Nephelauxetic Effects in the Electronic Spectra of Pr³⁺

Abstract

The well-known nephelauxetic series of ligands describes the change in interelectronic repulsion of the central metal ion, which is reduced on going from the vapor to crystalline state. This study examines the trends and quantifies the mechanism of this series for the lanthanide ion Pr(3+), with the 4f(2) electronic configuration. A new and concise measurement by a single parameter, σee, is introduced to quantify the overall strength of interelectronic repulsion, as the alternative to the Slater parameters, F(k) (k = 2, 4, 6). Energy parameters have been derived from the literature electronic spectra of Pr(3+), in the free ion and in various crystalline hosts, with new calculations in some cases. It is found that at least the first 12 of the 13 multiplet terms of Pr(3+) must be well-determined to obtain reliable parameter values. The shifts of various energy levels for changes in the Slater parameters are not uniform in direction. For the various Pr(3+) solid-state systems, the change in σee is only up to ∼5%, with the magnitude of σee in the order F(-) > Cl(-) > O(2-) ≈ Br(-) > C, and decreasing with lower coordination number of the ligand. The decreases of the Slater parameters from the free ion values are reasonably estimated by considering the dielectric constant of the medium. In particular, the magnitude of σee (and of the spin-orbit coupling constant) is proportional to the polarizability of the ligand for F(-), Cl(-), O(2-), and Br(-). The data point scatter for oxide systems is accounted for by considering the individual ligand bond distances. A fair estimation of nephelauxetic effects can be made from some luminescence transition energies, by contrast with Eu(3+) systems where crystal field effects also play a major role. In conclusion, the nephelauxetic effect of Pr(3+) is due to the polarization of the ligand by one 4f electron, and the interaction of the other electron with the induced multipolar moments, of which the dipole moment dominates.

BonnMag: Computer program for ligand‐field analysis of f n systems within the angular overlap model

“…The nephelauxetic ratio β describes the ratio F 2 (ion in complex)/ F 2 (free ion). The nephelauxetic effect is quite small for f n systems . The spin‐orbit coupling constant ζ undergoes a similar reduction as the SCS parameters in comparison to the free ion values.…”

The 4f n energy levels shift due to the van der Waals interaction in the Ln 3+ containing luminescent materials

“…(c) Energy of the 3 P 1 level as a function of the 3 P 0 level in crystals [14]. (d) Energy of the 1 D 2 level as a function of 3 P 1 level in crystals [18]. The energies for all energy levels are shown here with respect to the ground state.…”

Trends in Atomic Parameters for Crystals and Free Ions across the Lanthanide Series: The Case of LaCl3:Ln3+

“…The orthonomalized Racah parameters Êi and the normalization constants N i have been defined in eqs 4−8 of ref 8. The average standard deviation of all energy levels σ ee is given by eq 10 of ref 8 and is related to S NES by the following equation…”

“…8 The definition of σ ee demonstrates that it represents the spread of the energy levels, but at the same time, it depends on the number of energy levels. More precisely speaking, it depends on the atomic structure of the 4f-electron configuration (angular part of the Hamiltonian) in addition to the strength of the electrostatic repulsion (radial part of the Hamiltonian).…”