Hydrogen evolution and oxidation—a prototype for an electrocatalytic reaction

Abstract

Due to progress in the theory of electrocatalysis and in quantum chemistry, it has become possible to investigate the hydrogen reaction and perform quantitative calculations for the reaction rate. First, we demonstrate this with model calculations for the adsorption of hydrogen on Pt(111). In accordance with experimental data, we find hydrogen adsorption at a potential above the equilibrium potential and with an almost vanishing energy of activation. As a second example, we explain trends in the catalytic activity of palladium overlayers and clusters on Au(111) electrodes.

Appendix: Details of DFT calculations

All calculations were performed using the DACAPO code [33]. This utilizes an iterative scheme to solve the Kohn–Sham equations of DFT self-consistently. A plane-wave basis set is used to expand the electronic wave functions, and the elecron–ion interactions are accounted through ultrasoft pseudopotentials [34], which allows the use of a low-energy cutoff for the plane-wave basis set. An energy cutoff of 400 eV, dictated by the pseudopotential of each metal, was used in all calculations. The electron–electron exchange and correlation interactions are treated with the generalized gradient approximation in the version of Perdew, Burke, and Ernzerhof [35]. The Brillouin zone integration was performed using a 16 × 16 × 1 k-point Monkhorst–Pack grid [36] corresponding to the (1 × 1) surface unit cell. The surfaces were modeled by a (3 × 3) supercell with four metal layers and six layers of vacuum. Dipole correction was used to avoid slab–slab interactions [37]. The first two top layers were allowed to relax, while the bottom two layers were fixed at the calculated next neighbor distance (Au: 2.95 Å, Pd: 2.82 Å, Pt: 2.83 Å). The optimized surfaces (prerelaxed) in the absence of the hydrogen atom were used as input data to carry out the calculations to study the hydrogen desorption. For each system, we performed a series of calculations for a single atom adsorbed on a fcc hollow site and varied its separation from the surface. The prerelaxed surface was kept fixed while the H was allowed to relax in xy coordinates during these calculations. At each position, we calculated the adsorption energy and the DOS projected onto the 1-s orbital of hydrogen, and from the latter, we obtained the model DOS of Eq. 1 by fitting.