Density-Functional Description of Bond Disproportionation in ABO₃ Compounds Into Different Local Environments for the Same B Chemical Element

Some ABO₃ oxides can contain an identical B element observed to exist in two different local environments (LE). Traditionally, the two B atoms were designated by different formal oxidation states (FOS) (sometimes called Charge Ordering) such as Bi³⁺ and Bi⁵⁺ in the case of Ba₂Bi₂O₆. Close examination shows that the physical charge around such atoms, calculated by DFT, is almost identical, as the ligands conspire to change their hybridization to maintain nearly constant charge —the self-regulating response (Raebiger, Lany and Zunger Nature 453, 763, 2008). Such bond disproportionation—identical elements appearing in the solid with different LE at constant charge, while opening a band gap (metal-nonmetal transition) and concomitantly lowering the total energy—is described via DFT as energy-lowering broken symmetry. We demonstrate this via DFT calculations in CsTlF₃, SmNiO₃, CaFeO₃, PbCoO₃ and Ba₂Nb₅O₁₅, comparing total energies, geometries and total charge distributions. Although FOS are commonly used to understand and explain these compounds, we will show that the actual physical property that changes is not the atomic charges, but the local structural environment.