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arXiv:0805.3081

Quantum Theory of Radical-Ion-Pair Recombination: A New Physical Paradigm for Low-Magnetic-Field Effects

Iannis K. Kominis

Published May 20, 2008• 1 citation
arXivHTMLPDF

Abstract

A new paradigm emerging in the description of magnetic-sensitive radical-ion-pair recombination reactions is presented. This paradigm is founded on the realization that the recombination process of radical-ion pairs is a continuous quantum measurement. In the regime of low magnetic fields we describe the appearance of purely quantum phenomena, that fade away as the magnetic field increases. We will analyze the magnetic sensitivity of these reactions under this perspective and bridge the new full quantum theory with the existing classical reaction theory applicable at high magnetic fields. Based on the quantum theory of recombination we will then explain experimental observations incompatible with classical reaction theory, in particular the effect of deuteration on the magnetic sensitivity of radical-ion pair recombination yields.

DOI
10.48550/arxiv.0805.3081

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A new paradigm emerging in the description of magnetic-sensitive radical-ion-pair recombination reactions is presented. This paradigm is founded on the realization that the recombination process of radical-ion pairs is a continuous quantum measurement. In the regime of low magnetic fields we describe the appearance of purely quantum phenomena, that fade away as the magnetic field increases. We will analyze the magnetic sensitivity of these reactions under this perspective and bridge the new full quantum theory with the existing classical reaction theory applicable at high magnetic fields. Based on the quantum theory of recombination we will then explain experimental observations incompatible with classical reaction theory, in particular the effect of deuteration on the magnetic sensitivity of radical-ion pair recombination yields.
It has been recently shown that radical-ion pairs and their reactions are a paradigm biological system manifesting non-trivial quantum effects, so far invisible due to the phenomenological description of radical-ion-pair reactions used until now. We here use the quantum-mechanically consistent master equation describing magnetic-sensitive radical-ion-pair reactions to explain experimental data [C. R. Timmel and K. B. Henbest, Phil. Trans. R. Soc. Lond. A {\bf 362}, 2573 (2004); C. T. Rodgers, S. A. Norman, K. B. Henbest, C. R. Timmel and P. J. Hore, J. Am. Chem. Soc. {\bf 129} 6746 (2007)] on the effect of deuteration on the reaction yields. Anomalous behavior of radical-ion-pair reactions after deuteration, i.e. data inconsistent with the predictions of the phenomenological theory used so far, has been observed since the 70's and has remained unexplained until now.
Chemical reactions involving radical-ion pairs are ubiquitous in biology, since not only are they at the basis of the photosynthetic reaction chain, but are also assumed to underlie the biochemical magnetic compass used by avian species for navigation. Recent experiments with magnetic-sensitive radical-ion-pair reactions provided strong evidence for the radical-ion-pair magnetoreception mechanism, verifying the expected magnetic sensitivities and chemical product yield changes. It is here shown that the theoretical description of radical-ion-pair reactions used since the 70s cannot explain the observed data, because it is based on phenomenological equations masking quantum coherence effects. The fundamental density-matrix equation derived here from basic quantum measurement theory considerations naturally incorporates the quantum Zeno effect and readily explains recent experimental observations on low- and high magnetic-field radical-ion-pair reactions.
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.
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.
Radical-ion-pair reactions were recently shown to manifest a host of non-trivial quantum effects accounted for by quantum measurement theory. An alternative approach purporting to describe the fundamental quantum dynamics of spin-selective radical-ion pair reactions was introduced most recently, bringing to three the competing theories, including the one traditionally used in spin chemistry. We here consider entropy as a fundamental concept enabling a comparison of the predictions of these theories against what is physically acceptable on quite general grounds.