Comparison of chain versus sheet crystal structures for the cyanidesMCN(M=CuAu)and dicarbidesMC2(M=BeBa,ZnHg)

The cyanides $M\mathrm{C}\mathrm{N}$, $M=\mathrm{Cu},\mathrm{Ag},\mathrm{Au}$, have experimentally a structure with hexagonally packed, infinite $M\mathrm{C}\mathrm{N}M\mathrm{C}\mathrm{N}$ chains. Following our earlier study for AuCN, we now predict that all three $M\mathrm{C}\mathrm{N}$ could have an alternative ${M}_{3}{\mathrm{C}}_{3}{\mathrm{N}}_{3}$ sheet structure of comparable energy with the known one. The valence isoelectronic systems $M{\mathrm{C}}_{2}$ versus ${M}_{3}{\mathrm{C}}_{6}$, $M=\mathrm{Be}\mathrm{Ba},\mathrm{Zn}\mathrm{Hg}$, are also studied. Now, the known dicarbides have the $\mathrm{Ca}{\mathrm{C}}_{2}$ or $\mathrm{Mg}{\mathrm{C}}_{2}$ chain structures, which are well reproduced. The predicted sheets lie energetically below the chains for $M=\mathrm{Zn}$, Cd, and Hg. All these group-12 systems are experimentally unknown. Indeed, they are clearly endothermic, compared to the elements. For some sheet structures, the densities of states suggest rather small band gaps and even metallic character. When available, the experimental geometries agree well with the calculated ones.