Confirming the role of nuclear tunnelling in aqueous ferrous-ferric electron transfer

TL;DR

This study confirms the significance of nuclear tunnelling in aqueous ferrous-ferric electron transfer and clarifies the limitations of previous methods, supporting the traditional Marcus theory picture.

Contribution

The paper demonstrates that size inconsistency affects GR-QTST predictions and validates the use of LGR and Wolynes theory for accurate tunnelling analysis in this system.

Findings

GR-QTST results are dominated by size inconsistency errors.

LGR and Wolynes theory agree with established tunnelling picture.

Mapping onto the spin-boson model may overlook anharmonic effects.

Abstract

We revisit the well-known aqueous ferrous-ferric electron transfer reaction in order to address recent suggestions that nuclear tunnelling can lead to significant deviation from the linear response assumption inherent in the Marcus picture of electron transfer. A recent study of this reaction by Richardson and coworkers has found a large difference between their new path-integral method, GR-QTST, and the saddle point approximation of Wolynes (Wolynes theory). They suggested that this difference could be attributed to the existence of multiple tunnelling pathways, leading Wolynes theory to significantly overestimate the rate. This was used to argue that the linear response assumptions of Marcus theory may break down for liquid systems when tunnelling is important. If true, this would imply that the commonly used method for studying such systems, where the problem is mapped onto a spin-boson model, is invalid. However, we have recently shown that size inconsistency in GR-QTST can lead to poor predictions of the rate in systems with many degrees of freedom. We have also suggested an improved method, the path-integral linear golden-rule (LGR) approximation, which fixes this problem. Here we demonstrate that the GR-QTST results for ferrous-ferric electron transfer are indeed dominated by its size consistency error. Furthermore, by comparing the LGR and Wolynes theory results, we confirm the established picture of nuclear tunnelling in this system. Finally, by comparing our path-integral results to those obtained by mapping onto the spin-boson model, we reassess the importance of anharmonic effects and the accuracy of this commonly used mapping approach.