Trends in Atomic Parameters for Crystals and Free Ions across the Lanthanide Series: The Case of LaCl3:Ln3+

Analyses of the crystal field energy levels of the series LaCl3:Ln(3+) using a semiempirical Hamiltonian shows that only five ions (Pr, Nd, Pm, Dy, Ho) meet the criteria to avoid overfitting of the atomic part. A new parameter (S-NES) has been introduced to represent the strength of the normalized electrostatic repulsion for these ions. This parameter varies linearly (R-adj(2) = 0.9994, N = 5) with the reciprocal of the radius of the tripositive lanthanide ion, as expected from the form of repulsive Coulomb interaction. The Slater parameters from the crystal field analyses, F-k(corr) (i.e., corrected for the effects of the twoparticle component of the three-body operator associated with the T-2 parameter), exhibit an exponential variation with the number of electrons, n, in 4f. This is explained by reference to the radial part of a hydrogen-like wave function. The ratio of Fk(corr) with the ab initio free ion Slater parameter F-k(ab initio) varies linearly with n. Fitted parameters Fk(corr: free ion) from the free ion data for Pr3+ and Nd3+ show that the corresponding ab initio values are between 14 and 27% too high. The spin orbit coupling constant from crystal field analyses (zeta 4f) exhibits a quartic variation with atomic number, and the ratio zeta(4f)/zeta(4f)(ab initio) follows an exponential growth model with n. The results serve to confirm the hypothesis that smooth trends can be observed across the Ln(3+) series for the fitted parameters despite the fact that the majority of experimental data is lacking.