Electrochemical Potential Fluctuation Matters in Rate Constant Calculations for Proton-Coupled Electron Transfer

Proton-coupled electron transfer (PCET) reactions are core elementary steps in electrochemical energy conversion processes. Accurate quantification of their rate constants is crucial for understanding reaction mechanisms and designing electrocatalysts. However, developing appropriate methods to treat an exact grand canonical (GC) constant potential condition remains challenging and is still under debate. Here we compare two simulation strategies of introducing applied potentials: one incorporates microstates' electrochemical potential fluctuations to rigorously sample the GC ensemble distribution, while another fixes the potential by iteratively adjusting electron numbers for each microstate. Using the Volmer reaction at Pt(111) surface as a model system, and employing the Bennett-Chandler approach to calculate rate constants, we find that these two different approaches yield distinct thermal activations and dynamic recrossing behaviors, leading to non-negligible differences in predicted reaction rate constants. Our study highlights the criticality and necessity of capturing instantaneous potential fluctuations for rigorous and reliable dynamic simulations of electrochemical PCET steps.