First-principles calculations using the full-potential linearized augmented plane-wave method have been performed to investigate detailed electronic and optical properties of ${\mathrm{TiO}}_2$ in the anatase structure. The fully optimized structure, obtained by minimizing the total energy and atomic forces, are in good agreement with experiment. Stabilization of the structure by the trade off between a favorable coordination in the ${\mathrm{sp}}^2$ hybridization and the Coulomb repulsion among oxygen atoms is also demonstrated. We calculate band structure, densities of states and charge densities, and interpret their features in terms of the bonding structure in the molecular orbital picture. The optical properties, calculated within the dipole approximation, are found to agree with recent experiments on single crystals of anatase ${\mathrm{TiO}}_2.$ Near the absorption edge, the results show a significant optical anisotropy in the components parallel and perpendicular to the c axis. We demonstrate that this large dichroism results from the existence of nonbonding $d_{\mathrm{xy}}$ orbitals located at the bottom of the conduction bands, which allows direct dipole transitions dominantly for the perpendicular component.

• Received 17 August 1999

DOI:https://doi.org/10.1103/PhysRevB.61.7459