Direct simulation of electron transfer using ring polymer molecular dynamics: Comparison with semiclassical instanton theory and exact quantum methods

TL;DR

This paper evaluates the effectiveness of ring polymer molecular dynamics (RPMD) in simulating electron transfer reactions, comparing its predictions with semiclassical instanton theory and exact quantum methods across different regimes.

Contribution

It demonstrates that RPMD accurately predicts electron transfer rates and mechanisms in most regimes, clarifying its strengths and limitations compared to other methods.

Findings

RPMD accurately predicts rates in normal and activationless regimes

RPMD captures solvent reorganization mechanisms consistent with Marcus theory

RPMD and instanton methods fail to reproduce rate turnover in the inverted regime

Abstract

The use of ring polymer molecular dynamics (RPMD) for the direct simulation of electron transfer (ET) reaction dynamics is analyzed in the context of Marcus theory, semiclassical instanton theory, and exact quantum dynamics approaches. For both fully atomistic and system-bath representations of condensed-phase ET, we demonstrate that RPMD accurately predicts both ET reaction rates and mechanisms throughout the normal and activationless regimes of the thermodynamic driving force. Analysis of the ensemble of reactive RPMD trajectories reveals the solvent reorganization mechanism for ET that is anticipated in the Marcus rate theory, and the accuracy of the RPMD rate calculation is understood in terms of its exact description of statistical fluctuations and its formal connection to semiclassical instanton theory for deep-tunneling processes. In the inverted regime of the thermodynamic driving force, neither RPMD nor a related formulation of semiclassical instanton theory capture the characteristic turnover in the reaction rate; comparison with exact quantum dynamics simulations reveals that these methods provide inadequate quantization of the real-time electronic-state dynamics in the inverted regime.