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We use density functional theory methods to study the electronic structures of a series of $s-p$ cubic perovskites $ABX_{3}$: the experimentally available SrBiO$_{3}$, BaBiO$_{3}$, BaSbO$_3$, CsTlF$_{3}$, and CsTlCl$_{3}$, as well as the hypothetical MgPO$_{3}$, CaAsO$_{3}$, SrSbO$_{3}$, and RaMcO$_3$. We use tight-binding modeling to calculate the interatomic hopping integrals $t_{sp\sigma}$ between the $B-s$ and $X-p$ atomic orbitals and charge-transfer energies $\Delta$, which are the two most important parameters that determine the low-energy electron and hole states of these systems. Our calculations elucidate several trends in $t_{sp\sigma}$ and $\Delta$ as one moves across the periodic table, such as the relativistic energy lowering of the $B-s$ orbital in heavy $B$ cations leading to strongly negative $\Delta$ values. Our results are discussed in connection with the general phase diagram for $s - p$ cubic perovskites proposed in Ref. 26, where the parent superconductors SrBiO$_{3}$ and BaBiO$_{3}$ are found to be in the regime of negative $\Delta$ and large $t_{sp\sigma}$. Here, we explore this further and search for new materials with similar parameters, which could lead to the discovery of new superconductors. Also, some considerations are offered regarding a possible relation between the physical properties of a given $s - p$ compound (such as its tendency to bond disproportionate and the maximal achievable superconducting transition temperature) and its electronic structure., Comment: 7 pages, 5 figures

We develop a theory describing a parameter based phase diagram to be associated with materials incorporating skipped valence ions\cite{Varma}. We use a recently developed tight-binding approach for the bismuthates to study the phase diagram exhibiting the crossover from a bond disproportionated (BD) to a charge disproportionated (CD) system in addition to the presence of a new metallic phase. We argue that three parameters determine the underlying physics of the BD-CD crossover when electron correlation effects are small: the hybridization between O-2$p_{\sigma}$ and Bi-6$s$ orbitals ($t_{sp\sigma}$), the charge-transfer energy between Bi-6$s$ and O-a$_{1g}$ molecular orbitals ($\Delta$), and the width of the oxygen sublattice band ($W$). In the BD system, we estimate an effective attractive interaction $U$ between holes on the same O-a$_{1g}$ molecular orbital. Although here we concentrate on the example of the bismuthates, the basic ideas can be directly transferred to other perovskites with negative charge-transfer energy, like ReNiO$_{3}$ (Re: rare-earth element), Ca(Sr)FeO$_{3}$, CsTIF$_{3}$ and CsTlCl$_{3}$., Comment: 4 pages, 3 figures

Motivated by the recently renewed interest in the superconducting bismuth perovskites, we investigate the electronic structure of the parent compounds ABiO$_{3}$ (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 ABiO$_{3}$ bandstructure 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 bandstructure 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., Comment: 9 pages, 4 figures

We propose a microscopic description of the bond-disproportionated insulating state in the bismuth perovskites $X$BiO$_3$ ($X$=Ba, Sr) that recognizes the bismuth-oxygen hybridization as a dominant energy scale. It is demonstrated using electronic structure methods that the breathing distortion is accompanied by spatial condensation of hole pairs into local, molecular-like orbitals of the $A_{1g}$ symmetry composed of O-$2p_{\sigma}$ and Bi-$6s$ atomic orbitals of collapsed BiO$_6$ octahedra. Primary importance of oxygen $p$-states is thus revealed, in contrast to a popular picture of a purely ionic Bi$^{3+}$/Bi$^{5+}$ charge-disproportionation. Octahedra tilting is shown to enhance the breathing instability by means of a non-uniform band-narrowing. We argue that formation of localized states upon breathing distortion is, to a large extent, a property of the oxygen sublattice and expect similar hybridization effects in other perovskites involving formally high oxidation state cations., Comment: 5 pages, 4 figures