Quantum-mechanical description of ions in crystals: Electronic structure of magnesium oxide

Abstract

The electronic structure of the MgO crystal has been calculated with the recently reported ab initio perturbed-ion (PI) method, a scheme derived from the theory of electronic separability of multielectron systems and the ab initio model-potential approach of Huzinaga. The PI atomiclike orbitals are eigenfunctions of Fock operators that contain nuclear, Coulombic, and exchange lattice potentials plus lattice projection operators enforcing the ion-lattice orthogonality. These lattice-consistent ionic orbitals form a crystalline basis set that may be useful in a variety of applications. The PI bonding picture of MgO consists of lattice-stabilized ${\mathrm{Mg}}^{2+}$ and ${\mathrm{O}}^{2\mathrm{-}}$ ions described with well-separated wave functions. The PI electron density of ${\mathrm{Mg}}^{2+}$ is very close to the free-ion function, but that of the oxide is more contracted than the density of ${\mathrm{O}}^{2\mathrm{-}}$ in vacuo. The PI densities are tested and compared with others by computing diamagnetic susceptibilities, form factors, and the change of electronic kinetic energy upon crystal formation. The PI method also gives the bulk properties of the crystal. The predicted equilibrium geometry is 0.11 Å larger than the observed value, and the lattice binding energy is 100 kcal ${\mathrm{mol}}^{\mathrm{-}1}$ shorter. These results improve when the correlation energy is computed from the PI wave functions with the Coulomb-hole treatment of Clementi. The PI calculation including electron correlation reproduces the experimental equilibrium geometry within 0.001 Å, the bulk modulus within 1 GPa, and the binding energy within 25 kcal ${\mathrm{mol}}^{\mathrm{-}1}$. Furthermore, the computed pressure effects on the cell volume and bulk modulus of the rocksalt phase match the available experimental data up to at least 30 GPa.