Density functional theory simulations, including a correction for dispersive interactions, were performed to investigate the adsorption of water on the main cleavage plane of the fluorite, namely, the (111) surface. In the case of a single molecule of water, we observe that the molecular form is preferred over the dissociated one, and absorbs on the surface with an energy of 55 kJ mol(-1), including a significant contribution from the dispersion forces. Also, we show that the substitution of a fluorine atom by a hydroxyl group on the surface of fluorite is not energetically favorable. Then, the hydration of the surface in function of the coverage by water molecules was studied in a systematic way. It was shown that the geometries involving the formation of a cluster of water molecules on the surface, with half of the molecules adsorbed, are the most favorable. Finally, ab initio molecular dynamics conducted at 300 K confirms the trends observed at 0 K, albeit the adsorption energies are reduced by about 10 kJ mol(-1). Also, we observe that once put in the interaction with a large number of water molecules, half of the calcium atoms at the surface are in close interaction with a water molecule, whereas the rest of the molecules are further away but present a relatively well-defined structure showing similarities with the one of water clusters.