Self-consistent calculations of the energy bands and bonding properties of ${\mathrm{B}}_{12}$${\mathrm{C}}_3$

Using a basis set of ∼3580 plane waves, we perform ab initio self-consistent calculations of the energy bands and cohesive energy of ${\mathrm{B}}_{12}$${\mathrm{C}}_3$. Calculating stresses and forces, both the lattice constants and the positions of the atoms in the unit cell are determined. If trigonal symmetry is forced (i.e., all three carbons on the chain), the cohesive energy is 108.20 eV/(unit cell). In the experimentally observed structure with one boron on each chain and one carbon on each icosahedron, the cohesive energy is 109.48 eV/(unit cell). An indirect energy gap of 2.781 eV is obtained for this structure and charge-density–contour plots indicate that the ratio of the charge on the carbons to that on the borons is much greater than the 4:3 ratio of their valences.