First principles reaction modeling of the electrochemical interface: Consideration and calculation of a tunable surface potential from atomic and electronic structure

A method for calculating and subsequently tuning the electrochemical potential of a half cell using periodic plane-wave density functional theory and a homogenous counter-charge is presented and evaluated by comparison to simulations which explicitly model the countercharge by a plane of ions. The method involves the establishment of two reference potentials, one related to the potential of the free electron in vacuo, and the other related to the potential of ${\mathrm{H}}_{2}\mathrm{O}$ species far from the electrode. The surface potential can be specifically adjusted by the explicit introduction of excess or deficit surface charges in the simulation cell and the application of periodic boundary conditions. We demonstrate the absence of field emission from the electrode over the range of realistic electrochemical potentials covered and confirm that the method can explicitly determine reaction energies and adsorption geometries as a function of electrochemical potential. This latter point is most useful as it asserts the viability of this method to model electrochemical and electrocatalytical systems of academic as well as applied interest. We present two case studies. The first examines the changes in the structure of water at the metal interface as a function of potential over $\mathrm{Cu}(111)$. At cathodic potential, we observe the repulsion of ${\mathrm{H}}_{2}\mathrm{O}$ from the interface and the rotation of the water dipole toward the interface. The second study follows the initial pathways for the electrocatalytical activation of methanol over $\mathrm{Pt}(111)$ and the corresponding potential dependent reaction energetics for these paths. The results demonstrate that changes in the electrochemical potential can significantly alter the reaction energetics as well as the overall reaction selectivity. While the case studies presented herein described equilibrium geometries (i.e., the ideal forms at zero kelvin), the method is also suitable for application to ensembles of thermally activated systems.