First-principles calculations of the phonon dispersion curves of H on Pt(111)

We have calculated the surface phonon dispersion curves for H on Pt(111), using first-principles, total energy calculations based on a mixed-basis set and norm-conserving pseudopotentials. Linear response theory and the harmonic approximation are invoked. For one monolayer of H in the preferred adsorption site (fcc hollow) vibrational modes polarized parallel and perpendicular to the surface are found, respectively, at 73.5 meV and 142.6 meV, at the Gamma point of the surface Brillouin zone. The degeneracy of the parallel mode is lifted at the zone boundaries, yielding energies of 69.6 meV and 86.3 meV at the M point and 79.4 meV and 80.8 meV at the K point. The dispersion curves for H adsorption at the hcp hollow site differ only slightly from the above. In either case, H adsorption has considerable impact on the substrate modes; in particular the surface mode in the gap in the bulk phonon spectrum (around M point) is pushed into the bulk band. For on-top H adsorption, modes polarized parallel and perpendicular to the surface have respective energies of 47.4 meV and 277.2 meV, at the Gamma point. The former disperses to 49.1 meV and 59.5 meV at the M point and to 56 meV and 56.7 meV at the K point. The H vibrational mode polarized perpendicular to the surface shows little dispersion, in all three cases considered. Insights are obtained from the hybridization of the H and Pt electronic states.