Comparative analysis of radial expectation values in lanthanide compounds

[Display omitted] •A method is proposed for the first time for assessment of 4f of Ln3+ ions.•Seven sets of 4f arising from different 4f-wave functions are compared.•Fk(exp.) = f ( 4f2/R2k+1) has been studied in the dielectric screening model.•Lanthanide fluorides, chlorides, oxides and doped Ln3+:LaF3 have been included.•Predicted Slater integrals Fk for free ions Ln IV are compared with experiment. A method is proposed for assessment of sets of radial expectation values 〈rk〉4f of lanthanide ions (Ln3+ = Pr3+ through Tm3+) by means of the ratios 〈rk〉4f2/R2k+1 where k = 2, 4, and 6, R is the mean Ln3+ – ligand distance. These ratios have been related to experimental Slater parameters Fk in the dielectric screening model. The Fk0 values of certain free – ions Ln IV have been predicted. The compared 〈rk〉4f sets have been those known from relativistic, Hartree – Fock, and self – consistent field computations. The lanthanide compounds are elpasolites Cs2NaLnCl6, cubic sesquioxides (C-Ln2O3, C2– and C3i – sites), trifluorides LnF3, and doped Ln3+:LaF3. The results of the comparison have been discussed, as well as the factors influencing the deviations from experimental Fk0 values of the free – ions Ln IV.