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.

Platinum is a nearly perfect catalyst for the hydrogen evolution reaction, and its high activity has conventionally been explained by its close-to-thermoneutral hydrogen binding energy (G∼0). However, many candidate non-precious metal catalysts bind hydrogen with similar strengths, but exhibit orders-of-magnitude lower activity for this reaction. In this study, we employ electronic structure methods that allow fully potential-dependent reaction barriers to be calculated, in order to develop a complete working picture of hydrogen evolution on platinum. Through the resulting ab initio microkinetic models, we assess the mechanistic origins of Pt's high activity. Surprisingly, we find that the G∼0 hydrogen atoms are kinetically inert, and that the kinetically active hydrogen atoms have ∆G's much weaker, similar to that of gold. These on-top hydrogens have particularly low barriers, which we compare to those of gold, explaining the high reaction rates, and the exponential variations in coverages can uniquely explain Pt's strong kinetic response to the applied potential. This explains the unique reactivity of Pt that is missed by conventional Sabatier analyses, and suggests true design criteria for non-precious alternatives.

Many electrochemical processes are governed by the transfer of protons to the surface, which can be coupled with electron transfer; this electron transfer is in general non-integer and unknown a priori, but is required to hold the potential constant. In this study, we employ a combination of surface spectroscopic techniques and grandcanonical electronic-structure calculations in order to rigorously understand the thermodynamics of this process. Specifically, we explore the protonation/deprotonation of 4-mercaptobenzoic acid as a function of the applied potential. Using grand-canonical electronic-structure calculations, we directly infer the coupled electron transfer, which we find to be on the order of 0.1 electron per proton; experimentally, we also access this quantity via the potential-dependence of the pK a . We show a striking agreement between the potential-dependence of the measured pK a and that calculated with electronic-structure calculations. We further employ a simple electrostatics-based model to show that this slope can equivalently be interpreted to provide information on the degree of coupled electron transfer or the potential change at the point of the charged species.

The ability to simulate electrochemical reactions from first-principles has advanced significantly in recent years. Here, we discuss the atomistic interpretation of electrochemistry at three scales: from the electronic structure to elementary processes to constant-potential reactions. At each scale, we highlight the importance of the grand-canonical nature of the process and show that the grand-canonical energy is the natural thermodynamic state variable, which has the additional benefit of simplifying calculations. We show that atomic forces are the derivative of the grand-potential energy when the potential is fixed. We further examine the meaning of potential at the atomic scale and its link to the chemical potential and discuss the link between charge transfer and potential in several situations.

We present a modified nudged elastic band routine that can reduce the number of force calls by more than 50% for bands with non-uniform convergence. The method, which we call "dyNEB", dynamically and selectively optimizes states based on the perpendicular PES-derived forces and parallel spring forces acting on that region of the band. The convergence criteria are scaled to focus on the region of interest, i.e., the saddle point, while maintaining continuity of the band and avoiding truncation. We show that this method works well for solid state reaction barriers-nonelectrochemical in general and electrochemical in particular-and that the number of force calls can be significantly reduced without loss of resolution at the saddle point.

A strategy is presented for the machine-learning emulation of electronic structure calculations carried out in the electronically grand-canonical ensemble. The approach relies upon a dual-learning scheme, where both the system charge and the system energy are predicted for each image. The scheme is shown to be capable of emulating basic electrochemical reactions at a range of potentials, and coupling it with a bootstrap-ensemble approach gives reasonable estimates of the prediction uncertainty. The method is also demonstrated to accelerate saddle-point searches, and to extrapolate to systems with one to five water layers. We anticipate that this method will allow for larger length- and time-scale simulations necessary for electrochemical simulations.

We report that sulfur-doping of molybdenum carbide catalysts produces a good hydrogen evolution electrocatalyst. The doped sulfur atoms weaken the hydrogen bonding energy, enhancing the catalyst's activity in hydrogen evolution.

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