ИСТИНА

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: Russel–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, and including low-spin states into the calculation of high-spin ions (e.g., triplets for septet–quintet gaps in f6 or f8 configurations). 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. We found some important factors that determine the accuracy of the calculation: (1) basis set size affects the accuracy, but Quadruple-Zeta quality is sufficient, and in some cases it can be replaced by Triple-Zeta quality set; (2) there is an optimal number of averaged states ensuring the trade-off between the need to include more states interacting with the target states and deterioration of the state-averaged wavefunction with respect to description of the target states; (3) Low-spin states interacting with the target states should be included. Calculation of optical spectra of lanthanide compounds NaYF4:Eu,Tb, YAG:Eu,Tb, and Tb(acac)3bpm showed that the calculated spectra are very sensitive not only to the nearest environment of the central ion, but to the next coordination spheres as well. At the same time, the quality of description of the ligands (e.g., polarization functions in the second coordination sphere) only slightly affect the transition intensities. The calculated spectra satisfactorily agree with the experimental data.