Ab initio calculation of energy levels of trivalent lanthanide ionsElectronic supplementary information (ESI) available. See DOI: 10.1039/c7cp08366a - Freidzon, Alexandra Ya; Kurbatov, Ilia A; Vovna, Vitaliy I (2018)
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. A fully ab initio computational scheme employing CASSCF/XMCQDPT2/SO-CASSCF for the absorption and emission spectra of trivalent lanthanide complexes is presented.