Abstract
Elements of scattering theory are combined with the treatment of the boundary conditions to give an exact analysis which holds for any system with inherently discrete structure. The two problems explicitly discussed are incomplete crystals - e.g., free surfaces or vacancies - and interfaces. For incomplete crystals the results allow for a critical appraisal of atom removal methods, which are assessed as constituting in general an approximation to the exact results. Attention is drawn to the role of the orthogonality properties of the basis in tight binding electronic calculations for incomplete crystals.
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