Lanthanide tetrad effect in the Ln3+ ionic radii and refined spin-pairing energy theory

TLDR: In this paper, the refined spin-pairing energy theory (RSPET) has been improved in order to understand quantitatively the tetrad or double-double effects recognized in the Ln3+ ionic radii.

Abstract: The refined spin-pairing energy theory (RSPET) has been improved in order to understand quantitatively the tetrad or double-double effects recognized in the Ln3+ ionic radii. Since the ionic radii have been determined from the lattice constants and structural parameters of LnO1.5 and LnF3, the lattice energies of the compounds and the enthalpy difference of ΔHfo(LnF3)-ΔHfo(LnO1.5) have been examined by the improved RSPET. The RSPET parameters for the lowest levels of 4fq electronic configurations strongly depend upon the effective nuclear charge (Z*). Such effects due to Z* have been taken into account. This made it possible to separate the variations in the lattice energies and the enthalpy difference across the Ln3+ series into the following two parts: (1) the large variation as a smooth function of q (the lanthanide contraction trend), and (2) the small zig-zag variation referred to the tetrad or double-double effect. The lattice energy of LnO1.5 and ΔHfo(LnF3) − ΔHfo(LnO1.5) exhibit upward concave tetrad curves in their plots against q of Ln3+. The tetrad effect in the lattice energy of LnF3 is less conspicuous. This means that the Racah parameters for Ln3+ decrease very slightly in going from the gaseous free Ln3+ to LnF3, and then decrease greatly to LnO1.5, in accordance with the nephelauxetic series. The differences in Racah parameters between LnF3 and LnO1.5 have been estimated from ΔHfo(LnF3) − ΔHfo(LnO1.5) by means of an inversion technique based on the improved RSPET. The RSPET results for the thermochemical data are consistent with the careful spectroscopic determinations of Racah parameters for NdF3 and NdO1.5. Both the tetrad effect and the smooth lanthanide contraction seen in the Ln3+ ionic radii can be interpreted in terms of the quantum mechanical energetics of 4f electrons.