We show how a theory for electrocatalysis developed in our group can be combined with density-functional theory in order to obtain free-energy surfaces for electrochemical reactions. The combined theory is applied to the first step in the hydrogen evolution reaction, which is a proton transfer from an electrolyte solution to a metal electrode. Explicit calculations have been performed for five metals: Pt, Au, Ag, Cu, and Cd. In accord with experimental findings we find a high activation energy for Cd, medium values for the coin metals, and on Pt the transfer occurs with little activation. These results are explained in terms of the position of the $d$ band of these metals and their interactions with the hydrogen $1s$ orbital as the latter passes the Fermi level in the presence of the solvent.

• Received 13 January 2009

DOI:https://doi.org/10.1103/PhysRevB.79.235436