Significant Differences between Hartree-Fock and Local-Exchange Energy Bands for TiO

Abstract

Hartree-Fock (HF) energy-band calculations on TiO are in qualitative disagreement with those obtained with use of statistical exchange ($X\alpha$). While all $X\alpha$ results have a 2-8-eV gap between the Ti $3d$ and O $2p$ bands, the HF results show largely overlapping $2p-3d$ bands. The HF result is supported experimentally by the absence of any gap in the experimental valence x-ray-photoemission-spectroscopy spectrum. Reasons for the apparent failure of $X\alpha$ theory on this material, and not on other materials are suggested.