Phonons and librons in nitrogen monolayers adsorbed on graphite.

Abstract

For the ordered commensurate and incommensurate ${\mathrm{N}}_{2}$ monolayers that are formed at low T on the basal plane of graphite, we have calculated the structure and lattice dynamics by means of the quantum-mechanical mean-field and time-dependent Hartree methods. The potential used is an ab initio potential for the ${\mathrm{N}}_{2}$-${\mathrm{N}}_{2}$ interactions, with its anisotropy expanded in spherical harmonics, and an empirical atom-atom potential for the ${\mathrm{N}}_{2}$-graphite interactions, with variable parameters. The molecular center-of-mass vibrations are expanded in three-dimensional harmonic-oscillator functions and the librations in a free-rotor basis; translation-rotation coupling is explicitly included. We discuss the anharmonic shifts in the frequencies of the in-plane and out-of-plane phonons and librons, but we find that these shifts, with the exception of the soft out-of-plane libration in the compressed incommensurate herringbone phase, are not larger than in bulk nitrogen in the ordered \ensuremath{\alpha} and \ensuremath{\gamma} phases. For the incommensurate monolayer, we find at zero pressure that the planar herringbone ordering, which occurs also in the commensurate phase, is more stable than the pinwheel structure. At higher pressures, but probably still before bilayer formation, the pinwheel structure seems to be more stable, however. For the commensurate monolayer we obtain good agreement with the phonon frequencies from inelastic neutron scattering, except for the acoustic-phonon gap. Since this gap is directly related to the corrugation in the ${\mathrm{N}}_{2}$-graphite potential, we must conclude that this corrugation cannot be correctly reproduced by an atom-atom model, even when the parameters are varied within reasonable limits.