Understanding of the complex behavior of particles at surfaces requires detailed knowledge of both macroscopic and microscopic processes that take place; also certain processes depend critically on temperature and gas pressure. To link these processes we combine state-of-the-art microscopic, and macroscopic phenomenological, theories. We apply our theory to the O/Ru(0001) system and calculate thermal desorption spectra, heat of adsorption, and the surface phase diagram. The agreement with experiment provides validity for our approach which thus identifies the way for a predictive simulation of surface thermodynamics and kinetics. The outline is sketched below: [C. Stampfl,  H.J. Kreuzer, S.H. Payne, H. Pfnüur, M. Scheffler, Phys. Rev. Lett. 83, 2993 (1999)]

Lattice gas Hamiltonian: the E are the adsorption energies of the isolated O atom in the fcc and hcp sites and the V are the interaction parameters between neighboring O atoms.

Calculated adsorption structures: for purely fcc sites as well as purely hcp sites and hcp-fcc mixtures.

The results, namely (left) the heat of formation at different temperatures as a function of coverage, and (right) the calculated and experimental temperature programmed desorption spectra (TPD). The peaks and dips in the heat of adsorption indicate the energetic preference for the formation of ordered phases with coverages 0.25, 0.5, 0.75, 1ML as in complete agreement with experiment. The TPD spectra show a clear shift to lower temperatures for higher O coverages reflecting the strongly repulsive O-O interactions.