Interplay between breathing and polar instabilities in transition metal perovskites with active A-sites

Active A-site cations like Bi or Pb in ABO3 perovskites are known for their valence-skipping nature as well as for the stereochemical activities connected to lone pairs. While the former gives rise to breathing distortions in compounds like BiNiO3 or PbCrO3, the latter has been held responsible for ferroelectric, polar distortions in compounds like BiFeO3 or PbVO3. The microscopic origins of both distortions have been argued to stem from the hybridization between Bi(Pb) and O. Employing first-principles calculations, together with a variational solution of the first-principles-inspired model Hamiltonian, we investigate the interplay of two types of distortion instabilities in Bi/Pb-based transition metal perovskites. Our study reveals that in the absence of orbital degeneracy of the B site, the preference of one over the other is dictated by the relative positioning of O 2p level with respect to the A-site 6p level. Closeness of the two levels favors polar distortion over the breathing and vice versa, level positioning of O 2p being dictated by the strength of B-O hybridization.