Bands and bonds ofB12

Using an expansion of ∼2870 plane waves, we have performed ab initio calculations of the energy bands, equilibrium lattice constants and atomic positions, and cohesive energy of ${\mathrm{B}}_{12}$. We find an indirect gap of 1.427 eV and a direct gap of 1.780 eV. The lattice constants and atomic positions are in good agreement with x-ray data, and charge-density contour plots reveal strong intraicosahedral and interplanar intericosahedral bonding but weak intraplanar intericosahedral bonding.