Polarizabilities of anions in anisotropic environments the fluoride ion in the perovskite lattices NaMgF₃, KMgF₃ and KCaF₃

Coupled Hartree-Fock calculations are used to find the polarizability of the in-crystal fluoride ion in the perovskite-like compounds NaMgF₃, KMgF₃ and KCaF₃. In all three cases calculations on ion clusters embedded in idealized lattices give a mean polarizability ᾱ(F⁻) in the range 5·8 ± 0·1 au and a small negative anisotropy Δα(F⁻) (0·3% of the mean for NaMgF₃ and 4-5% for the potassium compounds). The sign of the anisotropy denotes a smaller polarizability along the direction of contact with the divalent cation. A correlated MP2 calculation for F⁻ in NaMgF₃ predicts an increase of 1·4 au in the mean and brings the fractional anisotropy up to 5%. An extended Clausius-Mossotti treatment is used to derive the analytical relationship between the dielectric constant/refractive index of a general undistorted perovskite and the effective polarizabilities of ions in the unit cell. Derived fluoride polarizabilities ᾱ(F⁻) for the three compounds fall in the range 7·1± 0·7 au.