  Far from being conclusively understood, the reactive interaction of water
with rutile does still present a challenge to atomistic modelling techniques
rooted on quantum mechanics. We show that static geometries of stoichiometric
TiO$_2$/water interfaces can be described well by Density Functional Tight
Binding (DFTB). However, this method needs further improvements to reproduce
the low dissociation propensity of H$_2$O after adsorption predicted by Density
Functional Theory (DFT). A reliable description of the surface reactivity of
water is fundamental to investigate the non-stoichiometric reconstruction of
the (001) facet rich in Ti interstitials. Calculations based on (DFT) predict
the transition temperature for the onset of reconstruction in remarkable
agreement with experiments and suggest that this surface, in contact with
liquid water, can promote spontaneous H$_2$O splitting and formation of H$_2$
molecules.
