Effects of dopant states on the electronic structures in tungsten doped TiO$_2$

Despite the broad range of applicabilities for TiO$_2$ as a photocatalytic material, only about $3\%$ of the solar spectrum (ultraviolet) can be utilized due to its wide intrinsic band gap. Therefore, considerable efforts have been made to extend the photoresponse of TiO$_2$-based systems further into the visible-light region using dopants. In this work, we explore the electronic structures of tungsten doped TiO$_2$ using an {\it ab-initio} tight-binding method, called F{\small IREBALL}, which is based on density functional theory (DFT) with nonlocal pseudopotentials within the local density approximation (LDA). Our calculations provide an initial glance into electronic properties required for acceptable photocatalysis.