Mirrors\nof Bonding in Metal Halide Perovskites

Abstract

We explore the chemical bonding and\nband gap in the metal halide\nperovskites ABX₃ (where A is a cation, B a metal dication,\nand X a halide) through detailed calculations and a qualitative, symmetry-based\nbonding analysis that moves between chemical and physical viewpoints,\ncovering every aspect of bonding over a range of 15 eV around the\nband gap. We show how the gap is controlled by metal–halide\norbital interactions that give rise to a characteristic mirror of\nbands, a bonding signpost which first shows up in turning on and off\nthe scalar relativistic effects in computation of the band structure\nof CsPbBr₃. The mirror is made up by a Pb <i>6s</i> and Br <i>4p</i> combination that moves in an understandable\nway through the Brillouin zone, setting the valence band maximum.\nThe mirror is also there when the A cation is changed to an organo­cation\nand is robust enough to persist through moderate distortions of the\nlattice. The analysis predicts how a modification of Pb²⁺ to Sn²⁺ and Ge²⁺ and a variation of the halide\nX influence the band gap. In describing in equal detail the lowest\nthree conduction bands, a second mirror of bonding emerges. For CsPbBr₃, this mirror is made up by Pb <i>6p</i> and Br <i>4p</i> combinations. An understanding of the way these combinations\nmove in reciprocal space to set the conduction band minimum allows\nus to see why the band gap is direct. The orbital analysis provides\na chemical and intuitive picture of band gap engineering in this popular\nclass of materials.