What use are crystal field parameters? A chemist's viewpoint

Although first principles methods are gaining interest, the crystal field model is at present the only practicable model to analyze and simulate the energy level structures of lanthanide ions (Ln³⁺) in crystal hosts at the accuracy level of ∼10 cm^-1. Three criteria are suggested to assess the use of energy parameters, especially crystal field parameters, from the crystal field parametrization of 4f^N energy level data sets for the entire lanthanide ion (Ln³⁺) series, except Pm³⁺. Systematic analyses have been performed upon the most complete energy level data sets available for Ln³⁺ situated at sites of high symmetry in crystals of Cs₂NaLnCl₆. This presents a stringent test for theory because the number of energy parameters is considerably reduced, and the data sets are representative and fairly complete. The results from these data set fittings are shown to comply with the three criteria put forward. First, the fittings of data sets are accurate, and a predictive capability has been employed to calculate the energy levels of Pm³⁺ and to elucidate and list all of the potentially luminescent levels of Ln³⁺ in the hexachloroelpasolite hosts. Second, the systematic and smooth variations of parameter values over the lanthanide series have been described by simple equations and rationalized. Third, a physical insight of the crystal field parameter variation across this series of elements has been achieved by utilizing a simple semiquantitative model considering the distributions of the 4f radial wave functions at the edge of the Ln³⁺ ions, where the ligand orbitals extend. The parameter trends for an individual Ln³⁺ ion have been shown to be consistent also for the Cs₂NaLnF ₆ host lattice, and predictions of the individual crystal field parameter values are made. © 2010 American Chemical Society.