We present a model study of the vibrational excitation of NO molecules
scattering from a Ag(111) surface using time-dependent wave packet me
thods. The molecule-surface interaction is described by a two-dimensio
nal potential energy surface in the vibrational and center-of-mass coo
rdinates. Surface motion is modeled by a single atomic oscillator This
model reproduces the experimentally observed increase in the vibratio
nal excitation as a function of both increasing initial translational
energy of the molecule and surface temperature. The surface temperatur
e only enters via the Boltzmann weighting of initial surface vibration
al states. We simplify the simulation to a two-dimensional surface-mas
s model, where the gas-surface interaction is analogous to a classical
''cube'' model. It is shown that the relative velocity of the incomin
g molecule, with respect to the surface, causes the observed dependenc
e of the vibrational excitation on surface temperature. The savings in
computational time achieved with this model allows a study of the eff
ect of the potential topology and surface mass on the temperature depe
ndence of the vibrational excitation.