Density functional theory calculations were performed in conjunction with ab initio thermodynamics, bond valence calculations, and density of states studies to investigate the chemical reactivity of \ensuremath{\alpha}-Al${}_{2}$O${}_{3}$ and \ensuremath{\alpha}-Fe${}_{2}$O${}_{3}$ $(1\overline{1}02)$ surfaces in a humid environment. Isostructural \ensuremath{\alpha}-Fe${}_{2}$O${}_{3}$ $(1\overline{1}02)$ displays a much higher degree of surface reactivity with respect to water adsorption and aqueous heavy metal ions than \ensuremath{\alpha}-Al${}_{2}$O${}_{3}$. The reason for these differences has not been fully explained. We have found that, while both metal oxides exhibit a similar stable $(1\overline{1}02)$ surface at and below room temperature, corresponding to a stoichiometric surface with the first layer of metal ions missing, the degree of hydroxylation of the surface oxygen atoms leads to differences in the atomic layer relaxation in $\ensuremath{\alpha}\ensuremath{-}{\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ $(1\overline{1}02)$ compared to \ensuremath{\alpha}-Fe${}_{2}$O${}_{3}$ $(1\overline{1}02)$, which has also been confirmed previously by crystal truncation rod x-ray diffraction studies. Also in agreement with these experimental studies, we find the atomic layer spacing of the most energetically stable (1$\stackrel{\underline{}}{1}$02) ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ surface is relatively insensitive to the inclusion of multiple layers of physisorbed water. This is in contrast to previously reported density functional theory studies of hydrated (1$\stackrel{\underline{}}{1}$02) $\ensuremath{\alpha}\ensuremath{-}{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}$ surfaces, the results of which are confirmed in this work, that a monolayer of water is required for good agreement with experimental measurements of the atomic layer relaxation. These changes in atomic spacing result in changes in electron charge distributions and in Lewis and Br\o{}nsted acid/base properties of surface sites, which influence the relative reactivities of the two surfaces. However, the higher reactivity of the hydrated $(1\overline{1}02)$ surface of \ensuremath{\alpha}-Fe${}_{2}$O${}_{3}$ can be attributed mainly to the empty $d$ states of the surface Fe atoms, which exhibit a first peak at \ensuremath{\sim}1 eV above the Fermi level and act as very strong Lewis acid sites. In comparison, the empty $p$ states of Al in the hydrated $(1\overline{1}02)$ \ensuremath{\alpha}-Al${}_{2}$O${}_{3}$ surface, which are \ensuremath{\sim}5 eV above the Fermi level, should be much less reactive to potential adsorbates.
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