Trends in Atomic Parameters for Crystals and Free Ions across the Lanthanide Series: The Case of LaCl3:Ln(3+)

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 (SNES) has been introduced to represent the strength of the normalized electrostatic repulsion for these ions. This parameter varies linearly (R(2)adj = 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 two-particle component of the three-body operator associated with the T(2) parameter), exhibit an exponential variation with the number of electrons, n, in 4f(n). This is explained by reference to the radial part of a hydrogen-like wave function. The ratio of F(k)(corr) with the ab initio free ion Slater parameter F(k)(ab initio) varies linearly with n. Fitted parameters F(k)(corr: free ion) from the free ion data for Pr(3+) and Nd(3+) show that the corresponding ab initio values are between 14 and 27% too high. The spin-orbit coupling constant from crystal field analyses (ζ4f) exhibits a quartic variation with atomic number, and the ratio ζ4f/ζ4f(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.