Quadrupole antishielding factors and polarizabilities in ionic crystals

Abstract

Using nonrelativistic Hartree-Fock-Slater wave functions and Sternheimer's perturbation-numerical method, the quadrupole antishielding factor ${\ensuremath{\gamma}}_{\ensuremath{\infty}}$ and quadrupole polarizability ${\ensuremath{\alpha}}_{q}$ 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 ${\mathrm{O}}^{2\ensuremath{-}}$, ${\mathrm{S}}^{2\ensuremath{-}}$, ${\mathrm{Se}}^{2\ensuremath{-}}$, ${\mathrm{Te}}^{2\ensuremath{-}}$, ${\mathrm{P}}^{3\ensuremath{-}}$, ${\mathrm{As}}^{3\ensuremath{-}}$, ${\mathrm{Sb}}^{3\ensuremath{-}}$, ${\mathrm{Si}}^{4\ensuremath{-}}$, ${\mathrm{Ge}}^{4\ensuremath{-}}$, and ${\mathrm{Sn}}^{4\ensuremath{-}}$ have been generated in order to calculate ${\ensuremath{\gamma}}_{\ensuremath{\infty}}$ and ${\ensuremath{\alpha}}_{q}$ for a total of 45 closed-shell ions in crystals. In the presence of the spherical potential, the negative-ion ${\ensuremath{\gamma}}_{\ensuremath{\infty}}$ and ${\ensuremath{\alpha}}_{q}$ 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 ${\ensuremath{\gamma}}_{\ensuremath{\infty}}$ and ${\ensuremath{\alpha}}_{q}$ 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.