The Molecular Orbital Theory of the Interaction between an Atom and a Crystal Surface

The LCAO method of finding approximate one-electron wave functions is applied to an atom and crystal in mutual interaction. The case of a hydrogen-like atom and a crystal whose valence electrons occupy a band of states derived, in the LCAO approximation, from a single atomic state is discussed with the help of the simplifying assumptions of the tight binding approximation. Formulae are derived for the wave functions and energy levels of this system. If the interaction extends only over a group Ω of crystal atoms near the foreign atom then, depending on the values of the interaction parameters, there may be localized states associated with the foreign atom and the group Ω. The energies of these states lie outside the normal band (including any surface band) of crystal states and their existence allows for the formation of localized bonds between the atom and the crystal.