  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 &#915; 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 &#915; 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.
