First-principles calculation of the electronic structure of sapphire: Bulk states

The electronic structure of sapphire, α-${\mathrm{Al}}_2$ ${\mathrm{O}}_3$, was calculated using the self-consistent-field discrete variational method in the local-density framework. Clusters of the size of 26–80 atoms embedded in the infinite host lattice were used to model the sapphire single crystal. A three-dimensional Ewald summation was used to obtain the Coulomb potential of the infinite lattice. Calculations were performed on ten clusters centered at four points of different point-group symmetries in bulk sapphire. The consistency of the calculated electronic structure among these ten clusters and good agreement with experimental data and recent first-principles band-structure calculations indicate that the bulk values can be achieved with clusters of modest size. Features in the valence density of states are interpreted with the help of the bond densities between the O atom and its near neighbors. Bulk sapphire is found to be mostly ionic measured by about 2% orbital overlaps between nearest-neighbor Al and O atoms, with no charge accumulation in the bonding region.