The ab initio full-potential linearized-augmented-plane-wave method for a free-slab geometry was used to calculate the electronic structure and geometry of a clean ${\mathrm{TiO}}_2$ (110) rutile surface. Surface induced states were found in the density of states, such as an s-like surface state at -15 eV. Band bending states of width 0.5 eV appear just below the Fermi energy, in agreement with photoemission experiments. The positions of the atoms in the surface and subsurface layers and the corresponding change of Ti-O bond lengths were derived by total-energy minimization. In general, downward relaxations were obtained for which the fivefold-coordinated Ti experienced the largest relaxation of -0.180 Å, whereas the second most important relaxation effect, -0.156 Å, occurred for the surface O. The calculated Ti-O bond lengths are in very good agreement with experimental data for the ${\mathrm{TiO}}_2$ (100) surface. The calculated work function 6.79 eV compares favorably with the experimental result of 6.83 eV. Based on an extension of density-functional theory to excited states the valence- and conduction-band gap was calculated to be 1.99 eV, which is in reasonable agreement with the experimental gap of 2.6 eV when compared to the one-particle band gap of 0.65 eV.

• Received 30 June 1993

DOI:https://doi.org/10.1103/PhysRevB.49.2099