Electron Transfer Reactions: Generalized Spin-Boson Approach

TL;DR

This paper presents a rigorous mathematical framework for analyzing electron transfer reactions using a generalized spin-boson model, accounting for complex system-environment interactions and multi-level systems, with explicit rate and efficiency calculations.

Contribution

It introduces a generalized, rigorous spin-boson approach that includes non energy-conserving interactions and multi-level systems, advancing the theoretical understanding of electron transfer processes.

Findings

Rate increases with multi-level acceptors.

Efficiency remains unchanged despite multi-level acceptors.

Explicit expressions for reaction rates and efficiency are derived.

Abstract

We introduce a mathematically rigorous analysis of a generalized spin-boson system for the treatment of a donor-acceptor (reactant-product) quantum system coupled to a thermal quantum noise. The donor/acceptor probability dynamics describes transport reactions in chemical processes in presence of a noisy environment -- such as the electron transfer in a photosynthetic reaction center. Besides being rigorous, our analysis has the advantages over previous ones that (1) we include a general, non energy-conserving system-environment interaction, and that (2) we allow for the donor or acceptor to consist of multiple energy levels lying closely together. We establish explicit expressions for the rates and the efficiency (final donor-acceptor population difference) of the reaction. In particular, we show that the rate increases for a multi-level acceptor, but the efficiency does not.