Influence of the electronic core polarization on the electric-field gradients in solids

In conventional band-structure calculations it is normally assumed that closed electronic shells have a spherically symmetric charge density. As a consequence of this approximation, these core states give no contribution to the electric-field gradient (efg) at the nuclear site. In the present paper two equivalent methods for the computation of the actual contribution of closed electron shells to the efg are presented. In the first method the potential of the nuclear quadrupole moment is considered as a perturbation for the core electrons, which causes a polarization of the core states, i.e., a deviation of the core-charge density from spherical symmetry. In this case the core contribution to the efg can be calculated with the help of the Sternheimer function {γ}(r). The second method considers the nonspherical parts of the effective crystal potential near the nucleus under consideration as a perturbation for the core electrons. These two methods yield identical results for the interaction energy of the nuclear quadrupole moment with the calculated efg. They are compared with alternative treatments of energetically high-lying core states within the framework of the full-potential linearized-augmented-plane-wave method (semicore calculations and use of local orbitals). As test cases we calculate the efg at the nearest-neighbor sites of a substitutional Ni (Fe) atom in Cu (Al) and the efg at a regular lattice site in hexagonal Mg. Additionally, results for the relaxed atomic positions, the efg, and the asymmetry parameters around a substitutional Pd (V) atom in Cu (Al) are presented.