The augmented-plane-wave (APW) band structure of ReO3 is analyzed in terms of the Slater-Koster linear-combination-of-atomic-orbitals (LCAO) interpolation scheme with nonorthogonal orbitals. This approach has several advantages over an earlier treatment involving orthonormal basis functions. First, it provides insight into the physical origin of the crystal-field splittings in ReO3 and other transition-metal compounds. Second, it leads to more physically meaningful LCAO parameters. Finally, it provides a direct relationship between the crystal-field levels of an isolated transition-metal ion or molecular complex and the band structure of the periodic crystal. In the case of ReO3, it is shown that the crystal-field effects are due to overlap and covalency between the rhenium 5d orbitals and the 2s, 2p sigma, and 2p pi orbitals of the neighboring oxygen ligands. The splitting between the e(g) and t(2g) bands is due to the 2(s) contribution Delta(s). The difference between the 2(s) and 2p sigma contributions Delta(sigma)-Delta(s) is responsible for the e(g) bandwidth. This same difference is proportional to the effective transfer integral b in Anderson's theory of superexchange. The t(2g) bandwidth is due to Delta(pi) the 2p pi overlap-covalency parameter. This LCAO method is applied to KNiF3, using LCAO integrals determined from the Sugano-Shulman molecular- orbital calculation for the (NiF6)(4-) complex. The resulting KNiF3 band structure is qualitatively similar to the APW results for ReO3, except the bandwidths are narrower by about a factor of 4. In the limit where the Coulomb energy U is large compared with the e(g) and t(2g) bandwidths so that the electrons localize, it is shown that the crystal-field splitting between the localized e(g) and t(2g) Wannier functions is identical with that obtained by Sugano and Shulman via the molecular-orbital method.
