Bond versus charge disproportionation and nature of the holes in s−p ABX3 perovskites

We use density functional theory methods to study the electronic structures of a series of $s\\text{\\ensuremath{-}}p$ cubic perovskites, $AB{X}_{3}$: the experimentally available $\\mathrm{Sr}\\mathrm{Bi}{\\mathrm{O}}_{3}, \\mathrm{Ba}\\mathrm{Bi}{\\mathrm{O}}_{3}, \\mathrm{Ba}\\mathrm{Sb}{\\mathrm{O}}_{3}, \\mathrm{Cs}\\mathrm{Tl}{\\mathrm{F}}_{3}$, and $\\mathrm{Cs}\\mathrm{Tl}{\\mathrm{Cl}}_{3}$, as well as the hypothetical $\\mathrm{Mg}{\\mathrm{PO}}_{3}, \\mathrm{Ca}\\mathrm{As}{\\mathrm{O}}_{3}, \\mathrm{Sr}\\mathrm{Sb}{\\mathrm{O}}_{3}$, and $\\mathrm{Ra}\\mathrm{Mc}{\\mathrm{O}}_{3}$. We use tight-binding modeling to calculate the interatomic hopping integrals ${t}_{sp\\ensuremath{\\sigma}}$ between the $B\\phantom{\\rule{4pt}{0ex}}s$ and $X\\phantom{\\rule{4pt}{0ex}}p$ atomic orbitals and charge-transfer energies $\\mathrm{\\ensuremath{\\Delta}}$, 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 ${t}_{sp\\ensuremath{\\sigma}}$ and $\\mathrm{\\ensuremath{\\Delta}}$ as one moves across the periodic table, such as the relativistic energy lowering of the $B\\phantom{\\rule{4pt}{0ex}}s$ orbital in heavy $B$ cations, leading to strongly negative $\\mathrm{\\ensuremath{\\Delta}}$ values. Our results are discussed in connection with the general phase diagram for $s\\text{\\ensuremath{-}}p$ cubic perovskites proposed by Khazraie et al. [Phys. Rev. B 98, 205104 (2018)], who find the parent superconductors $\\mathrm{Sr}\\mathrm{Bi}{\\mathrm{O}}_{3}$ and $\\mathrm{Ba}\\mathrm{Bi}{\\mathrm{O}}_{3}$ to be in the regime of negative $\\mathrm{\\ensuremath{\\Delta}}$ and large ${t}_{sp\\ensuremath{\\sigma}}$. Here, we explore this further and search for different 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 $s\\text{\\ensuremath{-}}p$ compound (such as its tendency to bond disproportionate and the maximal achievable superconducting transition temperature) and its electronic structure.