Systematic analysis of spectroscopic characteristics of the lanthanide and actinide ions with the 4f^N-15d and 5f^{N -1}6d electronic configurations in a free state

Systematic consideration of the spectroscopic properties of the f ^N-1d excited electronic configurations of the di-, tri- and tetravalent lanthanide and actinide ions in a free state is presented. Variations of the Hartree-Fock calculated Slater parameters for the f ^N-1d electron configurations, spin-orbit (SO) interaction constant ζ for the f and d electrons, and averaged values of the second, fourth and sixth powers of the 4f, 5f, 5d, 6d electrons' radial coordinate across both series were considered; functional dependencies between the mentioned quantities were obtained. It has been shown that the Coulomb interaction parameters F²(ff), F⁴(ff), and F ⁶(ff) for the f^N-1 core increase linearly with the atomic number Z, whereas the direct and exchange Coulomb parameters F ²(fd), F⁴(fd), G¹(fd), G³(fd), G⁵(fd) for the f^N-1d configuration decrease linearly with Z. Since the SO interaction constant ζ^1/4 is also proportional to Z, it was possible to find linear relationships between the Coulomb interaction parameters and SO constants for the f and d electrons, which effectively reduce the number of independent parameters in the free ion Hamiltonian. The constraining relations between the free ion Hamiltonian's parameters obtained in the present paper can be used for simulations of the f-d transition spectra of these ions in various crystals.