Electronic structure and optical properties of layered dichalcogenides: TiS2and TiSe2

The electronic-energy-band structure of the layered dichalcogenides Ti${\mathrm{S}}_2$ and Ti${\mathrm{Se}}_2$ has been determined using the Korringa-Kohn-Rostoker (KKR) method. Crystal potentials were constructed from overlapping atomic charge densities in the muffin-tin approximation for both full Slater exchange and Kohn-Sham-Gaspár exchange and several different starting atomic configurations. Detailed results are given here for the potential based on the atomic configuration $3d^{2}4s^2$ on the titanium atoms, $3p^4$ on the sulfur atoms, and $4p^4$ on the selenium atoms and with full Slater exchange. An energy gap of 2.0-2.7 eV between the occupied $3p$ sulfur bands and the empty $3d$ titanium bands is found for all potentials studied thereby confirming the traditional view of Ti${\mathrm{S}}_2$ as a semiconductor. Ti${\mathrm{Se}}_2$ is also found to be a semiconductor with a direct energy-band gap of 1.2 eV. The joint density of states calculated from the energy bands of these ab initio calculations are found to agree quite well with recently measured transmission spectra.