The Tetrad Effect

What became known as the tetrad effect was first observed in the late 1960s during lanthanide separation experiments [25]. Fig. 1.3 shows a plot of log K, where is the distribution ratio between the aqueous and organic phases in a liquid-liquid extraction system. There are four humps separated by three minima, first at the f /f pair, secondly at the f point, and thirdly at the pair. 

Calls for an explanation were answered by Jorgensen and elaborated by Nugent [26]. When a lanthanide ion moves from the aqueous to the organic phase, the nephelauxetic effect leads to a small decrease in inter-electronic repulsion within the 4f shell. This decrease varies irregularly with atomic number and is responsible for the irregularities in Fig. 1.3. 

Very often, the tetrad effect is not clearly discernible in the energies of processes in which 4f electrons are conserved. It may, for example, be obscured by irregularities caused by structural variations in either reactants or products. This is especially likely given the willingness of lanthanide ions to adopt a variety of coordination geometries. There is, however, no doubt that tetrad-like patterns are often observed. But does Table 1.2 provide a convincing explanation of what is seen  

Imagine a thoroughly convincing test of the explanation. We begin with a reaction in which the 4f electrons are conserved. In the sequence La Lu, each 

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These have been calculated from Caro s spectroscopic analyses [35]. The ligands come from opposite ends of the nephelauxetic series, so for a lanthanide reaction, A rep(irteg) should be relatively large. Even so, although it proves to be the largest contributor to the overall change, AEqs and AEso are significant Quantitative analyses of claimed examples of the tetrad effect must take such terms into account... 

It is striking that, despite its small size, the tetrad effect was discovered before the diad effect. This is because the diad effect occurs in d-electron systems and is therefore masked by the orbital stabilization energies produced by the stronger ligand field. 

Charlet, L., P. W. Schindler, L. Spadini, G. Furrer, M. Zysset, and S. M. McLennan. 1994. Rare earth element geochemistry and the tetrad effect. Geochim. Cosmochim. Acta 58 2025-2033. 

There is a similar phenomenon for trivalent actinide elements. Thus, the tetrad effect is a common characteristic of f-group elements. 

To discuss the tetrad effect quantitatively, Nugent analyzed lanthanide and actinide elements using the approximate electronic repulsive energy equation proposed by Jprgensen [15]. He suggested that the electronic repulsive energy between the electrons of the f configuration is related to the electron number q. In fact, the macro tetrad effect is a representation of the relationship between and q. 

Reprinted from Journal of Inorganic and Nuclear Chemistry, 32, L.J. Nugent, Theory of the tetrad effect in the lanthanide(III) and actinide(III) series, 3485-3491, 1970, with permission from Elsevier). 

Figure 1.16 The ground state electronic repnlsive stahilization energy 1 as a fnnction of the 4f electron nnmher q (the contribution from the F term in Eqnation 1.3, solid hne the contribntion from the term in Eqnation 1.3, dashed line) [15]. (Reprinted from Journal of Inorganic and Nuclear Chemistry, 32, L.J. Nngent, Theory of the tetrad effect in the lanthanide(lll) and actinide(lll) series, 3485-3491, 1970, with permission from Elsevier.)...

It can be seen from Table 1.7 that although increases regularly as q increases, changes periodically. The dashed line in Figure 1.16 shows the plot of versus q. Two maxima are observed at f (Nd +-Pm +) and fiO H (Ho +-Er +), respectively. This result implies that three steady states are present at f, f , and fio-n, respectively. This explains the tetrad effect because the three intersections in the tetrad effect are in the same position. However, the two maxima at and fiO H are six times smaller than the one at f. It is very difficult to observe such small stabilization energies in chemical reactions. This explains why the tetrad effect was discovered so much later than the gadolinium broken effect. 

It should be pointed out that not all the ions discussed here are affected by the outer fields. In fact, lanthanide ions may be affected by solvents or coordination fields in chemical reactions. For example, E and E will change because of the coordination effect of water or organic molecules in an extraction. In addition, the amount of change would be different in different media. The tetrad effect would thus be different in different systems. The tetrad effect not only relates to the electronic configurations of lanthanide elements but is also affected by the surrounding conditions. Currently it is still not possible to predict the tetrad effect or to calculate it quantitatively. Tetrad effect theory still needs to be improved and further data need to be accumulated. 

Soon after the appearance of the note by Peppard etal. (41) in 1969, a chemical battle brewed up as to the priority of the postulation of the tetrad effect. Fidelis and Siekierski (45) in a note maintained that We wish to point out that the tetrad effect is not a new one but has been described by us much earlier. Our first publication on this problem (46), does not report experimental data but claims ... 

It should be remarked here, that the tetrad effect is really not a new one" (our italics), and can be traced back to Endres (48) who divided the whole of the lanthanide series into four subdivisions, very much similar to those in the modern tetrad series. The paper of Fidelis and Siekierski (46) prompted Rowlands (49) to review the regularities . He plotted some 21 plots for 15 ligands and observed that the regularity proposed was based on insufficient data and this leaves doubt as to its general validity . Although the phosphoric acid systems exhibit the regularity, the same correlation could not be obtained for several other ligands. 

Jtfrgensen (55) and Nugent (56) quite independent of each other tried to provide a theoretical explanation for the tetrad effect in the lanthanide and actinide series. Both authors have emphasized the importance of the change in Racah parameter E3. 

In his theoretical treatment, Nugent (5(5) has pointed out that the relativistic spin-orbit coupling would not contribute considerably towards the tetrad effect, and he based his explanation of the tetrad theory on Russell-Saunders states for the lantha-... 

Thus it seems that more than a passing reference is appropriate as to the relation of L-quantum number and the tetrad effect, and indeed Sin ha (58) has recently shown that the L-values exhibit the same periodicity as the tetrad effect in the lanthanide (actinide) series (Fig. 6), as well as that the properties of the/-transition metal ions vary linearly within each tetrad (58). It is a great pity that Klemm did not divide the lanthanide series based on the repeatation of the total angular momentum (L-values) values (see the above table), rather he showed and supported the classification of Endres (48). 

It is not excluded that other effects may contribute to the tetrad effect. If the covalent bonding is stronger when 4fi i 5d has low excitation energy, an irregularity would be introduced by the stronger effect in Tb(III) than in Eu(III) and Gd(III) whereas the opposite [stronger effects in Sm(III) and Eu(III) than in Gd(III)] stabilization would occur if the position of the electron-transfer bands were important. No such effect has been detected with certainty in the electric polarizabilities derived from measurements of refractive indices (127, 128). Nevertheless,... 

The tetrad effect, however, should not be ignored. There is a difference between explaining chemistry by resorting to tetrads and exploiting the observed tetrad effect to efificiently separate adjacent lanthanides. Purely electrostatic bonding models form an adequate foundation for describing the solution chemistry of rare-earth cations, but intralanthanide separations are performed as a function of atomic number, not ionic radius. The variations in the intra-lanthanide separation factors that create the breaks between tetrads in fig. 14a are real and can be exploited in separations even if the immediate cause is electrostatic. 

In each of the systems found to display the tetrad effect, each of the separate curves is concave downward. Sometimes one or more of the curves is nearly straight, but no instance of upward concavity has yet been found. The plot has maxima in some systems but not in all. In a number of systems, the plot has a minimum at Gd (Z = 64). 

Some of the examples of the tetrad effect are shown in Fig. 6. The half-filled shell effect has been joined by the quarter-filled and three-quarter-filled effects. We make no attempt at explanation. 

The tetrad effect has important implications for the mutual separation of lanthanides(III), and presumably actinides(III), since in even the plots with no maximum the beginning of a tetrad differs markedly from the end of the same tetrad with respect to r, the ratio of Kz+i/Kz- In curve (A) of Fig. 6, for example, the r for the Ce-La pair is 7.8 while that for the Nd-Pr... 

McLeiman reviewed the geochemical literature on the tetrad effect and concluded that many of the cited examples could be explained as artifacts related to a variety of factors including incomplete analyses, analytical error, inappropriate choices for normalization, and complex mixing processes that resulted in apparent discontinuities. In addition, for many sample varieties (e.g., seawater, shales), the apparent effect is observed by some laboratories but not by others. The most... 

Although high-quality data can now be relatively easily obtained, there are still issnes with poor data that pass peer review and gets published, and data quality remains a lessening but still significant issue. Although there are many international standards available for comparisons (probably too many ), anomalous samples for which data quality may still be an issue (e.g., the tetrad effect) would benefit from international interlaboratory comparisons. 

The tetrad trends of Ln + hydrates are known as the tetrad effects [46, 47]. Herein, ATR-FUV spectroscopy reveals that the A X transition energies of the Ln + electrolyte solutions show a tetrad trend across the 4f period, which accounts for the ligand field splitting (LFS) of the 4f electronic states of the Ln + hydrates... 

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... 

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