Spin-pairing energy theory

As reviewed by Fidelis and Mioduski57) the formation constant K of a complex with a given" ligand (or the distribution coefficient for extraction in another solvent, or an ion-exchange resin) shows a ratio (in the case of two consecutive lanthanides) which provides perceptible variations (from a constant) not only at the half-filled shell (q = 7) Gd(III) but also at the plateaux q = 3 and 4, as well as 10 and 11. These quarter-shell effects can be rationalized 217,218) by the refined spin-pairing energy theory. If D of Eq. (3) is decreased 1 % (65 cm 1) by the nephelauxetic effect in a... 

Refined spin-pairing energy theory introduced by Jorgensen involves adding coefficients to 3 and spin-orbit coupling stabilization values to the lowest 7-levels by —Vi(L + 1 ) 4f for q 7 and — 1 /2Z+4f for q >7, with V as the zero-point energy and (E — A) as a parameter due to the stabilization of 4/ electrons from one element to another. For q = 1 to 14 we have the expressions for the spin-pairing... 

Though it is obvious that the decimal lacks physical significance, it is quite characteristic to find the same development (the double zig-zag curve) repeated between q = 1 and 7, and between q = 8 and 14. The almost horizontal plateaux at q = 3, 4, 5 and 10, 11, 12 are very characteristic features of the refined spin-pairing energy theory. Whereas eq. (23.22) is intended for applications to... 

A number of studies have reported a tetrad effect for the geochemical behaviour of the lanthanide series, including stability constants and distribution coefficients (Kawabe, 1992 Kawabe and Masuda, 2001 Ekberg, Englund and Persson, 2012). Kawabe and Masuda (2001) utilised refined spin-pairing energy theory (RSPET) to describe the tetrad effect on distribution coefficients. The RSPET equation is derived from the Slater-Condon-Racah theory that has been applied to free Ln " ions in a vacuum (Kawabe, 1992). As applied to the stability/solubility constants of the lanthanide metals, the RSPET equation has the form... 

Figure 8.9 Stability constants (log at 25 °C) for LnOH + Illustrating a dear tetrad effect (solid lines) and application of the refined spin-pairing energy theory to describe the constants (dashed line). Only...

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