  In this supplemental document we explain the details of our ab initio density
functional theory calculations and crystal structure searches performed in CaF2
under pressure. Also we report the computed P-dependence of the formation
energy of Frenkel pair defects in the cubic fluorite phase, and the vibrational
phonon spectra and structural data of the predicted high-T monoclinic P2_1/c
phase. Calculated enthalpy energies in compressed SrF2 and BaF2 are also
presented.
