Sternheimer valence shielding and antishielding factors for some ions of interest in Mössbauer spectroscopy

Using nonrelativistic Hartree-Fock-Slater wave functions and Sternheimer's uncoupled perturbation-numerical method the valence shielding-antishielding factor $R$ including exchange has been calculated for Cr, ${\mathrm{Mn}}^{+}$, ${\mathrm{Fe}}^{2+}$, ${\mathrm{Co}}^{3+}$, ${\mathrm{Ni}}^{4+}$ (all in $3d^6$ isoelectronic configuration), ${\mathrm{Ru}}^{2+}$ ($4d^6$), ${\mathrm{Os}}^{2+}$ ($5d^6$), ${\mathrm{Pr}}^{3+}$ ($4f^2$), ${\mathrm{Tm}}^{3+}$ ($4f^{12}$), and ${\mathrm{Np}}^{6+}$ ($5f^1$) to be 0.26, 0.15, 0.12, 0.10, 0.08, -0.06, -0.12, 0.12, 0.18, and 0.01, respectively. The quadrupole splitting data on ${\mathrm{Fe}}_2$${\mathrm{O}}_3$, ${\mathrm{Al}}_2$${\mathrm{O}}_3$·${\mathrm{Fe}}^{3+}$, yttrium iron garnet ($T_d$ and $O_h$ ${\mathrm{Fe}}^{3+}$ sites), and FeSi${\mathrm{F}}_6$·6${\mathrm{H}}_2$O have been reinterpreted using more reliable values of Sternheimer shielding-antishielding factors to obtain $Q\left({}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}_{}^m{}_{}{}^{}\right)$ as 0.154, 0.179, 0.146, 0.139, and 0.156 b, respectively. The repercussions of the changes in the charge spread of the $3d^6$ ions in the crystalline lattice on $R$ have also been discussed.