Self-consistent calculation of energy bands in aluminum

Results of a self-consistent linear-combination-of-atomic-orbitals calculation of the band structure of aluminum are reported. The basis set consisted of nine individual Gaussian-type orbitals (GTO's) of $s$ symmetry, six GTO's for the radial part of each function of $p$ symmetry, and five for the radial part of the $d$ symmetry. This basis set is not atomic in nature. The initial Coulomb potential was constructed from the superposition of overlapping neutral-atom charge densities, the atom being in the $3s^{1}3p^2$ configuration. The exchange potential was included according to a variation on the $X\alpha$ approximation. The charge density was sampled at 89 points $(\frac{1}{48\mathrm{th}}$ of the Brillouin zone). The final self-consistent potential was then utilized to compute energy levels at 505 regularly spaced points in the irreducible zone. The results are compared with other reported band structures for the same metal. The density of states was calculated and the predicted Fermi surface was analyzed in detail. No value for the exchange parameter ($\alpha$) lying between 1 and $\frac{2}{3}$ was found to reproduce the proper connectivity of the surface unless the Fermi level is shifted artificially by a small amount.