  The local crystal structures of many perovskite-structured materials deviate
from the average space group symmetry. We demonstrate, from lattice-dynamics
calculations based on quantum chemical force constants, that all the
caesium-lead and caesium-tin halide perovskites exhibit vibrational
instabilities associated with octahedral titling in their high-temperature
cubic phase. Anharmonic double-well potentials are found for zone-boundary
phonon modes in all compounds with barriers ranging from 108 to 512 meV. The
well depth is correlated with the tolerance factor and the chemistry of the
composition, but is not proportional to the imaginary harmonic phonon
frequency. We provide quantitative insights into the thermodynamic driving
forces and distinguish between dynamic and static disorder based on the
potential-energy landscape. A positive band gap deformation (spectral
blueshift) accompanies the structural distortion, with implications for
understanding the performance of these materials in applications areas
including solar cells and light-emitting diodes.
