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 LnO_1.5 and LnF₃, the lattice energies of the compounds and the enthalpy difference of ΔH_f^o(LnF₃)-ΔH_f^o(LnO_1.5) have been examined by the improved RSPET. The RSPET parameters for the lowest levels of 4f^q 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 LnO_1.5 and ΔH_f^o(LnF₃) − ΔH_f^o(LnO_1.5) 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 LnO_1.5, in accordance with the nephelauxetic series. The differences in Racah parameters between LnF₃ and LnO_1.5 have been estimated from ΔH_f^o(LnF₃) − ΔH_f^o(LnO_1.5) 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 NdO_1.5. 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.