Multiquantum vibrational energy transfer into adsorbates on solid surfaces by atomic collisions: A semiclassical treatment based on dynamical correlations

A semiclassical treatment for vibrational excitation of adsorbates on surfaces by atomic collisions in the superthermal energy regime (0.5 ≲E≲5 eV), which was introduced previously in one dimension [Vilallonga and Rabitz, J. Chem. Phys. 85, 2300 (1986)], is here extended to three dimensions. The projectile motion is represented in the limit of short de Broglie wavelengths, i.e., by classical trajectories and their associated phases, whereas adsorbate-surface vibrations are treated quantum mechanically. Using the Feynman-path integral representation of the transition operator, this limit is approached in a flexible way that does not require a priori assumptions about the gas-surface potential and allows for strong surface corrugation, e.g., due to molecules adsorbed at low surface coverage. Distributions of transferred energies are approximated nonperturbatively by algebraic methods using time-correlation functions of the semiclassical transition operator. A large number of energetically open states are thus incorporated as well as the thermal average over initial vibrational states. The treatment is well suited for investigating multiquantum transitions of adsorbate modes and lattice phonons. The differential (in final angles and energy) scattered intensity is given in a form that is convenient for numerical calculations, since it requires integration of the Hamilton equations for the projectile, plus a straightforward sequence of fast Fourier transforms. This result is analyzed further in terms of adsorbate-localized vibrations and of lattice phonons in order to investigate how adsorbates can influence the structure of collisional energy-loss spectra. Particular attention is paid to the role of surface temperature, which can lead to different distributions for the energies going into adsorbates and into phonons. Comparisons are made with Born-type approximations and with impulsive treatments.