Oxygen vacancies in vanadium dioxide: A DFT$+V$ study

We present a density-functional theory study of the effects of oxygen vacancies on the structural and electronic properties of vanadium dioxide (VO$_2$). Our motivation is the reported suppression of the metal-insulator transition by oxygen vacancies and the lack of a clear consensus on its origin. We use the DFT$+V$ method with a static intersite vanadium-vanadium interaction term, $V$, to calculate the properties of the oxygen-deficient metallic rutile and insulating monoclinic M1 phases of VO$_2$ on the same footing. We find that oxygen vacancies induce local distortions in the M1 phase, but do not destroy the dimerization usually associated with the insulating behavior. In spite of this, we find that the M1 phase becomes metallic as a result of the partial filling of the conduction band due to a rigid-band-like doping effect.