Mirrors of Bonding in Metal Halide Perovskites.

We explore the chemical bonding and band gap in the metal halide perovskites ABX (where A is a cation, B a metal dication, and X a halide) through detailed calculations and a qualitative, symmetry-based bonding analysis that moves between chemical and physical viewpoints, covering every aspect of bonding over a range of 15 eV around the band gap. We show how the gap is controlled by metal-halide orbital interactions that give rise to a characteristic mirror of bands, a bonding signpost which first shows up in turning on and off the scalar relativistic effects in computation of the band structure of CsPbBr. The mirror is made up by a Pb 6s and Br 4p combination that moves in an understandable way through the Brillouin zone, setting the valence band maximum. The mirror is also there when the A cation is changed to an organocation and is robust enough to persist through moderate distortions of the lattice. The analysis predicts how a modification of Pb to Sn and Ge and a variation of the halide X influence the band gap. In describing in equal detail the lowest three conduction bands, a second mirror of bonding emerges. For CsPbBr, this mirror is made up by Pb 6p and Br 4p combinations. An understanding of the way these combinations move in reciprocal space to set the conduction band minimum allows us to see why the band gap is direct. The orbital analysis provides a chemical and intuitive picture of band gap engineering in this popular class of materials.