  Some ABX3 perovskites exhibit different local environments (DLE) for the same
B atoms in the lattice, an effect referred to as disproportionation,
distinguishing such compounds from perovskites that have single local
environments (SLE). The basic phenomenology of disproportionation involves the
absence of B-atom charge ordering, the creation of different B-X bond length
for different local environments, the appearance of metal (in SLE) to insulator
(in DLE) transition, and the formation of ligand holes. We point out that this
phenomenology is common to a broad range of chemical bonding patterns in ABX3
compounds, either with s-p electron B-metal cations (BaBiO3, CsTlF3), or noble
metal cation (CsAuCl3), as well as d-electron cations (SmNiO3, CaFeO3). We show
that underlying much of this phenomenology is the self-regulating response,
whereby in strongly bonded metal-ligand systems with high lying ligand
orbitals, the system protects itself from creating highly charged cations by
transferring ligand electrons to the metal, thus preserving a nearly constant
metal charge in DLE, while creating B-ligand bond alternation and ligand-like
conduction band (ligand hole). We are asking what are the minimal theory
ingredients needed to explain the main features of this SLE-to-DLE
phenomenology, such as its energetic driving force, bond length changes,
possible modifications in charge density and density of state changes. Using as
a guide the lowering of the total energy in DLE relative to SLE, we show that
density functional calculations describe this phenomenology across the whole
chemical bonding range without resort to special strong correlation effects,
beyond what DFT naturally contains. In particular, lower total energy
configurations (DLE) naturally develop bond alternation, gaping of the metallic
SLE state, and absence of charge ordering with ligand hole formation.
