Overlap effects in the theory of adsorption using Anderson's Hamiltonian

When Anderson's model Hamiltonian is applied to the adsorption of atoms by metals, the basis orbitals cannot be regarded as orthogonal, and overlap effects must therefore be included in the theory. This is easily accomplished, not only in the Hartree-Fock approximation, but also in the exact many-body theory. Only the former is discussed in detail. Numerical calculations with parameters chosen to represent some features of the adsorption of hydrogen, and sodium atoms by tungsten are reported, and it is shown that, whereas overlap is essential in a quantitative treatment of the binding energies, the work of elucidating the electronic structures of adsorbed atoms can be started without including it explicitly in the theory.