A simple evaluation of adiabatic proton tunneling across the electrified double layer

Coupled proton-electron transfer (CPET) reactions are likely to play a pivotal role in the global transition to a sustainable energy future. Our atomic scale understanding of this class of reactions has been significantly improved by developments in density functional theory (DFT) simulations. The ultimate goal of such simulations is to intelligently predict rates of CPET reactions at the electrified double layer, leading to the design of new catalysts. These studies often utilize harmonic transition state theory (HTST), which assumes that quantum tunneling through energy barriers is negligible. In this study, we present a simple evaluation of the contribution of quantum tunneling in the adiabatic limit of CPET reactions. We investigate the effect of different potential profiles on tunneling probabilities and compare these profiles with calculated CPET minimum energy paths (MEPs). We find that the calculated CPET MEPs can be significantly stiffer than the commonly used Eckart profile, and study the effect of changing barrier height and width on overall zero curvature tunneling correction factors. Depending on the reaction of interest and the bulk pH, proton tunneling can be a non-negligible phenomenon for CPET reactions at the electrified double layer. In particular, reactions involving large barriers are predicted to have significant contributions from non-classical tunneling, possibly explaining observed kinetic isotope effects for the hydrogen evolution reaction (HER) in alkaline media. Our model choices are significantly simplified -- for example, neglecting the effects of reaction coordinate curvature and vibronic coupling -- suggesting that our predicted tunneling contributions may be underestimated. However, our findings provide a simple way to evaluate whether tunneling is relevant for a particular CPET reaction of interest.