Ligand polarizability contributions to the lanthanide crystal field

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Abstract
An independent systems model for the electrostatic crystal field of a lanthanide (III) ion in a crystalline or molecular environment is developed. The two leading multipolar interaction terms retained in the model are the lanthanide multipole-ligand net charge and lanthanide multipole-ligand dipole terms. The former interaction is the basis of the familiar point charge crystal field model. The latter interaction can be expressed in terms of a potential that depends upon the polarizability of the ligands. The combination of the point charge and polarizability crystal fields is the independent systems crystal field (ISCF). Calculations of the ISCF for Pr3+, Eu3+ and Tb3+ in the Cs2NaLnCl6 crystal system are reported. The calculations show that the point charge and polarizability components of the ISCF are of comparable magnitude. Excellent agreement between the calculated and observed crystal field coefficients is obtained for these systems.