Motivated by the recently renewed interest in the superconducting bismuth perovskites, we investigate the electronic structure of the parent compounds $A{\mathrm{BiO}}_3$ ($A=$ Sr, Ba) using ab initio methods and tight-binding (TB) modeling. We use the density functional theory (DFT) in the local density approximation (LDA) to understand the role of various interactions in shaping the $A{\mathrm{BiO}}_3$ band structure near the Fermi level. It is established that interatomic hybridization involving Bi-$6s$ and O-$2p$ orbitals plays the most important role. Based on our DFT calculations, we derive a minimal TB model and demonstrate that it can describe the properties of the band structure as a function of lattice distortions, such as the opening of a charge gap with the onset of the breathing distortion and the associated condensation of holes onto $a_{1g}$-symmetric molecular orbitals formed by the O-$2p_{\sigma }$ orbitals on collapsed octahedra. We also derive a single band model involving the hopping of an extended molecular orbital involving both Bi-$6s$ and a linear combination of six O-$2p$ orbitals which provides a very good description of the dispersion and band gaps of the low energy scale bands straddling the chemical potential.

• Received 8 November 2017
• Revised 22 January 2018

DOI:https://doi.org/10.1103/PhysRevB.97.075103