The ligand-field induced splitting energies of f-levels in lanthanide-containing elpasolites are derived using the first-principles universal orbital-free embedding formalism [Wesolowski and Warshel, J. Phys. Chem. 1993, 97, 8050]. In our previous work concerning chloroelpasolite lattice (Cs₂NaLnCl₆), embedded orbitals and their energies were obtained using an additional assumption concerning the localization of embedded orbitals on preselected atoms leading to rather good ligand-field parameters. In this work, the validity of the localization assumption is examined by lifting it. In variational calculations, each component of the total electron density (this of the cation and that of the ligands) spreads over the whole system. It is found that the corresponding electron densities remain localized around the cation and the ligands, respectively. The calculated splitting energies of f-orbitals in chloroelpasolites are not affected noticeably in the whole lanthanide series. The same computational procedure is used also for other elpasolite lattices (Cs₂NaLnX₆, where X=F, Br, and I)—materials which have not been fabricated or for which the ligand-field splitting parameters are not available.

Metal (4f)−ligand (Cl 3p) bonding in LnCl₆^3- (Ln = Ce to Yb) complexes has been studied on the basis of 4f→4f and Cl,3p→4f charge-transfer spectra and on the analysis of these spectra within the valence bond configuration interaction model to show that mixing of Cl 3p into the Ln 4f ligand field orbitals does not exceed 1%. Contrary to this, Kohn−Sham formalism of density functional theory using currently available approximations to the exchange-correlation functional tends to strongly overestimate 4f−3p covalency, yielding, for YbCl₆^3-, a much larger mixing of Cl 3p→4f charge transfer into the f¹³ ionic ground-state wave function. Thus, ligand field density functional theory, which was recently developed and applied with success to complexes of 3d metals in our group, yields anomalously large ligand field splittings for Ln, the discrepancy with experiment increasing from left to the right of the Ln 4f series. It is shown that eliminating artificial ligand-to-metal charge transfer in Kohn−Sham calculations by a procedure described in this work leads to energies of 4f−4f transitions in good agreement with experiment. We recall an earlier concept of Ballhausen and Dahl which describes ligand field in terms of a pseudopotential and give a thorough analysis of the contributions to the ligand field from electrostatics (crystal field) and exchange (Pauli) repulsion. The close relation of the present results with those obtained using the first-principles based and electron density dependent effective embedding potential is pointed out along with implications for applications to other systems.

Ligand field splitting energies of lanthanides Ln³⁺ (Ln = from Ce to Yb) in octahedral environment are calculated using the Hohenberg–Kohn theorems based orbital-free embedding formalism. The lanthanide cation is described at orbital level whereas its environment is represented by means of an additional term in the Kohn–Sham-like one-electron equations expressed as an explicit functional of two electron densities: that of the cation and that of the ligands. The calculated splitting energies, which are in good agreement with the ones derived from experiment, are attributed to two main factors: (i) polarization of the electron density of the ligands, and; (ii) ion–ligand Pauli repulsion.