Ab initio calculation of energy levels of trivalent lanthanide ions

• Published in: Physical chemistry chemical physics : PCCP Vol. 20; no. 21; pp. 14564 - 14577
• Main Authors: Freidzon, Alexandra Ya, Kurbatov, Ilia A., Vovna, Vitaliy I.
• Format: Journal Article
• Language: English
• Published: England Royal Society of Chemistry 2018
• Subjects: Accuracy; Aluminum; Cerium; Emission spectra; Empirical analysis; Energy gap; Energy levels; Field theory; Group theory; Ligands; Parameterization; Perturbation theory; Yttrium; Yttrium-aluminum garnet
• DOI: 10.1039/C7CP08366A
• ISSN: 1463-9076; 1463-9084

The energy levels of Ln 3+ ions are known to be only slightly dependent on the ion environment. This allows one to predict the spectra of f–f transitions in Ln 3+ complexes using group theory and simple semiempirical models: Russell–Saunders scheme for spin–orbit coupling, ligand-field theory for the splitting of the electronic levels, and Judd–Ofelt parameterization for reproducing the intensity of f–f transitions. Nevertheless, a fully ab initio computational scheme employing no empirical parameterization and suitable for any asymmetrical environment of Ln 3+ would be instructive. Here we present such a scheme based on the multireference SA-CASSCF/XMCQPDT2/SO-CASSCF (state-averaged complete active space SCF, quasi-degenerate perturbation theory, and spin–orbit CASSCF) approach for trivalent lanthanide ions from Ce 3+ (4f 1 ) to Yb 3+ (4f 13 ). To achieve the most accurate results, we analyse the factors that influence the accuracy of the calculation: basis set size, state averaging scheme, effect of the low-spin states on the energy gap between the high-spin states ( e.g. , effect of triplets on the septet–quintet gaps in f 6 or f 8 configurations), and radial and angular correlations in the 4f shell. Our calculated energy levels agree well with the experimental values. We have shown that low-lying highest-spin and second-highest spin states are reproduced very well, while for higher-lying states the accuracy of the calculation decreases. The procedure was verified by calculating optical emission spectra of NaYF 4 :Eu,Tb; YAG:Eu,Tb; and Tb(acac) 3 bpm (bpm is 2,2′-bipyridine, acac is acetylacetonate, and YAG is yttrium aluminium garnet). For these compounds ligand-field induced electric-dipole transition intensities were calculated.