Electronic structure of alumina and ruby

Abstract

We report fully self-consistent local-density calculations of the energy eigenvalue spectrum, charge density, and density of states of ${\mathrm{Al}}_2$ ${\mathrm{O}}_3$ and ${\mathrm{Al}}_2$ ${\mathrm{O}}_3$:${\mathrm{Cr}}^{3+}$ using the linear combination of atomic orbitals–molecular orbital embedded-cluster discrete variational method. A variety of different clusters of formula ${\mathrm{Al}}_{\mathrm{m}}$ ${\mathrm{O}}_{\mathrm{n}}$ were treated to verify the essential independence of results on cluster size and geometry, which are in reasonable agreement with experiment and the first-principles band structure of Batra, but not in agreement with later semiempirical models. Upon substituting Cr for Al to form ruby, substantial lattice relaxation is required to produce the nearly cubic environment seen in the optical spectra. By deforming near-neighbor positions to obtain a match with experiment we obtain an estimate of the local geometry. Interaction with neighboring ${\mathrm{Al}}^{3+}$ ions is included for the first time in modeling the impurity-host interaction.