Spin-selective electron transfer reactions of radical pairs: beyond the Haberkorn master equation

TL;DR

This paper derives an advanced quantum master equation for radical pair electron transfer reactions, revealing significant reactive spin coupling effects beyond traditional models, with implications for biological processes like magnetoreception.

Contribution

It introduces a new master equation incorporating reactive scalar electron spin coupling and dephasing, extending beyond the Haberkorn approach using perturbation and Marcus theory.

Findings

Reactive scalar electron spin coupling is often significant.

Beyond Fermi golden rule, additional singlet-triplet dephasing appears.

The derived equations accurately model radical pair reactions with spin selectivity.

Abstract

Radical pair recombination reactions are normally described using a quantum mechanical master equation for the electronic and nuclear spin density operator. The electron spin state selective (singlet and triplet) recombination processes are described with a Haberkorn reaction term in this master equation. Here we consider a general spin state selective electron transfer reaction of a radical pair and use Nakajima-Zwanzig theory to derive the master equation for the spin density operator, thereby elucidating the relationship between non-adiabatic reaction rate theory and the Haberkorn reaction term. A second order perturbation theory treatment of the diabatic coupling naturally results in the Haberkorn master equation with an additional reactive scalar electron spin coupling term. This term has been neglected in previous spin chemistry calculations, but we show that it will often be quite significant. We also show that beyond second order in perturbation theory, i.e., beyond the Fermi golden rule limit, an additional reactive singlet-triplet dephasing term appears in the master equation. A closed form expression for the reactive scalar electron spin coupling in terms of the Marcus theory parameters that determine the singlet and triplet recombination rates is presented. By performing simulations of radical pair reactions with the exact Hierarchical Equations of Motion (HEOM) method, we demonstrate that our master equations provide a very accurate description of radical pairs undergoing spin-selective non-adiabatic electron transfer reactions. The existence of a reactive electron spin coupling may well have implications for biologically relevant radical pair reactions such as those which have been suggested to play a role in avian magnetoreception.