We have investigated the origin of the experimentally observed change in photoactivity of anatase and rutile ${\mathrm{TiO}}_2$ induced by substitutional $\mathrm{N}$-doping using state-of-the-art density functional theory calculations. Our results show that in both polymorphs $\mathrm{N}2p$ localized states just above the top of the $\mathrm{O}2p$ valence are present. In anatase these states cause a redshift of the absorption band edge towards the visible region. In rutile, instead, this effect is offset by the concomitant $\mathrm{N}$-induced contraction of the $\mathrm{O}2p$ band, resulting in an overall increase of the optical transition energy. Experimental trends are well described by these results.

Hybrid functional density functional theory calculations of the oxygen vacancy (VO) in monoclinic bulk WO3 provide a coherent rationalization for the strong dependence of WO3$-${}x electronic properties on the VO concentration and of the semiconductor-to-metal transition, a phenomenon intimately connected to the electrochromic effect. Different VO centers containing W4+, W5+, and W6+ species are expected to coexist. Optical transition levels are 0.7\char21{}1.0 eV below the conduction band minimum, in agreement with experiments. The complex nature of VO in WO3 can only be detected with methods that properly describe band gaps and polaronic distortions at defect sites.