Coloring in the ZrBeSi-type structure

The ZrBeSi type is a superstructure variant of the aristotype AlB${}_2$ with an ordering of the beryllium and silicon atoms on the boron network. Every other layer of Be${}_3$Si${}_3$ hexagons is rotated by 60°, leading to an ABAB stacking sequence and a sandwich-like coordination of zirconium by two Be${}_3$Si${}_3$ hexagons. The ZrBeSi type shows a pronounced coloring on its three crystallographic sites. Among the numerous compounds are electron-precise Zintl phases in the field of tetrelides, pnictides and chalcogenides, selenide hydrides and fluorides as well as intermetallic compounds. A variety of element combinations leads to distinctly differing c/a ratios and different bonding patterns. Several compounds are rather isopointal than isotypic. The present work focuses on a crystal chemical description of selected ZrBeSi related compounds and the results of theoretical studies for evaluating the bonding peculiarities. From quantum theory (DFT) based investigations, the trends of charge transfer according to Bader's AIM theory have been established. These are in general agreement with the course of the electronegativities. For the prototype ZrBeSi, the main characteristics are illustrated through the electron localization function, manifesting the sp${}^2$-like planar hybridization for the silicon atoms. The site-projected densities of states PDOS of a series of compounds underline a continuous trend from metallic (e.g. ZrBeSi) to semi-conducting (e.g. LiBC) compounds in agreement with the observed electron exchanges.