Effect of the long-range order in the vacancy distribution on the electronic structure of titanium monoxide TiO$_{1.0}$

The effect of the long-range order in the vacancy distribution according to the type of monoclinic Ti$_5$O$_5$ superstructure on the electronic structure of titanium monoxide TiO$_y$ with the stoichiometric composition has been studied by the supercell method within the DFT-GGA approximation with the use of pseudopotentials. It has been established that, in spite of an increase in the Fermi energy, the stability of the compound increases with increasing degree of the long-range order $\eta$. The ordering of the structural vacancies leads to the considerable increase in the depth of the pseudogap at the Fermi level. It has been shown that the effect of the long-range order on the electronic structure in the range of $\eta$ from $0$ to $1.0$ is much weaker than the effect of the nonstoichiometry of TiO$_y$ in the range of $y$ from $0.75$ to $1.33$.