The refined spin-pairing energy theory (RSPET) has been improved in order to understand quantitatively the tetrad or double-double effects recognized in the Ln
3+ ionic radii. Since the ionic radii have been determined from the lattice constants and structural parameters of LnO
1.5 and LnF
3, the lattice energies of the compounds and the enthalpy difference of Δ
Hfo(LnF
3)-Δ
Hfo(LnO
1.5) have been examined by the improved RSPET. The RSPET parameters for the lowest levels of 4
fq 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 Ln
3+ 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 Δ
Hfo(LnF
3) − Δ
Hfo(LnO
1.5) exhibit upward concave tetrad curves in their plots against
q of Ln
3+. The tetrad effect in the lattice energy of LnF
3 is less conspicuous. This means that the Racah parameters for Ln
3+ decrease very slightly in going from the gaseous free Ln
3+ to LnF
3, and then decrease greatly to LnO
1.5, in accordance with the nephelauxetic series. The differences in Racah parameters between LnF
3 and LnO
1.5 have been estimated from Δ
Hfo(LnF
3) − Δ
Hfo(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 NdF
3 and NdO
1.5. Both the tetrad effect and the smooth lanthanide contraction seen in the Ln
3+ ionic radii can be interpreted in terms of the quantum mechanical energetics of 4
f electrons.
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