Calculations of monolayer and bilayer lattices of methane on MgO(001) are reported for a spherical model of the molecule. The observed stability of c(2×2) [also termed (• ] commensurate square monolayer and bilayer lattices is reproduced with a surface energy corrugation that implies a large gap in the monolayer phonon density of states of the commensurate CH4. This gap is present in the incoherent inelastic neutron scattering measurements reported here.