Molybdenum supported thin films of ScN, MgO and NaF with a Cu adatom have been studied in the framework of density functional theory. We have observed a charge transfer from the metal/film interface to the Cu atom and investigated its relation to surface and interface deformations. We find that a weak interaction between the metal and the film is a promising prerequisite for adatom charging. The detailed study of Cu/NaF/Mo and NaF/Mo indicates that the distortion of the NaF film caused by the Cu adsorption has essentially anharmonic character, as it is coupled to a strong charge redistribution in the system.