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In this paper, I demonstrate a density functional theory plus dynamical meanfield theory study on the electronic properties of doped $TiO_2$ rutile as wellas another tetragonal phase anatase with oxygen vacancy. The density of statesand optical properties have been obtained from the electronic structureapplying screened hybrid exchange correlation density functionals. All thesingle-particle excitations are treated within the dynamical mean field theoryfor independent quasiparticles. For optical properties, excitations areconsidered by solving the Bethe-Salpeter equation for Coulomb correlatedelectron-hole duo. On this theoretical basis, band structure and opticalspectra for the two structures of $TiO_2$ are provided. Further, I compared thepresent results with earlier optical data of parent structure and establishedthe increased optical efficiency in doped $TiO_2$ with oxygen vacancy in boththe structure.

Engineering Si doping in anatase and rutile TiO$_2$ with oxygen vacancy for efficient optical application