Lattice summation of multipole interaction energies in crystals. Calculation of the outer-sphere contribution to the crystal-field splitting in nickel(II) oxide

Abstract

The Bertaut method for calculating the lattice energy of an ionic crystal is extended to include multipole–multipole interactions. Equations are obtained for the electrostatic-interaction energy of compact multipolar ions or molecules of any symmetry in a crystal of arbitrary structure, and their application is illustrated using α-N₂, K[HF₂], and Pb[NO₃]₂ as examples. The method is used to estimate the contribution to the ligand-field splitting Δ in NiO from outside the first co-ordination sphere; the interaction between cation multipoles is too small to account forobserved differences between spectroscopic and thermochemical estimates of Δ.