Tolerance Factor and Cation–Anion Orbital Interactions Differentiating the Polar and Antiferrodistortive Structures of Perovskite Oxides AB O 3

We explored under what conditions perovskite oxides ABO 3 adopt a polar or an antiferrodistortive structure from the viewpoint of the tolerance factor τ and the orbital interactions of the empty orbitals of the A and B cations with the filled orbitals of their surrounding O 2– ions. Polar structures require the presence of a substantial size‐mismatch as well as strong cation‐anion orbital interactions at A or B cation sites. A tetragonal polar structure is preferred when the A cation empty orbitals are extended or when the B‐cation empty orbitals are contracted. A trigonal polar structure is favored in opposite cases. An antiferrodistortive structure is found for perovskites with weak size‐mismatch or those with substantial size‐mismatch if both A and B cations do not generate strong cation‐anion orbital interactions. Antiferrodistortive structures result from interactions involving the A cations with the O 4 squares of the face‐sharing A O 8 square‐prisms in a two‐in‐two‐out manner, and are found only when the A/O cation‐anion interactions are substantial.