We develop $p$-$d$ orthogonal tight-binding (OTB) models for the description of TiC${}_x$ and TiN${}_x$ compounds in the $1.0>x>0.5$ composition range. For the parametrization of bond integrals we use a recently developed method allowing projection of the one-electron wave functions obtained within the density functional theory onto optimized atom-centered orbitals. The performance of the OTB models is investigated for a wide range of properties: binding energy of elements and compounds, density of states, formation energy of vacancy-ordered defects, elastic constants, and phonon dispersions. The models provide a good description of the ground state properties at 1:1 composition and show a fair transferability for various atomic environments in elemental and binary phases.

• Received 4 July 2011

DOI:https://doi.org/10.1103/PhysRevB.84.155120