Energy and Phase Relaxations of Adsorbate Vibrations at Surfaces via Interaction with Electron-Hole Pairs or Phonons

We study the dynamic processes at surfaces responsible for the broadening of adsorbate vibrations, using two model systems. In the first model, we calculate the vibrational lineshape of adsorbates at metal surfaces damped by the generation of electron-hole pairs. Two vibrational excitations are considered, one fundamental and one overtone; and contributions to the total absorption from both polarizations are included, the one perpendicular to the surface, and the one tangential to the surface. The generalized asymmetric Fano lineshape formula is shown to apply to both the fundamental and the overtone. For each case, the isotope effect on the lineshape parameters is obtained both in the limits of weak and strong breakdown of adiabaticity. It is found that a strong breakdown of adiabaticity weakens the isotope dependence of the asymmetry factor and the linewidth, while the isotope effect for the excitation strength remains the same as in the weak breakdown limit. The magnitude of the excitation strength is modified as the strong breakdown limit is reached. These conclusions remain valid whether the vibration contributes to the perpendicular polarization, or to the parallel polarization. When the theory is applied to the wag overtone of hydrogen on W(100), reasonably good agreement with experiment is found in the strong breakdown limit. In the second model, we consider a localized vibration of linearly bonded adsorbate with displacement coordinate u interacting with a substrate atom of coordinate v, and propose a new dephasing contribution to the vibrational linewidth arising from the cubic term u^2v by going to fourth order perturbation theory. Such a contribution is shown through a specific example to be equally important as the leading order dephasing contribution of the quartic term u^2v ^2, which has been considered by others. We also present a more complete picture of phonon dephasing, where all possible dephasing processes originating from pure and mixed vertices of cubic and quartic anharmonicities are taken into account. Furthermore, it is shown that the cubic term (u^2v) produces much stronger sidebands than the quartic term (u^2 v^2) does; and it is suggested that this fact may be used in some cases to verify or eliminate phonon dephasing as the linewidth mechanism.