We present an ab initio density-functional investigation of the structure and energetics of several stoichiometric $1\times 1$ low-index surfaces of anatase, a ${\mathrm{TiO}}_2$ polymorph $\sim 9\%$ less dense and $\sim 1.2$ kcal/mol less stable than rutile. Although our calculations do not reproduce the relative ordering of the two phases that is observed experimentally, the calculated bulk structural and elastic properties of both polymorphs are in excellent agreement with the experiment, suggesting that surface relaxations are correctly described as well. As expected, the surface energies of anatase appear to be related to the presence of undercoordinated Ti atoms: the surfaces with fourfold-coordinated Ti atoms have a larger energy than those with fivefold-coordinated Ti. Furthermore, we find that the average surface energy of a ${\mathrm{TiO}}_2$ anatase macroscopic crystal is smaller than that of rutile. Finally, patterns in the relaxation of the surface atoms which are common to different surfaces are analyzed.

We present density functional calculations of ${\mathrm{H}}_2\mathrm{O}$ interacting with the (101) and (001) surfaces of ${\mathrm{TiO}}_2$ anatase at various coverages $\theta$. On the (101) surface, nondissociative molecular adsorption at fivefold coordinated Ti sites is favored at both low and monolayer coverage. On the (001) surface, for $\theta \le 0.5$, ${\mathrm{H}}_2\mathrm{O}$ is adsorbed dissociatively, with an adsorption energy $\Delta H_{\mathrm{H},\mathrm{OH}}\sim 1.6\mathrm{eV}$. At $\theta =1\mathrm{}$, ${\mathrm{H}}_2\mathrm{O}$ can be adsorbed molecularly ( $\Delta H_{{\mathrm{H}}_2\mathrm{O}}=0.82\mathrm{}\mathrm{eV}/\mathrm{molecule}$), but a state with half of the ${\mathrm{H}}_2\mathrm{O}$ adsorbed dissociatively and the other half H bonded in a “second layer” is energetically more favorable. These results are discussed in the context of the available experimental information.