An analysis of isomorphic RPMD in the golden rule limit
Abstract
We analyze the golden rule limit of the recently proposed isomorphic ring polymer (isoRP) method. This method aims to combine an exact expression for the quantum mechanical partition function of a system with multiple electronic states with a preexisting mixed quantumclassical (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 nonadiabatic (e.g., electron transfer) reaction in the high temperature limit. Having made this assumption, we obtain an expression for the isoRP 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 spinboson models. We find that the isoRP 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 analyzed and their implications discussed for the applicability of the isoRP method to more general nonadiabatic reactions.
 Publication:

Journal of Chemical Physics
 Pub Date:
 December 2019
 DOI:
 10.1063/1.5138913
 arXiv:
 arXiv:1912.11834
 Bibcode:
 2019JChPh.151x4109L
 Keywords:

 Physics  Chemical Physics
 EPrint:
 8 pages, 2 figures