  The cyanides $M$CN, $M$=Cu, Ag, Au, have experimentally a structure with
hexagonally packed, infinite -$M$-CN-$M$-CN- chains. Following our earlier
study for AuCN, we now predict that all three $M$CN could have an alternative
$M_3$C$_3$N$_3$ sheet structure of comparable energy with the known one. The
valence isoelectronic systems $M$C$_2$ versus $M_3$C$_6$, $M$=Be-Ba; Zn-Hg are
also studied. Now, the known dicarbides have the CaC$_2$ or MgC$_2$ chain
structures. The predicted sheets lie energetically below the chains for $M$ =
Zn, Cd, and Hg. All these systems are experimentally unknown. Indeed, they are
clearly endothermic, compared to the elements. For some sheet structures the
densities of states suggests rather small band gaps and even metallic
character. When available, the experimental geometries agree well with the
calculated ones for both cyanides and dicarbides.
