Phonon spectrum and density of states for commensurate monolayer phases ofH2, HD, andD2on graphite

A self-consistent-phonon approximation was used to calculate the ground-state properties and phonon density of states for the √3 × √3 R 30° commensurate phase of monolayer ${\mathrm{H}}_2$, HD, and ${\mathrm{D}}_2$ adsorbed on graphite. The adsorbed molecules were assumed to be in a pure J=0 rotational state, and the wave function for the solid included coordinates both parallel and perpendicular to the surface. The proper inclusion of the surface-normal terms in the wave function was found to have a significant effect on both the phonon spectrum and the ground-state properties. The calculations for the ground-state energy and the phonon spectrum of these solids were done both with and without the inclusion of short-range correlations, these short-range correlations being treated within a version of the T-matrix approximation. The possible effects of various substrate-mediated interactions, anisotropic admolecule-carbon interactions, and finite temperatures were also investigated. The current theoretical results are compared to those of recent inelastic-neutron-scattering experiments and to previous theoretical results for these systems.