Effects of overlap and next-nearest-neighbor interactions in tight-binding calculations

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Abstract
Effects due to overlap between orbitals on neighboring atoms and to next-nearest-neighbor interactions, on the electronic structure, are investigated. As an illustration of their importance, analytic results are obtained for the density of states of a Bethe lattice and numerical calculations are carried out to obtain the band structure of a diamond lattice, starting from a realistic Hamiltonian. We show that overlap and next-nearest-neighbor interactions have important effects which are of opposite sign and tend to cancel each other in the valence band, but they are additive in the conduction band. The implications of our results for transition metals and surfaces are briefly discussed.