We have calculated the ground-state geometry, vibrational frequencies, and bonding properties of MgF2 at the Hartree-Fock (HF), second-order (MP2), and fourth-order Moller-Plesset (MP4(SDTQ)) levels of calculation. Several high-quality basis sets have been used, with special attention on the influence of polarization and diffuse functions on the above properties. The best HF and MP2 calculations predict that MgF2 is a linear molecule. MP2 and MP4 results are very similar. The MP2 symmetric (yl) and asymmetric (nu (3)) stretching frequencies are about 5-7% smaller than the HF values and agree well with the observed data. The MP2 nu (2) (bending) frequency is close to that found in other ab initio calculations and the experimental gas-phase value but is 80 cm(-1) smaller than the value observed in the IR spectrum of MgF2 trapped in solid argon. Polarization functions shorten noticeably the magnesium-fluorine equilibrium distance and increase yl and nu (3) An atoms in molecules (AIM) analysis of the wave functions reveals that MgF2 is a highly ionic molecule, the net charge of Mg being about +1.8 e, and that most basis set effects are due to the poor convergence properties of the atomic electron dipole moments. This suggests a polarizable ions model that is shown to account for the trends found in most of the properties studied. The origin of the bending problem in these compounds is traced back to the polarizability of the cation.