Effective axial symmetry

All complexes for which effective axial symmetry can be applied (eq. (47), see sect. 2.4.2). 

Since in the crystal structure the metallic sites are not located on the threefold axis (but on mirror planes), the rhombic term /6B%Hi in eqs. (46), (48), (49) cannot be neglected and eqs. (74), (75) hold. However, it is worth noting that the 5f ara/(5z) - vs a/(Sz)j plot for H1-H2 in [/ 3(L16-3H)2(H20)6]3+ (R = Pr-Yb except Pm and Gd) indeed gives a straight line which strongly suggest that the rotation of the cyclohexane backbone provides effective axial symmetry in solution (Chapon, 2001 Briggs et al., 1972). 

In the amorphous regions of PTFE we identify d with the time average of the local chain direction and with its instantaneous direction. Since the torsional motion about the chain axis above -68°C is such that we retain effective axial symmetry of the chemical shift with respect to the molecular chain axis, we do have the angular dependence required by condition (i) ... 

Given the uncertainties of solution studies, e.g. lack of knowledge of the exact coordination geometry and symmetry axes in complexes, progress can be made only by empirical procedures1043. We have adopted the following rules as guide-lines to those circumstances in which effective axial symmetry (see below) holds. (N.B. The assumption of axial symmetry is critical to the method.)... 

It is a matter of some concern that we do not know which ligands Y will generate effective axial symmetry in Ln(III)Y in the last part of the series while it would appear to be obtained almost invariably for Pr(III). Dobson, Delepine and Menear29) in a careful study of the complexes of a dicarboxylate ligand which has a rigid frame showed that the Ln(III) ions of the second part of the series do not give axial complexes. They come to no firm, final, conclusions as to why this is. Now it is not just the physical structural properties which are of interest. Very similar problems have arisen in the discussion of stability constants and rates of reaction of Ln(III) ions. 

Previous attempts at factoring the isotropic NMR shifts in uranocene and substituted uranocenes have assumed that these systems can be viewed as having effective axial symmetry. The temperature dependent 1h NMR spectra of uranocene and a variety of substituted uranocenes clearly verify this assumption and show that eq. 9 can be used to evaluate the pseudocontact contribution to the total isotropic shift in uranocenes. In this equation xx = Xy f°r substituted uranocenes and are replaced by Xj. ... 

Novel lanthanide fi-diketonate complexes have been synthesized, Their properties include thermal, hydrolytic and oxidative stabilities, volatility, Lewis acidity, and unusually high solubility in nonpolar organic solvents. Various combinations of these properties make lanthanide complexes useful as NMR shift reagents and fuel antiknock additives and in other applications. NMR spectral studies revealed that the Pr(III), Yb(III), and Eu(III) complexes of 1,1,1,2,2,3,3,7,7,7- decafluoro-4,6-heptanedione have sufficient Lewis acidity to induce appreciable shifts in the proton resonances of weak Lewis bases such as anisole, acetonitrile, nitromethane, and p-nitrotoluene. Data from single-crystal structure determinations indicate that the NMR shift reagent-substrate complexes are not stereochemically rigid and that effective axial symmetry may exist by virtue of rapid intramolecular rearrangements. 

In this situation of effective axial symmetry, the new proportionality constant C is related to D and Z>2 via equation (9), where a and p are the Euler angles that define the position of the effective axis with respect to the (old) principal magnetic susceptibility axis. It should be noted that equations (8) and (9) are valid as well when the rotation takes place via dissociation-association as long as the fast exchange conditions with respect to the NMR timescale are met, leading to a random variation of the axis of the susceptibility tensor of the complex. 

The pinnacle of the application of lanthanide shift reagents seemed to be in their assistance in the elucidation of the structure of molecules in solution. It must be borne in mind, however, that the intrinsic dipolar shift, 4d, due to the central lanthanide ion is the only part of the observed shift useful in this respect and then only in cases of effective axial symmetry is it readily applicable. Therefore great care should be exercised in the use of lanthanide induced shifts to solve structural problems. Generally the following types of problems may successfully be approached. 

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