Energy Bands for KNi${\mathrm{F}}_3$, SrTi${\mathrm{O}}_3$, KMo${\mathrm{O}}_3$, and KTa${\mathrm{O}}_3$

The nonrelativistic augmented-plane-wave (APW) method has been applied to calculate the electronic band structures for several cubic perovskite-type compounds, including KNi${\mathrm{F}}_3$, SrTi${\mathrm{O}}_3$, KMo${\mathrm{O}}_3$, and KTa${\mathrm{O}}_3$. These calculations involve ad hoc crystal potentials that are derived from neutral-atom charge densities. The energy-band results for the $2p$ valence bands and the $t_{2g}-e_g$ conduction bands in these ternary compounds are similar to the tight-binding results of Kahn and Leyendecker for SrTi${\mathrm{O}}_3$ and the previous APW results for Re${\mathrm{O}}_3$. It is found that the additional conduction bands associated with the metal $s-p$ and the potassium or strontium $d$ orbitals lie several electron volts above the Fermi level for each compound. The APW results for the $2s-2p$ valence bands and the lowest $t_{2g}-e_g$ conduction bands have been fitted with the Slater and Koster linear-combination-of-atomic-orbitals (LCAO) interpolation scheme, including orbital-overlap effects. The LCAO parameters which determine the $p-d$ band gaps in the oxides have been adjusted in accordance with optical and cyclotron-mass data. Assuming a rigid-band model and including spin-orbit effects, this adjusted LCAO model is applied to calculate constant-energy surfaces, cyclotron masses, and density-of-states curves for the $n$-type semiconductors SrTi${\mathrm{O}}_3$ and KTa${\mathrm{O}}_3$ as well as the nonstoichiometric metallic bronze ${\mathrm{K}}_{0.92}$Mo${\mathrm{O}}_3$. It is found that (a) the conduction bands in $n$-type SrTi${\mathrm{O}}_3$ and KTa${\mathrm{O}}_3$ consist of warped bands at the zone center rather than many valleys at $X$, as Kahn and Leyendecker have proposed; (b) the fundamental $p-d$ band gaps in both SrTi${\mathrm{O}}_3$ and KTa${\mathrm{O}}_3$ are direct; (c) the LCAO joint-density-of-states results for SrTi${\mathrm{O}}_3$ and KTa${\mathrm{O}}_3$ provide a qualitative interpretation of the optical data; (d) the calculated extremal areas for orbits on the ${\mathrm{K}}_{0.92}$Mo${\mathrm{O}}_3$ Fermi surface agree to within 10% with recent de Haas-van Alphen data.