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 $\ensuremath{\theta}$. 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 $\ensuremath{\theta}\ensuremath{\le}0.5$, ${\mathrm{H}}_{2}\mathrm{O}$ is adsorbed dissociatively, with an adsorption energy $\ensuremath{\Delta}{H}_{\mathrm{H},\mathrm{OH}}\ensuremath{\sim}1.6\mathrm{eV}$. At $\ensuremath{\theta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$, ${\mathrm{H}}_{2}\mathrm{O}$ can be adsorbed molecularly ( $\ensuremath{\Delta}{H}_{{\mathrm{H}}_{2}\mathrm{O}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.82\mathrm{eV}/\mathrm{molecule}$), 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.
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