Knowledge Bank

An independent Systems model for the electrostatic crystal field of a lanthanide (III) ion in a crystalline or molecular environment is described. The two leading multipolar interaction terms retained in the model are the lanthanide multipole-ligand net charge and the 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 on the polarizabilities of the ligands. The combination of the point charge and polarizabililty 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. Moreover, while the point charge crystal field alone substantially underestimates the observed field, excellent agreement between the ISCF and observed crystal field coefficients is obtained for these systems.