Electron spin relaxation in radical pairs: Beyond the Redfield approximation

TL;DR

This paper introduces a Nakajima-Zwanzig based relaxation theory for radical pair spin dynamics, overcoming limitations of Redfield theory, and applies it to model electron transfer reactions, revealing new insights into triplet yields.

Contribution

It develops an alternative perturbative relaxation approach using Nakajima-Zwanzig equations, improving modeling of radical pair spin dynamics beyond Redfield theory.

Findings

The new method avoids positivity issues in static disorder.

Simulations match experimental data on radical pair reactions.

Evidence of a field-independent contribution to triplet yields.

Abstract

Relaxation processes can have a large effect on the spin selective electron transfer reactions of radical pairs. These processes are often treated using phenomenological relaxation superoperators or with some model for the microscopic relaxation mechanism treated within Bloch-Redfield-Wangsness theory. Here, we demonstrate that an alternative perturbative relaxation theory, based on the Nakajima-Zwanzig equation, has certain advantages over Redfield theory. In particular, the Nakajima-Zwanzig equation does not suffer from the severe positivity problem of Redfield theory in the static disorder limit. Combining the Nakajima-Zwanzig approach consistently with the Schulten-Wolynes semiclassical method, we obtain an efficient method for modeling the spin dynamics of radical pairs containing many hyperfine-coupled nuclear spins. This is then used to investigate the spin-dependent electron transfer reactions and intersystem crossing of dimethyljulolidine-naphthalenediimide (DMJ-NDI) radical ion pairs. By comparing our simulations with experimental data, we find evidence for a field-independent contribution to the triplet quantum yields of these reactions which cannot be explained by electron spin relaxation alone.