  Nelson et al. [Phys. Rev. B 95, 054118 (2017)] recently have reported
first-principles calculations on the behaviour of group-II difluorides
(BeF$_{2}$, MgF$_{2}$, and CaF$_{2}$) under high-pressure and low- and
high-temperature conditions. The calculations were based on ab initio random
structure searching and the quasi-harmonic approximation (QHA). Here, we point
out that, despite the of inestimable value of such calculations at
high-pressure and low-temperature conditions, the high-$P$ high-$T$ phase
diagram proposed by Nelson et al. for CaF$_{2}$ neither is in qualitative
agreement with the results of previous ab initio molecular dynamics simulations
nor with the existing corps of experimental data. Therefore, we conclude that
the QHA-based approach employed by Nelson et al. cannot be applied reliably to
the study of phase boundaries involving superionic phases. This conclusion is
further corroborated by additional ab initio calculations performed in the
superionic compounds SrF$_{2}$, BaF$_{2}$, Li$_{3}$OCl, and AgI.
