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We analyse the golden rule limit of the recently proposed isomorphic ringpolymer (iso-RP) method. This method aims to combine an exact expression forthe quantum mechanical partition function of a system with multiple electronicstates with a pre-existing mixed quantum-classical (MQC) dynamicsapproximation, such as fewest switches surface hopping. Since the choice of theMQC method adds a degree of flexibility, we simplify the analysis by assumingthat the dynamics used correctly reproduces the exact golden rule rate for anon-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 thegolden rule limit that is valid at any temperature. We then compare this ratewith the exact rate for a series of simple spin-boson models. We find that theiso-RP method does not correctly predict how nuclear quantum effects affect thereaction rate in the golden rule limit. Most notably, it does not capture thequantum asymmetry in a conventional (Marcus) plot of the logarithm of thereaction rate against the thermodynamic driving force, and it alsosignificantly overestimates the correct quantum mechanical golden rule rate foractivationless electron transfer reactions. These results are analysed andtheir implications discussed for the applicability of the iso-RP method to moregeneral non-adiabatic reactions.

An analysis of isomorphic RPMD in the golden rule limit