Standard hydrogen electrode and potential of zero charge in density functional calculations

Methods to explicitly account for half-cell electrode potentials have recently appeared within the framework of density functional theory. The potential of the electrode relative to the standard hydrogen electrode is typically determined by subtracting the experimental value of the absolute standard hydrogen electrode potential (ASHEP) from the calculated work function. Although conceptually correct, this procedure introduces two sources of errors: (i) the experimental estimate of the ASHEP varies from 4.28 to 4.85 V and, as has been previously shown and is reconfirmed here, (ii) the calculated work function strongly depends on the structure of the water film covering the metal surface. In this paper, we first identify the most accurate experimental reference for the ASHEP by revisiting up-to-date literature, and validate the choice of electron reference level in single-electrode density functional setups. By analyzing a dozen different water structures, built up from water hexamers, in their uncharged potential of zero charge (PZC) states on Pt(111), we then determine three different criteria (no net dipole, no charge transfer, and high water flexibility) that a water structure should possess in order for its computed ASHEP to closely match the experimental benchmark. We capture and quantify these three effects by calculating trends in the ASHEP and PZC on eight close-packed transition metals, considering the four most simple and representative water models. Finally, it is also demonstrated how the work function changes with exchange-correlation functional.