First-principles calculations of the energetics of stoichiometric ${\mathrm{TiO}}_2$ surfaces

We present self-consistent ab initio total-energy calculations of the equilibrium relaxed structures and surface energies of the stoichiometric (1×1) (110), (100), (001), and (011) surfaces of ${\mathrm{TiO}}_2$. The relaxations of atoms on these surfaces are found to be substantial, and are responsible for a large reduction of the calculated surface energies. A Wulff construction is used to display the relative energetics of these surfaces. The (100) surface is found to be stable with respect to forming macroscpic (110) facets, while the (001) surface is nearly unstable with respect to forming macroscopic (1×1) (011) facets. These results shed light on published experimental results on the structures of these surfaces.