Chemical shift of the $K_{\alpha1}$- and $K_{\alpha2}$ lines of the X-ray emission spectrum of $\mathrm{Yb}(\mathrm{II})/\mathrm{Yb}(\mathrm{III})$ fluorides: a quantum-chemical investigation

Chemical shifts of the $K_{\alpha1}$- and $K_{\alpha2}$ lines (the $2p_{3/2}\to1s_{1/2}$ and $2p_{1/2}\to1s_{1/2}$ transitions, respectively) of the X-ray emission spectrum of the $\mathrm{Yb}$ atom in fluorides have been calculated by ab initio modeling the electronic structure. The valence transition $\mathrm{Yb}(\mathrm{II})\to\mathrm{Yb}(\mathrm{III})$ has been analyzed by examples of $\mathrm{YbF}_{2}$, $\mathrm{YbF}_{3}$, and $\mathrm{Yb}_{2}\mathrm{F}_{4}$ molecules and $\mathrm{YbF}_{2}^{+}$ cation. The relativistic pseudopotential and basis sets corresponding to it have been constructed for the ytterbium atom. They were used in calculations by the two-component noncollinear version of the density functional theory (DFT) with the PBE0 exchange-correlation functional. Results for the three-coordinated $\mathrm{Yb}(\mathrm{II})$ in the $\mathrm{FYbF}_{2}\mathrm{YbF}$ dimer demonstrated a very weak dependence of the chemical shift on the coordination number of the $\mathrm{Yb}$ atom and on the molecular association of ytterbium difluoride. Chemical shifts of the X-ray emission spectrum for the ytterbium compound are related mainly to the change in the occupation of the $4f$ shell.