Goesten Maarten G, Hoffmann Roald
Department of Chemistry and Chemical Biology , Cornell University , 259 East Avenue , Ithaca , New York 14853-1301 , United States.
J Am Chem Soc. 2018 Oct 10;140(40):12996-13010. doi: 10.1021/jacs.8b08038. Epub 2018 Oct 1.
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.
我们通过详细的计算以及一种基于对称性的定性键合分析，来探索金属卤化物钙钛矿ABX（其中A为阳离子，B为金属二价阳离子，X为卤化物）中的化学键和带隙。这种分析在化学和物理观点之间转换，涵盖了带隙周围15电子伏特范围内键合的各个方面。我们展示了带隙是如何由金属 - 卤化物轨道相互作用控制的，这种相互作用产生了一种特征性的能带镜像，这是一种键合标志，首次出现在计算CsPbBr能带结构时开启和关闭标量相对论效应的过程中。这种镜像是由Pb 6s和Br 4p的组合构成的，它以一种可理解的方式在布里渊区移动，确定了价带最大值。当A阳离子变为有机阳离子时，这种镜像依然存在，并且足够稳定，能够在晶格的适度畸变中持续存在。该分析预测了将Pb替换为Sn和Ge以及卤化物X的变化如何影响带隙。在同样详细地描述最低的三个导带时，出现了第二个键合镜像。对于CsPbBr，这个镜像是由Pb 6p和Br 4p的组合构成的。理解这些组合在倒易空间中移动以确定导带最小值的方式，使我们能够明白为什么带隙是直接带隙。这种轨道分析为这类热门材料中的带隙工程提供了一种化学且直观的图景。
