We presently conclude that the present study supplemented by previousobservations reveals that though the anharmonicity in CaF2 is very strong, high-T thermodynamic properties can be accurately obtained only by considering the volume dependence of the phonon frequencies. Sent Although, X-point softening in opticalmode is clearly obtained in the present case study via only thermal expansion effect, anharmonicity due to phonon decay process expected at -point of BZ still remainsthe subject of interest, so as the high-P melting curve and P-T phase diagram. Simpleapproach within the TB-SMA, which was originally designed for elemental metals, iscapable to mimic the principal Hugoniot for such strongly ionic materials."