Interplay of Octahedral Rotations and Lone Pair Ferroelectricity in CsPbF3

CsPbF3 is the only experimentally synthesized ABF3 fluoride perovskite with a polar ground state. We use CsPbF3 as a guide in our search for rules to rationally design new ABX3 polar fluorides and halides from first-principles and as a model compound to study the interactions of lone pairs, octahedral rotations, and A- and B-site driven ferroelectricity. We find that the lone pair cation on the B-site serves to stabilize a polar ground state, analogous to the role of lone pair cations on the A-site of oxide perovskites. However, we also find that the lone pair determines the pattern of nonpolar structural distortions, rotations of the PbF6 octahedra, that characterize the lowest energy structure. This result is remarkable since rotations are typically associated with bonding preferences of the A-site cation (here Cs(+)), whereas the Pb(2+) cation occupies the B site. We show that the coordination requirements of the A-site cation and the stereoactivity of the B-site lone pair cation compete or cooperate via the anionic displacements that accompany polar distortions. We consider the generalizability of our findings for CsPbF3 and how they may be extended to the oxide perovskites as well as to the organic-inorganic hybrid halide perovskite photovoltaics.