A simple, broadly applicable theory is developed to describe resonant vibra
tional coupling between adsorbates and a substrate lattice. This is one of
the principal mechanisms governing the relaxation of adsorbate vibrations.
This theory can be applied to widely varying surface coverages and arbitrar
y overlayer structures, and it correctly incorporates collective adsorbate
motion, which has been shown to have a critical impact on the relaxation dy
namics. Vibrational lifetimes predicted by this theory are in excellent qua
ntitative agreement with experiments on adsorbate systems ranging from a di
ffuse, disordered overlayer to a dense, periodic overlayer.