Ab initio calculation of energy levels of trivalent lanthanide ions

Abstract

The energy levels of Ln3+ ions are known to be only slightly dependent on the ion environment. This allows one to predict the spectra of f-f transitions in Ln3+ 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 Ln3+ 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 Ce3+ (4f1) to Yb3+ (4f13). 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 f6 or f8 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 NaYF4:Eu,Tb; YAG:Eu,Tb; and Tb(acac)3bpm (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.

Transition intensities of trivalent lanthanide ions in solids: Revisiting the Judd-Ofelt theory

“…Because the free ion has not been analyzed yet, the energies was determined by interpolation or extrapolation of known experimental values or by semiempirical calculation [35]. Table II shows a good agreement between these experimental values, our computed values and the theoretical values calculated by Freidzon and coworkers [34]. Our values are closer to the experimental ones in the 5 D manifold.…”

“…In consequence, the mixing between quintet and septet states of Eu 3+ is mainly due Table II. Comparison between the experimental, computed and other theory [34] values for the levels of 4f 6 configuration of Eu 3+ , with total angular momenta from J = 0 to 6 and energies up to 30000 cm −1 , as well as first three LS-coupling eigenvectors with their percentages. All energy values are in cm −1 .…”

Transition intensities of trivalent lanthanide ions in solids: Extending the Judd-Ofelt theory

“…Because the free ion has not been analyzed yet, the energies was determined by interpolation or extrapolation of known experimental values or by semi-empirical calculation [35]. Table 2 shows a good agreement between these experimental values, our computed values and the theoretical values calculated by Freidzon and coworkers [34]. Our values are closer to the experimental ones in the 5 D manifold.…”

“…Comparison between the experimental, computed and other theory[34] values for the levels of 4 6 configuration of Eu 3+ , with total angular momenta from = 0 to 6 and energies up to 30000 cm −1 , as well as first three LS-coupling eigenvectors with their percentages. All energy values are in cm −1 .…”

Ab-Initio Study of Circular Dichroism and Circularly Polarized Luminescence of Spin-allowed and Spin-forbidden Transitions: From Organic Ketones to Lanthanide Complexes

“…It has been shown recently that the use the CASSCF approach, with an AS containing the seven 4 orbitals, is able to recover at least some parts of the ED moments. 135,136 To obtain qualitative agreement with the experiment, one must also take into account the different mechanisms that drive the intensity of the chiroptical activity, namely the static and dynamic coupling. 27 The former corresponds to the mixing of the 4 electronic configurations with the excited configurations 4 ( −1) 5 1 in order to break the parity rule.…”