Compounds with high macroscopically- averaged symmetries and low local symmetries: The consequence of lone-pair nematicity on electronic properties

The knowledge of the appropriate unit cell for a compound is crucial for many physical studies e.g. band structure theory. Traditionally, one prefers to use the smallest cell consistent with the global symmetry, e.g. monomorphous cells containing a single structural motif. It is well known that at high temperatures local displacements have the well-known thermal origin due to dynamically thermal fluctuation. But besides thermal effects, some compounds have non-thermal intrinsic local displacements already at low temperatures (LT) due to the preference of chemical bonding for stabilizing certain low-symmetry structural motifs requiring for their representation larger than minimal unit cells. By calculating in DFT the relaxed total energies of numerous cubic phases of ABX₃ compounds (X=oxygen or halogen) we identify special cases where the energy per formula unit decreases due to atomic displacements as the cubic cell size increases. Examples include cubic CsMX₃ (M=Sn, Pb; X=Br, I), and PbMO₃ (M=Ti, Zr, Hf) etc. These intrinsic, LT polymorphous networks are interesting because their properties (band gaps, etc.,) can be very different than those gleaned from their macroscopic averaged counterparts represented as a minimal unit cell.