The formalism developed in molecular theory for calculation of local electronic-structure characteristics in a nonorthogonal atomic basis is generalized to systems with translational symmetry. Expressions have been derived to describe the bond orders, covalency, and valence in a crystal for restricted and unrestricted Hartree-Fock methods. Nonempirical electronic-structure calculations and an analysis of chemical bonding in the TiO₂, Ti₂O₃, and TiO titanium oxide crystals have been performed.