The YbF₂ and YbF₃ crystals were studied within the embedded cluster model. The small core relativistic pseudopotentials for the central Yb atom (42 valence electrons) and embedding potentials for Yb and F atoms were constructed. Chemical shifts of K_α1 and K_α2 lines of X-ray emission spectra (XES) were calculated using non-variation one-center restoration technique and relativistic density functional theory (relDFT) with the hybrid exchange-correlation functional PBE0. It was done in the YbF₉Yb₁₂F₂₄ cluster simulating the YbF₃ crystal with respect to YbF₈Yb₁₂F₂₄ one representing the YbF₂ crystal. The resulting estimates are 628 meV for K_α1 and 559 meV for K_α2 and their weighted mean agrees within 10% with the experimental value, 557±27 meV. In turn, the weighted relativistic Hartree−Fock (relHF) calculation is higher on 20%. It indicates that the incorporation of electron correlation effects is essential for reproducing the K_{α1, 2} chemical shifts.

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