Electronic structure and stability of nonstoichiometric titanium monoxide TiO$_y$ with structural vacancies in one of the sublattices

The electronic structure of nonstoichiometric titanium monoxide TiO$_y$ with different compositions $y$, which contains structural vacancies either in the metallic sublattice or in the nonmetallic sublattice, has been investigated using the supercell method within the DFT-GGA approximation with pseudopotentials. The cases of ordered and disordered arrangements of vacancies have been considered. It has been found that the complete removal of vacancies from the sublattice is energetically unfavorable, and the ordering of oxygen vacancies according to the type of the Ti$_6$O$_5\square_1$ superstructure, as well as titanium vacancies according to the Ti$_5\blacksquare_1$O$_6$ type, does not lead to the stabilization of the B1 basic structure of titanium monoxide.