First-principles theory of antishielding effects in the nuclear quadrupole interaction in ionic crystals: Application to /sup 57m/Fe in Fe/sub 2/O/sub 3/

A first-principles procedure is developed for the quantitative study of the widely differing Sternheimer antishielding effects that can be ascribed to the induced electric field gradients due to the various sources of electric field gradient in ionic crystals. The method involves the perturbation of the electronic states in the crystal by the nuclear quadrupole moment of the central ion, and the use of these perturbed functions in an evaluation of components of the energy of the crystal which are linear in the quadrupole moment. With each term in this energy, one can associate an induced field gradient due to a specific source in the crystal and a specific perturbation of the central-ion charge distribution. We have applied this ab initio method to a study of the nuclear quadrupole interaction for $^{57m}\mathrm{Fe}$ in ${\mathrm{Fe}}_{2}$${\mathrm{O}}_{3}$ using a model in which an ${\mathrm{Fe}}^{3+}$ ion is surrounded by six ${\mathrm{O}}^{2\ensuremath{-}}$ ligands whose charge distributions overlap the ${\mathrm{Fe}}^{3+}$ ion. The application of our procedure to the model of overlapping ions leads to the important conclusion that the field gradients due to the various sources in the central cluster and the surrounding lattice are all subject to very different antishielding effects. The sources involved can be grouped broadly into three classes: local, nonlocal, and distant, with the local sources involving charge densities purely central in character, nonlocal sources involving charge densities composed of one central-ion orbital and one ligand-ion orbital, and the distant sources involving two categories, a distant electronic one composed of charge densities from purely ligand-ion orbitals, and a distant nuclear one, comprising the nuclear charges on the ligand ions (${\mathrm{O}}^{2\ensuremath{-}}$). The effective antishielding factors ${\ensuremath{\gamma}}_{\mathrm{eff}}$ associated with these sources were found to be, respectively, -0.2, -0.7, -3.8, and -6.5, all very different from ${\ensuremath{\gamma}}_{\ensuremath{\infty}}=\ensuremath{-}9.19$ for the ${\mathrm{Fe}}^{3+}$ ion appropriate for a totally external point-charge source and $R=+0.07$, the shielding factor with the field gradient due to the $3d$ valence shell in the ${\mathrm{Fe}}^{2+}$ ion, which have both been used in the past as approximate choices for the various ${\ensuremath{\gamma}}_{\mathrm{eff}}$. The substantial differences between the various effective antishielding factors ${\ensuremath{\gamma}}_{\mathrm{eff}}$ found in the present work are explained physically by the consideration of the different degrees of penetration of the charge densities corresponding to the various sources producing the field gradients into the region of the ${\mathrm{Fe}}^{3+}$ ion. We have compared the calculated total electric field gradient at the $^{57m}\mathrm{Fe}$ nucleus in ${\mathrm{Fe}}_{2}$${\mathrm{O}}_{3}$, including the antishielding effects, with experimental M\"ossbauer data to obtain an estimate of the extent of charge-transfer covalency in this compound.