Spin relaxation in radical pairs from the stochastic Schrödinger equation

RadicalPy: A Tool for Spin Dynamics Simulations

Radical pairs (electron-hole pairs, polaron pairs) are transient reaction intermediates that are found and exploited in all areas of science, from the hard realm of physics in the form of organic semiconductors, spintronics, quantum computing, and solar cells to the soft domain of chemistry and biology under the guise of chemical reactions in solution, biomimetic systems, and quantum biology. Quantitative analysis of radical pair phenomena has historically been successful by a few select groups. With this in mind, we present an intuitive open-source framework in the Python programming language that provides classical, semiclassical, and quantum simulation methodologies. A radical pair kinetic rate equation solver, Monte Carlo-based spin dephasing rate estimations, and molecule database functionalities are implemented. We introduce the kine-quantum method, a new approach that amalgamates classical rate equations, semiclassical, and quantum techniques. This method resolves the prohibitively large memory requirement issues of quantum approaches while achieving higher accuracy, and it also offers wavelength-resolved simulations, producing time- and wavelength-resolved magnetic field effect simulations. Model examples illustrate the versatility and ease of use of the software, including the new approach applied to the magnetosensitive absorption and fluorescence of flavin adenine dinucleotide photochemistry, spin-spin interaction estimation from molecular dynamics simulations on radical pairs inside reverse micelles, radical pair anisotropy inside proteins, and triplet exciton pairs in anthracene crystals. The intuitive interface also allows this software to be used as a teaching or learning aid for those interested in the field of spin chemistry. Furthermore, the software aims to be modular and extensible, with the aim to standardize how spin dynamics simulations are performed.

Spin relaxation dynamics with a continuous spin environment: The dissipaton equation of motion approach

We investigate the quantum dynamics of a spin coupling to a bath of independent spins via the dissipaton equation of motion (DEOM) approach. The bath, characterized by a continuous spectral density function, is composed of spins that are independent level systems described by the su(2) Lie algebra, representing an environment with a large magnitude of anharmonicity. Based on the previous work by Suarez and Silbey [J. Chem. Phys. 95, 9115 (1991)] and by Makri [J. Chem. Phys. 111, 6164 (1999)] that the spin bath can be mapped to a Gaussian environment under its linear response limit, we use the time-domain Prony fitting decomposition scheme to the bare-bath time correlation function (TCF) given by the bosonic fluctuation-dissipation theorem to generate the exponential decay basis (or pseudo modes) for DEOM construction. The accuracy and efficiency of this strategy have been explored by a variety of numerical results. We envision that this work provides new insights into extending the hierarchical equations of motion and DEOM approach to certain types of anharmonic environments with arbitrary TCF or spectral density.

Spin Dynamics of Radical Pairs Using the Stochastic Schrödinger Equation in MolSpin

The chemical reactivity of radical pairs is strongly influenced by the interactions of electronic and nuclear spins. A detailed understanding of these effects requires a quantum description of the spin dynamics that considers spin-dependent reaction rates, interactions with external magnetic fields, spin-spin interactions, and the loss of spin coherence caused by coupling to a fluctuating environment. Modeling real chemical and biochemical systems, which frequently involve radicals with multinuclear spin systems, poses a severe computational challenge. Here, we implement a method based on the stochastic Schrödinger equation in the software package MolSpin. Large electron-nuclear spin systems can be simulated efficiently, with asymmetric spin-selective recombination reactions, anisotropic hyperfine interactions, and nonzero exchange and dipolar couplings. Spin-relaxation can be modeled using the stochastic time-dependence of spin interactions determined by molecular dynamics and quantum chemical calculations or by allowing rate coefficients to be explicitly time-dependent. The flexibility afforded by this approach opens new avenues for exploring the effects of complex molecular motions on the spin dynamics of chemical transformations.

The Effect of Spin Relaxation on Magnetic Compass Sensitivity in ErCry4a

This study explores the impact of thermal motion on the magnetic compass mechanism in migratory birds, focusing on the radical pair mechanism within cryptochrome photoreceptors. The coherence of radical pairs, crucial for magnetic field inference, is curbed by spin relaxation induced by intra-protein motion. Molecular dynamics simulations, density-functional-theory-based calculations, and spin dynamics calculations were employed, utilizing Bloch-Redfield-Wangsness (BRW) relaxation theory, to investigate compass sensitivity. Previous research hypothesized that European robin's cryptochrome 4a (ErCry4a) optimized intra-protein motion to minimize spin relaxation, enhancing magnetic sensing compared to the plant Arabidopsis thaliana's cryptochrome 1 (AtCry1). Different correlation times of the nuclear hyperfine coupling constants in AtCry1 and ErCry4a were indeed found, leading to distinct radical pair recombination yields in the two species, with ErCry4a showing optimized sensitivity. However, this optimization is likely negligible in realistic spin systems with numerous nuclear spins. Beyond insights in magnetic sensing, the study presents a detailed method employing molecular dynamics simulations to assess for spin relaxation effects on chemical reactions with realistically modelled protein motion, relevant for studying radical pair reactions at finite temperature.

Orientation of birds in radiofrequency fields in the absence of the Earth's magnetic field: a possible test for the radical pair mechanism of magnetoreception

The magnetic compass sense of migratory songbirds is thought to derive from magnetically sensitive photochemical reactions in cryptochromes located in photoreceptor cells in the birds' retinas. More specifically, transient radical pairs formed by light-activation of these proteins have been proposed to account for the birds' ability to orient themselves using the Earth's magnetic field and for the observation that radiofrequency magnetic fields, superimposed on the Earth's magnetic field, can disrupt this ability. Here, by means of spin dynamics simulations, we show that it may be possible for the birds to orient in a monochromatic radiofrequency field in the absence of the Earth's magnetic field. If such a behavioural test were successful, it would provide powerful additional evidence for a radical pair mechanism of avian magnetoreception.

Sensitivity enhancement of radical-pair magnetoreceptors as a result of spin decoherence

Electron spin relaxation is, on many occasions, considered an elephant in the room that challenges the idea of a radical-pair compass, a leading hypothesis for the navigation of migratory avian species. It has been widely recognized that an effective radical-pair magnetoreceptor requires a relaxation time that is long enough for an external magnetic field as weak as the geomagnetic field to significantly modify the coherent spin dynamics. However, previous studies proposed that certain spin relaxation, far quicker than the radical recombination reactions, could enhance, rather than degrade, the directional sensitivity of a radical-pair magnetoreceptor. Here, I investigate relaxation effects on the singlet-triplet interconversion of a model radical pair and find that the enhancement effect originates from population relaxation over a period of several microseconds as a result of efficient spin decoherence. Insights into the truncated spin systems shed light on the physics behind them. I further investigate the possibilities of such enhancement in cryptochrome-based magnetoreception, in which electron hopping takes place between tryptophan residues.

Spin selective charge recombination in chiral donor-bridge-acceptor triads

In this paper, we outline a physically motivated framework for describing spin-selective recombination processes in chiral systems, from which we derive spin-selective reaction operators for recombination reactions of donor-bridge-acceptor molecules, where the electron transfer is mediated by chirality and spin-orbit coupling. In general, the recombination process is selective only for spin-coherence between singlet and triplet states, and it is not, in general, selective for spin polarization. We find that spin polarization selectivity only arises in hopping-mediated electron transfer. We describe how this effective spin-polarization selectivity is a consequence of spin-polarization generated transiently in the intermediate state. The recombination process also augments the coherent spin dynamics of the charge separated state, which is found to have a significant effect on the recombination dynamics and to destroy any long-lived spin polarization. Although we only consider a simple donor-bridge-acceptor system, the framework we present here can be straightforwardly extended to describe spin-selective recombination processes in more complex systems.

Magnetic field effects on radical pair reactions: estimation of B1/2 for flavin-tryptophan radical pairs in cryptochromes

Magnetic field effects on the yields of radical pair reactions are often characterised by the "half-field" parameter, B_1/2, which encodes useful information on spin relaxation, radical recombination kinetics and electron-electron couplings as well as electron-nuclear hyperfine interactions. Here we use a variety of spin dynamics simulation methods to estimate the hyperfine-only values of B_1/2 for the flavin-tryptophan radical pair, [FAD˙^- TrpH˙⁺], thought to be the detector in the magnetic compass sense of migratory songbirds. The main findings are: (a) in the absence of fast recombination and spin relaxation, [FAD˙^- TrpH˙⁺] radical pairs in solution and in the putative magnetoreceptor protein, cryptochrome, have B_1/2 ≈ 1.89 mT and 2.46 mT, respectively. (b) The widely used expression for B_1/2 due to Weller et al. (Chem. Phys. Lett, 1983, 96, 24-27) is only applicable to small, short-lived (∼5 ns), rapidly tumbling radical pairs in solution, and is quantitatively unreliable in the context of magnetoreception. (c) In the absence of molecular tumbling, the low-field effect for [FAD˙^- TrpH˙⁺] is predicted to be abolished by the anisotropic components of the hyperfine interactions. Armed with the 2.46 mT "base value" for cryptochrome, measurements of B_1/2 can be used to understand the impact of spin relaxation on its performance as a magnetic compass sensor.

Driven Radical Motion Enhances Cryptochrome Magnetoreception: Toward Live Quantum Sensing

The mechanism underlying magnetoreception has long eluded explanation. A popular hypothesis attributes this sense to the quantum coherent spin dynamics and spin-selective recombination reactions of radical pairs in the protein cryptochrome. However, concerns about the validity of the hypothesis have been raised because unavoidable inter-radical interactions, such as the strong electron-electron dipolar coupling, appear to suppress its sensitivity. We demonstrate that sensitivity can be restored by driving the spin system through a modulation of the inter-radical distance. It is shown that this dynamical process markedly enhances geomagnetic field sensitivity in strongly coupled radical pairs via Landau-Zener-Stückelberg-Majorana transitions between singlet and triplet states. These findings suggest that a "live" harmonically driven magnetoreceptor can be more sensitive than its "dead" static counterpart.

Investigating radical pair reaction dynamics of B12 coenzymes 1: Transient absorption spectroscopy and magnetic field effects

B₁₂ coenzymes are vital to healthy biological function across nature. They undergo radical chemistry in a variety of contexts, where spin-correlated radical pairs can be generated both thermally and photochemically. Owing to the unusual magnetic properties of B₁₂ radical pairs, however, most of the reaction and spin dynamics occur on a timescale (picoseconds-nanoseconds) that cannot be resolved by most measurement techniques. Here, we describe a method that combines femtosecond transient absorption spectroscopy with magnetic field exposure, which enables the direct scrutiny of such rapid processes. This approach should provide a means by which to investigate the apparently profound effect protein environments have on the generation and reactivity of B₁₂ radical pairs.