The interaction potential between the Pt(111) surface and Xe atoms adsorbed upon it was calculated using the cluster method with the Kohn-Sham scheme. For a single Xe atom an energetically most favorable on-top adsorption site, 3.0 A above a Pt atom, was found, with an activation energy for surface diffusion of 22 meV and a perpendicular vibration energy of 8.5 meV. This vibration energy is reduced drastically by clustering of the adsorbed Xe atoms.PACS numbers: 68.35.Bs, 68.35.JaMonolayers of rare-gas atoms adsorbed on smooth clean single-crystal substrates have been studied extensively in recent years, for they are the simplest realization of two-dimensional (2D) matter. 1 The substrates not only provide the necessary support for the 2D adlayers but are also responsible for a large variety of 2D phases and phase transitions, dependent on their interaction with the adatoms. 2 Therefore, in order to understand the structure and dynamics of the 2D systems at the atomic level, a detailed knowledge of the shape of the adatom interaction potential is required, both perpendicular to and along the surface. This Letter presents the first ab initio calculation of such a potential, for the case of Xe atoms adsorbed on the Pt(lll) surface, and reports essential differences between the ab initio potential and empirical potentials used until now.The interaction of a rare-gas atom with a surface is usually expressed in terms of pair potentials, parametrized in such a way that observable quantities derived from the resulting potential agree with the measured values. 3 For the Xe/Pt(l 11) system, a large body of experimental information is available, allowing a detailed characterization of the interaction potential. Desorption data fix the minimum of the potential between 255 (Ref. 4) and 277 meV, 5 while the curvature at the minimum is given by the measured perpendicular vibration energy of 3.7 meV; 6 the attractive lateral Xe-Xe interaction was measured to be 43 meV per atom (14 meV per bond); 7 and from the difference between the isosteric heats of adsorption for commensurate and incommensurate phases, the lateral corrugation of the potential was estimated to be around 30 meV. 5 In spite of this rather complete picture of the interaction potential, dynamical simulations ultimately based on Pt-Xe and Xe-Xe pair potentials have had limited success in reproducing the observed structural phases and phase transformations of the adsorbed Xe layers. For example, in order to obtain the commensurate (V3xVJ)/?30° Xe lattice observed experimentally by Kern et a/., 8 Black and Janzen 9 had to choose potential parameters which, while tending to the observed lateral corrugation, 5 led to a perpendicular vibration energy more than twice the well established experimental value. 6 Recently, Bethune, Barker, and Rettner constructed a potential that yields the correct corrugation and vibration energy, by choosing an adsorption distance of 1.8 A for the Xe atom, 10 which is smaller than expected in view of the generally accepted size of the P...