Self-consistent tight-binding study of low-index titanium surfaces

We report development of a self-consistent tight-binding (SCTB) model for metallic titanium and its use to simulate relaxed, self-consistent low-index surfaces of hcp titanium. We find oscillations in atomic plane separation and electronic density as a function of depth below the surface that do not stabilize until the supercell slab used in the calculation is more than ten layers deep. The SCTB model can only give stable, structures and reasonable surface structures and energies if multipole (particularly dipole) moments are allowed to be induced at the atomic sites and if the first-principles data base includes calculations on short wave length ("frozen phonon") distortions of the bulk unit cell.