Nanoscale size effects in $α$-FAPbI$_3$ evinced by large-scale ab initio simulations

Formamidinium-lead-iodide (FAPbI3) has a rich phase diagram, and long-range correlation between the organic cations and lattice dipoles can influence phase transitions and optoelectronic properties. System size effects are crucial for an appropriate theoretical description of FAPbI3. We perform a systematic ab initio study on the structural and electronic properties of the photoactive phase of FAPbI3 as a function of system size. To ensure an accurate theoretical description, three criteria must be satisfied: the (correct) value of the band gap, the extent (or the absence of) structural distortions, and the zeroing out of the total dipole moment. The net dipole moment vanishes as the system size increases due to PbI6 octahedra distortions rather than due to FA+ rotations. Additionally, thermal band gap fluctuations are predominantly correlated with octahedral tilting. The optimal agreement between simulation results and experimental properties for FAPbI3 is only achieved by system sizes approaching the nanoscale.