Electronic structure of a single oxygen vacancy in rutile TiO₂

I report calculations of the electronic structure of an ideal (undistorted) oxygen vacancy in rutile TiO₂ using the equation-of-motion method. I use a full phenomenological tight-binding Hamiltonian due to Vos to describe the electronic structure. The bulk band structure is also discussed in detail using the traditional Green's-function method. I illustrate an efficient way to calculate the perfect-crystal Green's-function matrix elements for any structure, including those that belong to non-symmorphic space groups. The results show that the oxygen vacancy in rutile TiO₂ results in deeply localized states in its vicinty.