New Analytical Expressions to Account for the Spatial Distribution of Ligand Electron Density in Crystal Field Theory on Rare-Earth Ions

Analytical expressions for contributions to crystal fields on rare-earth ions due to the spatial distribution of electron densities of f-electrons and ligands have been derived. Numerical calculations of intrinsic parameters a2(2), a2(4), and a2(6) have been carried out on the Hartree–Fock wave functions of Nd3+–O2– and of Er3+–O2– pairs. The dependencies of the extended charge contribution to intrinsic parameters on the distance between ions are compared with those which are expected in the semiempirical model of exchange charges on the rare-earth ion–ligand bond.