Abstract
Excited $s$ states are added to the minimal-basis tight-binding theory of covalent solids using Louie's perturbation approach. This brings the conduction bands into better accord with experiment without appreciably complicating the calculation of properties in the bond-orbital approximation. Universal interatomic matrix elements are obtained by fitting the free-electron bands, and then adjusted to accord with the bands of germanium. Bands based upon these interatomic matrix elements, and upon Hartree-Fock term values, are then compared with pseudopotential bands for Si, Ge, Sn, GaAs, InSb, ZnSe, and CdTe. A single set of metallic, covalent, and polar energies for $s{p}^{3}$ hybrids obtained from the new matrix elements are found to predict good values for both the dielectric and elastic properties; in contrast, two different sets were required for the two classes of properties in the earlier theory.
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