However, the precision in the quantum circuit outputs is only sub-par at present, leaving room for further improvements.
The spin-chemical radical pair mechanism (RPM) has emerged as a leading theory for explaining the biological effects of low-intensity magnetic fields. These intriguing effects occur when the quantum system of radicals is well isolated from the disturbing influence of the environment. In other words, these effects are closely related to the spin coherence relaxation time τ, but an explicit relationship has not yet been established. In our study, we found an analytical solution to the Liouville-Neumann equation for an open system made up of two electrons and one nucleus, considering minimal interactions while concentrating on spin relaxation and chemical kinetics. This solution, supported by numerical integration, highlights the crucial role of quantum coherence. A straightforward expression is proposed that describes the RPM effect as a function of τ, within the ranges of magnetic field strength H and rate κ of chemical kinetics relevant to magnetobiology. Our findings reveal that RPM effects become significant only when fundamental relation γHτ>1+κτ holds: it controls the magnitude of the effects, and it is consistent with the principles of spin chemistry. Additionally, by comparing our results with existing experimental data, we estimate that the plausible spin decoherence times in magnetosensitive radical pairs within cryptochromelike proteins range from units to tens of nanoseconds. The effects of radio-frequency magnetic fields at the nT level were also examined, taking into account decoherence. These effects turned out to be negligible and incapable of disrupting the RPM patterns. The role of the quantum Zeno effect in magnetobiology is inspected from the perspective of the τ dependence of the RPM effect.
The simulation of electronically nonadiabatic dynamics and spectroscopy remains as a central challenge in computational chemistry. Amongst the reduced dynamic methods, various forms of the perturbative quantum master equation (QME) including Fermi's golden rule (FGR), Redfield equation, and Marcus theory enjoy widespread use for their efficiency in the perturbative regime, and provides important physical intuition for the underlying dynamics. In the first chapter of this dissertation, the accuracy of various QMEs that treat off-diagonal electronic coupling perturbatively (OD-QME) will be examined on a spin-boson model. OD-QME works in the interaction picture, limiting its application to population dynamics. A novel way of retrieving Schrodinger picture coherences from interaction picture dynamics will be introduced, and the resulting dynamics will be compared against the numerically exact multi-configuration time dependent Hartree method. It will be shown that OD-QME can generate accurate population and coherence in appropriate parameter ranges, and that the time-nonlocal QME is more accurate than time-local QME, especially if the QME uses a population only projection. In the second chapter, the aforementioned method of calculating electronic coherence via OD-QME is applied to the simulation of absorption spectra. The result will be compared against the numerically exact hierarchical equations of motion, as well as the Redfield time-local QME which is widely applied in the context of spectroscopy. It will be shown that OD-QME exhibits comparable accuracy to Redfield QME over a wide parameter range. Both QMEs fail to predict the spectra accurately in the case of a high-frequency bath at a low temperature, and this error is likely to be linked to the quantum behavior of the bath. In the third chapter, the FGR rates of electronically nonadiabatic reactions enhanced by a microcavity is calculated. It will be shown that the cavity-enhanced reaction rates can be evaluated from the cavity-free FGR correlation function with minimum additional effort, and this method will be applied to a model CT reaction. While a high-frequency cavity enhances reactions in the Marcus inverted region selectively, a low-frequency cavity enhances reactions in all regions uniformly. In the fourth chapter, the FGR charge transfer rate constants for a molecular triad system solvated in explicit solvent is calculated via linear semiclassical (LSC) approach. A Marcus-like expression can be derived after applying a hierarchy of approximations. The validity of such approximations will be confirmed for the triad model. It will also be shown that the charge transfer rate depends deeply on the conformation of the molecule, the fluctuation between which is the rate-limiting step of the charge transfer.