First approach to the band structure ofα-rhombohedral boron

We report a calculation of the energy-band structure of $\alpha$-rhombohedral boron. The lack of theoretical studies of solid B (a technologically interesting material) can be explained by the difficulties of a quantitative calculation: twelve atoms in the cell and a very open structure. The "muffin-tin-orbitals" method for atomic spheres having a large overlap has been used. The total potential is a superposition of individual potentials of finite range, built from the atomic charge density. The Kohn-Sham exchange potential is correctly calculated using the superposition of atomic densities and then numerically fitted with a superposition of individual functions. The results show a nonmetallic behavior of $\alpha -\mathrm{B}$ with an indirect bandgap. But this agreement with experiment is not quantitative: The gap is significantly too large and the occupied band too narrow. The modifications required for improving this calculation are reviewed.