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The local crystal structures of many perovskite-structured materials deviatefrom the average space group symmetry. We demonstrate, from lattice-dynamicscalculations based on quantum chemical force constants, that all thecaesium-lead and caesium-tin halide perovskites exhibit vibrationalinstabilities associated with octahedral titling in their high-temperaturecubic phase. Anharmonic double-well potentials are found for zone-boundaryphonon modes in all compounds with barriers ranging from 108 to 512 meV. Thewell depth is correlated with the tolerance factor and the chemistry of thecomposition, but is not proportional to the imaginary harmonic phononfrequency. We provide quantitative insights into the thermodynamic drivingforces and distinguish between dynamic and static disorder based on thepotential-energy landscape. A positive band gap deformation (spectralblueshift) accompanies the structural distortion, with implications forunderstanding the performance of these materials in applications areasincluding solar cells and light-emitting diodes.

Spontaneous Octahedral Tilting in the Cubic Inorganic Caesium Halide Perovskites CsSnX$_3$ and CsPbX$_3$ (X = F, Cl, Br, I)