Self-consistent numerical-basis-set linear-combination-of-atomic-orbitals investigation of the electronic structure and properties of TiS2

A fully-self-consistent numerical-basis-set linear-combination-of-atomic-orbitals calculation of the electronic structure of Ti${\mathrm{S}}_2$ is reported using the method described previously. The calculated band structure differs considerably from those previously obtained by non-self-consistent muffin-tin models. Comparison with experiment shows that the calculated optical properties for energies below 16 eV and the various characteristics of the valence and conduction bands agree very well with optical-absorption and electron-energy-loss data as well as with photoemission, x-ray absorption, and appearance-potential spectra. A small indirect gap (0.2-0.3 eV) occurs at the points $M$ and $L$ in the Brillouin zone with a larger direct gap (0.8 eV) at $\Gamma$. We suggest that the characteristic semi-metallic large $g$ value observed experimentally originates from a near coincidence of the band gap with the enhanced spin-orbit splitting which is consistent with the soft-x-ray data and our band model. The bonding mechanism in Ti${\mathrm{S}}_2$ is discussed in detail; it is shown by a direct calculation of the self-consistent charge density and the transverse effective charge that the system is predominantly covalent with small static ionic character and large dynamic ionicity. In contrast with muffin-tin $X\alpha$ models, the bonding is found to be largely due to Ti $4s4p$ to S $3p$ bonds and a much weaker Ti $3d$ to S $3p$ bond. The effects of muffin-tin approximation and self-consistency are discussed in detail. Extrapolation of these results to the case of Ti${\mathrm{Se}}_2$ is made and the possible origin of its charge-density wave is discussed.