Systematic analysis of spectroscopic characteristics of the lanthanide and actinide ions with the 4fN and 5fN (N = 1…14) electronic configurations in a free state

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Systematic consideration of the spectroscopic properties of the di-, tri- and tetravalent lanthanide and actinide ions in a free state is presented. Variations of the Hartree–Fock calculated Slater parameters F2, F4, F6, spin–orbit interaction constant ζ and averaged values of the 4f, 5f electrons’ radial coordinate across both series were considered; functional dependencies between the mentioned quantities were obtained. It has been shown that the F2, F4, F6 parameters grow up linearly with the atomic number Z. The spin–orbit interaction constant ζ1/4 is also proportional to Z, and, therefore, to the Slater integrals as well. Moreover, the ratios F4/F2 and F6/F2 are practically constant for the isovalent ions in the considered series. The energy barycenters of all electronic configurations and the third, fourth and fifth ionization energies were all calculated. The energy barycenter moves up with increasing number of f-electrons until the f-shell becomes half-filled (7 f electrons) and then moves down. The ionization energies increase linearly with atomic number across the considered series. The established relations between F2, F4, F6 and ζ reduce the number of independent parameters in the free ion Hamiltonian and can be further applied to the case of crystal-field fitting calculations as the empirical constraints.