Some features of the interaction of the 4fᴺ configuration of tripositive lanthanide ions (Ln³⁺) with excited configurations have been investigated. The calculated barycenter energies of the same parity 4fᴺ⁻¹6p, 4fᴺ⁺¹5p⁵, and 4fᴺ⁻¹5f configurations for Ln³⁺, relative to those of 4fᴺ, are fitted well by exponential functions. The 4fᴺ barycenter energies of Ln³⁺ in Y₃Al₅O₁₂/Ln³⁺ lie in the band gap, with the exceptions of Tb³⁺ and Yb³⁺, where they are situated in the conduction and valence bands, respectively. The configuration interaction parameters α, β, and γ, which are fitted in the usual phenomenological Hamiltonian to calculate the crystal field energies of Ln³⁺, exhibit quite variable magnitudes in the literature due to incomplete energy level data sets, energy level misassignments and fitting errors. For LaCl₃/Ln³⁺, 83% of the variation of α and 50% of that for β can be explained by the change in the difference in barycenter energy with the predominant interacting configuration. The parameter γ is strongly correlated with the Slater parameter F² and is not well-determined in most calculations. The values of the electrostatically correlated spin–other orbit parameter P² vary smoothly across the Ln³⁺ series with the barycenter difference between the 4fᴺ and 4fᴺ⁻¹5f configurations. Calculations of the Pᵏ (k = 2, 4, and 6) values for Pr³⁺ show that 4f → nf excitations only account for ∼65% of the value of P² for LaCl3/Pr³⁺ and 35% of that in Y₃Al₅O₁₂/Ln³⁺. The role of the ligand is therefore important in determining the value, and a discussion is included of the present state of configuration-interaction-assisted crystal field calculations. Further progress cannot be made in the above areas until more reliable and complete energy level data sets are available for the Ln³⁺ series of ions in crystals. Copyright © 2014 American Chemical Society.
center of gravity
crystal field theory