We have characterised the Lewis acidity of unsaturated surface cations of MgF2 crystals using periodic calculations at the B3LYP level. The relative importance of low index surfaces was determined by calculating surface energies, and these surfaces were then probed by CO adsorption. We found that a MgF2 microcrystal should expose mainly (110), (100) and (101) surfaces in which the undercoordinated cations are fivefold coordinated. The adsorption energies and CO stretching frequencies are discussed with respect to the coordination number of surface cations and the stability of the surfaces and are compared to IR spectra from the literature.