Inclusion of the correlation short-range order in Ab initio calculations of the energy of the ground state by example of titanium monoxide TiO$_{1.0}$

A variant of the distribution of structural vacancies at which the crystal structure of ordered compounds simultaneously has a long-range order and correlation short-range order has been proposed and analyzed. The long-range order determines the fraction of vacancies in the atomic and vacancy sublattices of the superstructure formed because of ordering. The correlation short-range order takes into account energy favorable correlations in the arrangement of vacancies, which exist in disordered phases and are not determined by the long-range order. The possibility of the correlation short-range order has been examined by ab initio methods by example of ordering of vacancies in titanium monoxide TiO$_{1.0}$ according to the type of monoclinic superstructure M$_5$X$_{5\mathrm{mon}}$. It has been shown that partially ordered modifications with the correlation short-range order are energetically favorable as compared to the modifications without the correlation short-range order.