Chemical bonding in titanium-metalloid compounds

First-principles molecular-orbital calculations for titanium-metalloid compounds TiB, ${\mathrm{TiB}}_2,$ TiC, ${\mathrm{Ti}}_2\mathrm{N},$ TiN, TiO, ${\mathrm{TiO}}_2,$ TiSi, ${\mathrm{TiSi}}_2,$ TiP, TiS, and ${\mathrm{TiS}}_2$ have been made by the use of discrete-variational $X\alpha$ method with model clusters composed of about 100 atoms. In order to compare the covalent bonding quantitatively among these compounds with different crystal structures, we used covalent bond density in which both the strength and the number of each type of the bonds in the compounds are taken into account. The covalent bond density represents the strength of the covalent bonding per unit volume irrespective of crystal structures. The dominant covalent bonding in the titanium compounds except for TiO is found to be the $\mathrm{Ti}-X$ bonding, which mainly arises from the interaction between $\mathrm{Ti}-3d-X-np$ and $\mathrm{Ti}-4p-X-np$ orbitals. Each compound exhibits a wide variety of chemical bondings depending upon its crystal structure and local coordinations. However, their total covalent bond density simply decreases and the ionic character increases with rising the atomic number of X atoms. The trend agrees with a simple expectation from the electronegativity differences between Ti and X.