A finite temperature theory of rotationally inelastic diffraction: H2, HD, and D2 on Cu(100)

Abstract

The rotationally inelastic diffraction probabilities for H2, HD, and D2 from Cu(100) were computed as a function of surface temperature. The surface is treated in a quantum mechanical fashion using a recently developed formalism. The center of mass molecular translational motion is treated semiclassically, using Gaussian wave packets (GWPs), and the rotations are described quantum mechanically. Strong attenuation of the phonon elastic diffraction peaks with temperature is observed. This Debye–Waller-like attenuation increases with increasing molecular mass and kinetic energy, and decreases as the peaks become more off-specular. The phonon summed rotation–diffraction probabilities show a moderate temperature dependence for the most part. The 0→2 rotational excitation of D2 appears to be strongly phonon assisted above 300 K. At low temperatures our method reproduces the selection rules predicted by previous studies. As the temperature is increased these selection rules become less restrictive. The probability distribution for a scattering molecule exchanging an amount of energy ΔE with the surface was also computed. Rayleigh phonons were found to dominate the energy transfer, with bulk vibrations becoming more important for larger molecular masses, beam energies, and surface temperatures.