An analysis of isomorphic RPMD in the golden rule limit

TL;DR

This paper critically evaluates the isomorphic ring polymer (iso-RP) method in the golden rule limit, revealing its limitations in accurately predicting nuclear quantum effects and reaction rates in non-adiabatic electron transfer reactions.

Contribution

It provides an analytical expression for the iso-RP rate in the golden rule limit and compares it with exact rates, highlighting its inaccuracies and limitations.

Findings

Iso-RP does not correctly predict quantum effects on reaction rates.

It overestimates rates for activationless electron transfer.

It fails to capture quantum asymmetry in Marcus plots.

Abstract

We analyse the golden rule limit of the recently proposed isomorphic ring polymer (iso-RP) method. This method aims to combine an exact expression for the quantum mechanical partition function of a system with multiple electronic states with a pre-existing mixed quantum-classical (MQC) dynamics approximation, such as fewest switches surface hopping. Since the choice of the MQC method adds a degree of flexibility, we simplify the analysis by assuming that the dynamics used correctly reproduces the exact golden rule rate for a non-adiabatic (e.g., electron transfer) reaction in the high temperature limit. Having made this assumption, we obtain an expression for the iso-RP rate in the golden rule limit that is valid at any temperature. We then compare this rate with the exact rate for a series of simple spin-boson models. We find that the iso-RP method does not correctly predict how nuclear quantum effects affect the reaction rate in the golden rule limit. Most notably, it does not capture the quantum asymmetry in a conventional (Marcus) plot of the logarithm of the reaction rate against the thermodynamic driving force, and it also significantly overestimates the correct quantum mechanical golden rule rate for activationless electron transfer reactions. These results are analysed and their implications discussed for the applicability of the iso-RP method to more general non-adiabatic reactions.