What Factors Affect the ⁵D₀ Energy of Eu³⁺? An Investigation of Nephelauxetic Effects

Relationships involving the interelectronic repulsion parameters, <i>F</i>^<i>k</i> (<i>k</i> = 2, 4, 6), the spin–orbit coupling constant, ζ_f, and <i>J</i>-mixing, with the ⁵D₀–⁷F₀ energy, <i>E</i>, have been investigated for Eu³⁺ using various approaches. First, the linear relationship between <i>E</i> and the ⁷F₁ splitting (or the second rank crystal field parameter) is shown to be applicable not only to glasses but also to solid-state crystalline systems with Eu³⁺ site symmetry of <i>C</i>₂, <i>C</i>_2<i>v</i>, or lower. In these cases, the change in ⁵D₀–⁷F₀ energy is mainly due to the <i>J</i>-mixing effect of ⁷F_<i>J</i> (<i>J</i> = 2, 4, 6: most notably <i>J</i> = 2) which depresses ⁷F₀, whereas the ⁵D₀ energy is relatively constant. The ⁵D₀–⁷F₀ energy also depends upon certain energy parameters in the Hamiltonian, in particular, <i>F</i>^<i>k</i> and ζ_f. Model calculations show that increase in <i>F</i>⁴ or <i>F</i>⁶ produces an increase in <i>E</i>, whereas increase in <i>F</i>² produces a decrease in <i>E</i>. An increase in ζ_f produces a decrease in <i>E</i>. These findings are rationalized. Most previous 4f⁶ crystal field calculations have only considered the F and D terms of Eu³⁺ so that the Slater parameters are not well-determined. More reliable energy level data sets and crystal field calculations for Eu³⁺ with fluoride, oxide, or chloride ligands have been selected, and certain of these have been repeated since most previous calculations have errors in matrix elements. The fitted Slater parameters have been corrected for the effects of three-body Coulomb interactions. Some systems do not follow the ligand trend F ∼ O > Cl for Slater and spin–orbit parameters. From the limited data available, the average values of the corrected Slater parameters are greater for fluoride compared with chloride ligands, but the differences are comparable with the standard deviations of the parameters. There is no clear nephelauxetic series for these three types of ligands, with respect to spin–orbit coupling. Previous correlations of <i>E</i> with various parameters are of limited value because the ⁵D₀–⁷F₀ energy difference not only depends upon the <i>F</i>^<i>k</i> and ζ_f parameters but in addition is sensitive to the importance of <i>J</i>-mixing for low symmetry systems