Controlled-Potential Simulation of Elementary Electrochemical Reactions: Proton Discharge on Metal Surfaces

The simulation of electrochemical reaction dynamics from first principles remains challenging, since over the course of an elementary step, an electron is either consumed or produced by the electrode. For example, the hydrogen evolution reaction begins with a simple proton discharge to a metal surface, but with conventional electronic structure methods, the simulated potential, which is manifested as the metal's workfunction, varies over the course of the simulation as the electron is consumed in the new metal hydrogen bond. Here, we present a simple approach to allow the direct control of the electrochemical potential via charging of the electrode surface. This is achieved by changing the total number of electrons in the self-consistent cycle, while enforcing charge neutrality through the introduction of a jellium counter charge dispersed in an implicit solvent region above the slab. We observe that the excess electrons localize selectively at the metal's reactive surface and that the metal workfunction responds nearly linearly to the variation in electronic count. This linear response allows for control of the potential in simulations with a minimal computational penalty compared to standard electronic structure calculations. This scheme can be straightforwardly implemented with common electronic structure calculators (density functional theory in the present work), and we find this method to be compatible with the commonly used computational hydrogen electrode model, which we expect will make it useful in the construction of potential-dependent free-energy diagrams in electrochemistry. We apply this approach to the proton-deposition (Volmer) step on both Au(111) and Pt(111) surfaces and show that we can reliably control the simulated electrode potential and thus assess the potential dependence of the initial, transition, and final states. Our method allows us to directly assess the location along the reaction pathway with the greatest amount of charge transfer, which we find to correspond well with the reaction barrier, indicating this reaction is a concerted proton-electron transfer. Interestingly, we show that the Pt electrode has not only a more favorable equilibrium energy with adsorbed hydrogen but also a lower intrinsic barrier under thermoneutral conditions.