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A comprehensive phase diagram of lowest-energy structures and compositions ofthe rutile TiO_2(110) surface in equilibrium with a surrounding gas phase atfinite temperatures and pressures has been determined using density functionaltheory in combination with a thermodynamic formalism. The exchange of oxygen,hydrogen, and water molecules with the gas phase is considered. Particularattention is given to the convergence of all calculations with respect tolateral system size and slab thickness. In addition, the reliability ofsemilocal density functionals to describing the energetics of the reducedsurfaces is critically evaluated. For ambient conditions the surface is foundto be fully covered by molecularly adsorbed water. At low coverages, in thelimit of single, isolated water molecules, molecular and dissociativeadsorption become energetically degenerate. Oxygen vacancies form in stronglyreducing, oxygen-poor environments. However, already at slightly more moderateconditions it is shown that removing full TiO_2 units from the surface isthermodynamically preferred. In agreement with recent experimental observationsit is furthermore confirmed that even under extremely hydrogen-richenvironments the surface cannot be fully hydroxylated, but only a maximumcoverage with hydrogen of about 0.6-0.7 monolayer can be reached. Finally,calculations of migration paths strongly suggest that hydrogen prefers todiffuse into the bulk over desorbing from the surface into the gas phase.

Composition, structure, and stability of the rutile TiO_2(110) surface: oxygen depletion, hydroxylation, hydrogen migration and water adsorption