The anharmonic frequency shifts of the phonons in monolayer solids of Ar/Pt
(lll) and commensurate Xe/Pt(lll) are calculated with quasiharmonic perturb
ation theory and with self-consistent-phonon theory. Results from the two m
ethods are in good agreement for Ar/Pt(lll). Uncertainties in the frequency
shifts for the Ar/Pt(lll) modes are small compared to present uncertaintie
s in the interaction model and in the experimental data. Anharmonic effects
in the commensurate Xe/Pt(lll) solid at 80 K are large, both because of th
e small adatom-adatom force constants in this dilated lattice and because o
f the large degree of thermal excitation. A version of the improved self-co
nsistent-phonon approximation is used for comparison to experimental data,
and it is found that the anharmonic terms cause changes on the scale of adj
ustments in Xe-Pt forces previously found necessary to achieve fits of the
harmonic theory to the data. The contribution of static adsorption-induced
dipole moments to the monolayer lattice dynamics is analyzed and is found t
o be negligible for Xe/Pt(111).