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We use density functional theory methods to study the electronic structuresof a series of $s-p$ cubic perovskites $ABX_{3}$: the experimentally availableSrBiO$_{3}$, BaBiO$_{3}$, BaSbO$_3$, CsTlF$_{3}$, and CsTlCl$_{3}$, as well asthe hypothetical MgPO$_{3}$, CaAsO$_{3}$, SrSbO$_{3}$, and RaMcO$_3$. We usetight-binding modeling to calculate the interatomic hopping integrals$t_{sp\sigma}$ between the $B-s$ and $X-p$ atomic orbitals and charge-transferenergies $\Delta$, which are the two most important parameters that determinethe low-energy electron and hole states of these systems. Our calculationselucidate several trends in $t_{sp\sigma}$ and $\Delta$ as one moves across theperiodic table, such as the relativistic energy lowering of the $B-s$ orbitalin heavy $B$ cations leading to strongly negative $\Delta$ values. Our resultsare discussed in connection with the general phase diagram for $s - p$ cubicperovskites 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 withsimilar parameters, which could lead to the discovery of new superconductors.Also, some considerations are offered regarding a possible relation between thephysical properties of a given $s - p$ compound (such as its tendency to bonddisproportionate and the maximal achievable superconducting transitiontemperature) and its electronic structure.

Holes' character and bond versus charge disproportionation in $s-p$ $ABX_{3}$ perovskites