Quadrupole antishielding factors and polarizabilities in ionic crystals

Using nonrelativistic Hartree-Fock-Slater wave functions and Sternheimer's perturbation-numerical method, the quadrupole antishielding factor ${\gamma }_{\infty }$ and quadrupole polarizability ${\alpha }_q$ have been calculated for 35 free ions isoelectronic with He, Ne, Ar, Kr, Xe, and Rn configurations. Assuming an additional potential due to a charged hollow sphere of Watson type around the ion in crystals, the self-consistent wave functions for 10 additional negative ions ${\mathrm{O}}^{2-}$, ${\mathrm{S}}^{2-}$, ${\mathrm{Se}}^{2-}$, ${\mathrm{Te}}^{2-}$, ${\mathrm{P}}^{3-}$, ${\mathrm{As}}^{3-}$, ${\mathrm{Sb}}^{3-}$, ${\mathrm{Si}}^{4-}$, ${\mathrm{Ge}}^{4-}$, and ${\mathrm{Sn}}^{4-}$ have been generated in order to calculate ${\gamma }_{\infty }$ and ${\alpha }_q$ for a total of 45 closed-shell ions in crystals. In the presence of the spherical potential, the negative-ion ${\gamma }_{\infty }$ and ${\alpha }_q$ values decrease while the positive-ion values increase as compared to the corresponding free-ion values, respectively. The effect of contraction of wave functions on ${\gamma }_{\infty }$ and ${\alpha }_q$ for singly and doubly negative ions has been studied as a function of the radius of the hollow sphere over a range of values around the Pauling ionic radius and in each case a satisfactory polynomial relationship has been assigned.