We develop analytical functional forms for the generation of full-dimensional representations of potential energy surfaces for polyatomic molecules of the type AX(1)..X-n, with one central atom A and peripheral atoms Xi, and for diatomic molecules adsorbed on surfaces. Examples are shown for NH3 and CO(ads)/Cu(100). Such forms are useful for realistic derivations of potential energy surfaces with applications on the calculation of ro-vibrational spectra and time-dependent molecular quantum dynamics. As an example, the effects of rotational motion and orientation on the vibrational wave packet dynamics of HF merged in an external electric field are discussed.