The coloring problem in the solid-state metal boride carbide ScB₂C₂. A theoretical analysis

The electronic properties of the layered ternary metal boride carbide ScB₂C₂, the structure of which consists of B/C layers made of fused five- and seven-membered rings alternating with scandium sheets, are analyzed. In particular, the respective positions of the B and C atoms (the so-called coloring problem) are tackled using density functional theory, quantum theory of atoms in molecules, and electron localizability indicator calculations. Results reveal that (i) the most stable coloring minimizes the number of B-B and C-C contacts and maximizes the number of boron atoms in the heptagons, (ii) the compound is metallic in character, and (iii) rather important covalent bonding occurs between the metallic sheets and the boron-carbon network.