Abstract
The electronic properties of vanadiumβdoped rutile TiO~2~ are investigated theoretically with a HartreeβFock/DFT hybrid approach. The most common oxidation states (V^2+^, V^3+^, V^4+^, and V^5+^) in different spin states are investigated and their relative stability is calculated. The most stable spin states are quartet, quintet, doublet, and singlet for V^2+^, V^3+^, V^4+^, and V^5+^ doping, respectively. By comparing the formation energy with respect to the parent oxides and gasβphase oxygen (Ξ__E__), we conclude that V^4+^ (Ξ__E__=145.3 kJβmol^β1^) is the most likely oxidation state for vanadium doping with the possibility of V^5+^ doping (Ξ__E__=283.5 kJβmol^β1^). The energetic and electronic properties are converged with dopant concentrations in the range of 0.9 to 3.2β%, which is within the experimentally accessible range. The investigation of electronic properties shows that V^4+^ doping creates both occupied and unoccupied vanadium states in the band gap and V^5+^ doping creates unoccupied states at the bottom of the conduction band. In both cases there is a significant reduction of the band gap by 0.65 to 0.75 eV compared to that of undoped rutile TiO~2~.