A parametrized non-orthogonal tight-binding (TB) method combined with the coherent-potential-approximation is applied to the study of the electronic structure of disordered off-stoichiometric TiC x , the lattice relaxation and the electronic spectra of the TiC (001) surface, the local relaxation and energetic states of TiC structures with one or two vacancies in both the non-metal and metal sublattices. The calculated results are in good agreement with available experimental and theoretical data. The importance of the overlap matrix elements of the TB Hamiltonian in describing the electronic structure of this class of compounds is emphasized.

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