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 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.
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.
An open quantum system refers to a system that is further coupled to a bath system consisting of surrounding radiation fields, atoms, molecules, or proteins. The bath system is typically modeled by an infinite number of harmonic oscillators. This system-bath model can describe the time-irreversible dynamics through which the system evolves toward a thermal equilibrium state at finite temperature. In nuclear magnetic resonance and atomic spectroscopy, dynamics can be studied easily by using simple quantum master equations under the assumption that the system-bath interaction is weak (perturbative approximation) and the bath fluctuations are very fast (Markovian approximation). However, such approximations cannot be applied in chemical physics and biochemical physics problems, where environmental materials are complex and strongly coupled with environments. The hierarchical equations of motion (HEOM) can describe the numerically "exact" dynamics of a reduced system under nonperturbative and non-Markovian system-bath interactions, which has been verified on the basis of exact analytical solutions (non-Markovian tests) with any desired numerical accuracy. The HEOM theory has been used to treat systems of practical interest, in particular, to account for various linear and nonlinear spectra in molecular and solid state materials, to evaluate charge and exciton transfer rates in biological systems, to simulate resonant tunneling and quantum ratchet processes in nanodevices, and to explore quantum entanglement states in quantum information theories. This article presents an overview of the HEOM theory, focusing on its theoretical background and applications, to help further the development of the study of open quantum dynamics.
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.
We investigate the quantum dynamics of Coulomb potential systems in thermal baths. We study these systems within the framework of open quantum dynamics theory, focusing on preserving the rotational symmetry of the entire system, including the baths. Thus, we employ a three-dimensional rotationally invariant system-bath model to derive numerically "exact" hierarchical equations of motion for atomic orbitals that enable a non-perturbative and non-Markovian treatment of system-bath interactions at finite temperatures. To assess the formalism, we calculated the linear absorption spectrum of an atomic system under an isotropic thermal environment, with systematic variation of system-bath coupling strength and temperature.
We use the "generalized hierarchical equation of motion" proposed in Paper I [C.-Y. Hsieh and J. Cao, J. Chem. Phys. 148, 014103 (2018)] to study decoherence in a system coupled to a spin bath. The present methodology allows a systematic incorporation of higher-order anharmonic effects of the bath in dynamical calculations. We investigate the leading order corrections to the linear response approximations for spin bath models. Two kinds of spin-based environments are considered: (1) a bath of spins discretized from a continuous spectral density and (2) a bath of localized nuclear or electron spins. The main difference resides with how the bath frequency and the system-bath coupling parameters are distributed in an environment. When discretized from a continuous spectral density, the system-bath coupling typically scales as ∼1/NB where N B is the number of bath spins. This scaling suppresses the non-Gaussian characteristics of the spin bath and justifies the linear response approximations in the thermodynamic limit. For the nuclear/electron spin bath models, system-bath couplings are directly deduced from spin-spin interactions and do not necessarily obey the 1/NB scaling. It is not always possible to justify the linear response approximations in this case. Furthermore, if the spin-spin Hamiltonian is highly symmetrical, there exist additional constraints that generate highly non-Markovian and persistent dynamics that is beyond the linear response treatments.