We report the vibrational and thermodynamic properties of four known CsPbI 3 polymorphs in the framework of the density functional theory. We compare the recently introduced strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation (meta-GGA) with the local density approximation (LDA). We found that the SCAN, compared to the LDA, could explain discrepancies between theoretical and experimental results. Evaluating the Helmholtz free energy as a function of temperature, we found that within the SCAN (a) all polymorphs had negative formation enthalpies at the room temperature and (b) CsPbI 3 underwent the phase transition from the δ- to α-phase at 480 K. This is not true for the LDA. In contrast to the previous reports based on the LDA, we did not find the ferroelectric instability in the phonon spectra of the cubic and tetragonal phases at the meta-GGA level. This result agrees with the lack of observation of the ferroelectricity in CsPbI 3 .

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The presented DFT+U calculations revealed that the doping of BiFeO3 with Al and Ga reduced the energy barrier between R3c-G and Cm-C phases whereas for Sc and In the energy difference between both phases increased.