On the polarizabilities of the doubly charged ions of group IIB

Abstract

New values are derived for the polarizabilities of the group IIB cations Zn⁺⁺, Cd⁺⁺ and Hg⁺⁺. Ab initio electronic structure computations show the polarizabilities of isolated Zn⁺⁺ and Cd⁺⁺ ions to be enhanced considerably by electron correlation, the best current polarizabilities being 2·83 au and 5·42 au. Analysis of experimental refractive index data for both aqueous solutions at infinite dilution and solid crystalline difluorides yields in-solution Zn⁺⁺, Cd⁺⁺ and Hg⁺⁺ polarizabilities of 4·02 au, 7·50 au and 15·40 au compared with values 4·72 au and 6·42 au for Zn⁺⁺ and Cd⁺⁺ in solid ZnF₂ and CdF₂. Ab initio computations also show the increases in the Zn⁺⁺ and Cd⁺⁺ polarizabilities in the condensed phase to originate from the mechanisms enhancing the polarizability of Ag⁺ in solid AgF. The increases predicted when Zn⁺⁺ and Cd⁺⁺ enter a point charge lattice originate from the component of the lattice potential which lifts the degeneracy of the free ion d orbitals. Location of these cations at the centre of an octahedron or cube of helium atoms modelling overlap with neighbouring anions also increases these cation polarizabilities. These enhancements are greater in octahedral than in cubic coordination because the environments of the e_g and t_2g d orbitals differ more in the former. The approximately octahedral coordination of Cd⁺⁺ in solution compared with its cubic coordination in solid CdF₂ explains why this cation polarizability is greater in solution than in the solid difluoride. The Zn⁺⁺ ion is octahedrally coordinated in both these environments, having a larger polarizability in the latter where it interacts more strongly with its surroundings. The total molar polarizability of solid CdO cannot be explained as a sum of contributions from individual ions having reasonable values for their polarizabilities.