Theoretical study of cubic structures based on fullerene carbon clusters: ${\mathrm{C}}_{28}$C and (${\mathrm{C}}_{28}$${)}_2$

We study a hypothetical form of solid carbon ${\mathrm{C}}_{28}$C, with a unit cell which is composed of the ${\mathrm{C}}_{28}$ fullerene cluster and an additional single carbon atom arranged in the zinc-blende structure. Using ab initio calculations, we show that this form of solid carbon has lower energy than hyperdiamond, the recently proposed form composed of ${\mathrm{C}}_{28}$ units in the diamond structure. To understand the bonding character of these cluster-based solids, we analyze the electronic structure of ${\mathrm{C}}_{28}$C and of hyperdiamond and compare them to the electronic states of crystalline cubic diamond.