The coupling of an atom (or molecule) to a metal converts originally discrete levels which fall in the energy bands of the metal to virtual levels (resonances) with fractional occupancies determined by their positions with respect to the Fermi level. The calculation of these resonances and occupancies is a major problem in the theory of adsorption: It is discussed here in terms of a model Hamiltonian of Anderson's type. The concept of a surface molecule, i.e., a local molecular structure whose molecular orbitals correspond to the resonances, arises with transition metal adsorbents. This concept is used for Na and S on Ni(100) in the pyramidalNi4Xlocal geometry. The experimental binding energy is used to predict the electronic structure and resonances for Na, and the experimental resonance to predict the structure and binding energy of S.