  The interaction of water with $\alpha$-alumina (i.e. $\alpha$-Al$_{2}$O$_{3}$
surfaces is important in a variety of applications and a useful model for the
interaction of water with environmentally abundant aluminosilicate phases.
Despite its significance, studies of water interaction with
$\alpha$-Al$_{2}$O$_{3}$ surfaces other than the $(0001)$ are extremely
limited. Here we characterize the interaction of water (D$_{2}$O) with a well
defined $\alpha$-Al$_{2}$O$_{3}$$(1\bar{1}02)$ surface in UHV both
experimentally, using temperature programmed desorption and surface-specific
vibrational spectroscopy, and theoretically, using periodic-slab density
functional theory calculations. This combined approach makes it possible to
demonstrate that water adsorption occurs only at a single well defined surface
site (the so-called 1-4 configuration) and that at this site the barrier
between the molecularly and dissociatively adsorbed forms is very low: 0.06 eV.
A subset of OD stretch vibrations are parallel to this dissociation coordinate,
and thus would be expected to be shifted to low frequencies relative to an
uncoupled harmonic oscillator. To quantify this effect we solve the vibrational
Schr\"odinger equation along the dissociation coordinate and find fundamental
frequencies red-shifted by more than 1,500 cm$^{\text{-1}}$. Within the context
of this model, at moderate temperatures, we further find that some fraction of
surface deuterons are likely delocalized: dissociatively and molecularly
absorbed states are no longer distinguishable.
