The emergence of collective vibrations in cluster models: Quantum chemical study of the methyl-terminated Si(111) surface

In this paper we present structures and harmonic vibrational frequencies for the methylated silicon (111) surface from quantum chemical calculations using both cluster models and periodic boundary conditions. The results from both calculations are in very good agreement with experimentally determined frequencies. We demonstrate that relatively small cluster models already show the emergence of collective vibrational modes and provide a general method for the assignment of vibrational frequencies for extended surfaces from cluster models. Finally, we discuss a vibrational mode that results from the coupling between near-surface phonons and the silicon-carbon bending modes.