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F-cluster: Reaction-induced spin correlation in multi-radical systems

DR Kattnig (21871391)

Published Aug 1, 2025• 0 citations

Abstract

We provide a theoretical analysis of spin-selective recombination processes in clusters of n ≥ 3 radicals. Specifically, we discuss how spin correlation can ensue from random encounters of n radicals, i.e., "F-clusters" as a generalization of radical F-pairs, acting as precursors of spin-driven magnetic field effects. Survival probabilities and the spin correlation of the surviving radical population, as well as transients, are evaluated by expanding the spin density operator in an operator basis that is closed under application of the Haberkorn recombination operator and singlet-triplet dephasing. For the primary spin cluster, the steady-state density operator is found to be independent of the details of the recombination network, provided that it is irreducible; pairs of surviving radicals are triplet-polarized independent of whether they are actually reacting with each other. The steady state is independent of the singlet-triplet dephasing, but the kinetics and the population of sister clusters of smaller size can depend on the degree of dephasing. We also analyze reaction-induced singlet-triplet interconversion in radical pairs due to radical scavenging by initially uncorrelated radicals ("chemical Zeno effect"). We generalize previous treatments for radical triads by discussing the effect of spin-selective recombination in the original pair and extending the analysis to four radicals, i.e., radical pairs interacting with two radical scavengers.

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We provide a theoretical analysis of spin-selective recombination processes in clusters of n ≥ 3 radicals. Specifically, we discuss how spin correlation can ensue from random encounters of n radicals, i.e., "F-clusters" as a generalization of radical F-pairs, acting as precursors of spin-driven magnetic field effects. Survival probabilities and the spin correlation of the surviving radical population, as well as transients, are evaluated by expanding the spin density operator in an operator basis that is closed under application of the Haberkorn recombination operator and singlet-triplet dephasing. For the primary spin cluster, the steady-state density operator is found to be independent of the details of the recombination network, provided that it is irreducible; pairs of surviving radicals are triplet-polarized independent of whether they are actually reacting with each other. The steady state is independent of the singlet-triplet dephasing, but the kinetics and the population of sister clusters of smaller size can depend on the degree of dephasing. We also analyze reaction-induced singlet-triplet interconversion in radical pairs due to radical scavenging by initially uncorrelated radicals ("chemical Zeno effect"). We generalize previous treatments for radical triads by discussing the effect of spin-selective recombination in the original pair and extending the analysis to four radicals, i.e., radical pairs interacting with two radical scavengers.

In the present work, we have shown that consistent derivation of the kinetic equations describing the electron spin-selective recombination of radical pairs confirms the conventional Haberkorn approach. The derivation has been based on considering the interaction of the reactive system (radical pair and product state) with the thermal bath. The consistency of this approach has also been substantiated by numerical simulations performed for the purely quantum mechanical model of the recombining radical pair. Finally, we have shown that the quantum Zeno effect on radical pair recombination is not an exclusive feature of the approach recently proposed by Kominis, as it should be present at any rate of the singlet-triplet dephasing in the radical pair, which always accompanies the recombination process.

Manifestations of the chemical Zeno effect (slowing down of the quantum evolution of radical pairs as a result of spin-selective recombination of exchange-bounded radical pairs) are considered. In radical pairs created in singlet and random spin states, the chemical kinetics is described by the sum of kinetic evolution (exponential) and oscillatory functions. The kinetic function is a superposition of two exponential functions. Recombination monotonically decreases the amplitude of quantum beats in singlet radical pairs. The dependence of the amplitude of quantum beats in noncorrelated radical pairs on the recombination rate constant is not monotonic.

Abstract We adapt the Monte-Carlo wavefunction (MCWF) approach to treat the open-system spin dynamics of radical pairs subject to spin-selective recombination reactions. For these systems, non-Lindbladian master equations are widely employed, which account for recombination via the non trace-preserving Haberkorn superoperator in combination with reaction-dependent exchange and singlet–triplet dephasing terms. We show that this type of master equation can be accommodated in the MCWF approach, by introducing a second type of quantum jump that accounts for the reaction simply by suitably terminating the propagation. In this way, we are able to evaluate approximate solutions to the time-dependent radical pair survival probability for systems that have been considered untreatable with the master equation approach until now. We explicate the suggested approach with calculations for radical pair reactions that have been suggested to be relevant for the quantum compass of birds and related phenomena.

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 represent a rich biophysical laboratory for the application of quantum measurement theory methods and concepts, casting doubt on the validity of the theoretical treatment of these reactions and the results thereof that has been at the core of spin chemistry for several decades now. The ensued scientific debate, although exciting, is plagued with several misconceptions. We will here provide a comprehensive treatment of the quantum dynamics of radical-ion-pair reactions, generalizing our recent work and elaborating on the analogy with the double-slit experiment having partial "which-path" information. This analogy directly leads to the general treatment of radical-ion pair reactions covering the whole range between the two extremes, that of perfect singlet-triplet coherence and that of complete incoherence.