Vibrational dephasing at surfaces: The role of cubic anharmonicity and Fermi resonances

We make a theoretical study of the vibrational contributions to the line shape of a top-bonded adsorbate. Dephasing of the adsorbate-substrate stretch occurs via anharmonic coupling to lower-frequency modes. We find the surprising result that central forces, which are often much larger than bond-bending forces, do not contribute to the linewidth, due to a cancellation between cubic and quartic terms in the effective coupling to the dephasing modes. This cancellation is complete whenever the probed mode has a frequency far above all others in the system, e.g., H/Si(111) or the C-O stretch in CO on metals. The C-metal stretch in CO on metals is more complicated, as it lies well below the C-O stretch. If the CO bond is treated as rigid, the cubic term introduces Fermi-resonance effects which greatly broaden the linewidth and also give rise to extra peaks in the absorption spectrum. However, we show that the internal motion of the molecule, no matter how small, causes a dramatic reduction in the magnitude of these effects, probably rendering them unobservable. We suggest that one must look to anharmonic terms in the noncentral (bending) interatomic forces to explain the magnitude of the experimental dephasing linewidth.