Local vibrations in systems of interacting adsorbed molecules

A lattice system of adsorbed molecules is treated that is characterized by two bands of vibrational excitations. The first one originates from the col lectivization of local high-frequency vibrations of individual molecules, w hich results from lateral intermolecular interactions. The second one arise s due to the analogous collectivization of low-frequency resonance molecula r modes, with their lifetimes governed by the coupling with substrate phono ns. The temperature dependence of the spectral line shape for local vibrati ons is analyzed in the model that includes all kinds of cubic and quartic a nharmonic coupling between high-frequency and low-frequency molecular modes in the fourth-order perturbation theory for the two-time retarded Green's functions in the coordinate-momentum representation. As shown, various proc esses that involve four vibrational excitations and contribute to the line broadening for local vibrations are dominated by quartic anharmonic coeffic ients renormalized in terms of the cubic one; the renormalization is caused by the effective anharmonic force acting on each harmonic oscillator. Base d on the translation symmetry of the system in surface-parallel directions, the quasimode approximation is substantiated, which enables the spectral l ine shift and width for local vibrations to be expressed in terms of disper sion laws and lifetimes for low-frequency molecular modes. The results obta ined permit spectral line characteristics of local vibrations to be estimat ed for H/Si(111) and H(D)/C(111) in nice accordance with the experimentally measured values. Lateral interactions of low-frequency modes are shown to result in their shorter lifetimes and hence in the additionally narrowed sp ectral lines. The contribution from lateral interactions of local vibration s proves to be significant for systems with the sufficiently wide local vib ration band and low frequencies of resonance modes, as, for instance, in OH /SiO2 and 2 x 1 phase of CO/NaCl(100). (C) 1999 American Institute of Physi cs. [S0021-9606(99)71209-2].