Outer sphere electron transfer rates can be calculated from simulation data by sampling the equilibrium statistics of the vertical energy gap. For this calculation, electron transfer is typically represented as an instantaneous change in the atomic partial charges. In this paper, we present an implementation of this procedure that utilizes an explicit path-integral representation of the transferring electron. We demonstrate our methodology by combining path integral molecular dynamics and Marcus–Hush–Chidsey theory to calculate the rate of electron transfer from a ferrocyanide complex to a constant potential gold electrode. We consider the dependence of this rate on electron transfer distance and applied potential. We find that when the electron is represented explicitly via path integral molecular dynamics, as opposed to implicitly via fixed atomic partial charges, the rates and thermodynamics are more consistent with experimental findings. We then apply our methodology to explore the role of bridging spectator cations in modifying electron transfer rates. We find, once again, that the path integral approach produces specific cation effects that are more consistent with experiment than those in which the transferring electron is represented implicitly.
Park et al. (Thu,) studied this question.