Axial symmetry chemical shift tensors

We have prepared a number of acylium ions on metal halide powders and measured the principal components of their chemical shift tensors (43-45). Most of these cations have isotropic l3C shifts of 154 1 ppm. Often insensitivity to substituents results from opposite and offsetting variations in the principal components. The acetylium ion has an axially symmetric chemical shift tensor because of its C3 rotation axis. When the symmetry is reduced from C3v to C2v or lower, a nonzero 27 value may be observed. The sensitivity of chemical shift tensors to symmetry is a powerful means of probing molecular structure and temperature-dependent molecular dynamics. Multiple orders of spinning sidebands may offend those who seek solution-like NMR spectra of solids, but discarding most of the information inherent in the chemical shift is a considerable concession to aesthetics. 

Fig. 10.20. Theoretical spectral patterns for NMR of solid powders. The top trace shows the example of high symmetry, or cubic site symmetry. In this case, all three chemical shift tensor components are equal in value, a, and the tensor is best represented by a sphere. This gives rise to a single, narrow peak. In the middle trace, two of the three components are equal, so the tensor is said to have axial site symmetry. This tensor is best represented by an ellipsoid and gives rise to the assymetric lineshape shown. If all three chemical shift components are of different values, then the tensor is said to have low-site symmetry. This gives rise to the broad pattern shown in the bottom trace.

The nature of the chemical shift tensor is a potential source of complications in relaxation studies. For sugar carbons, the CSAs are around 40 ppm and their contribution to relaxation of protonated carbons is nearly negligible. On the other hand, CSA values of the protonated carbons of the bases are between 120 and 180 ppm, the tensors deviate quite significantly from axial symmetry and none of their principal components is colli-near with the C-H bond. This makes interpretation of the relaxation rates in terms of molecular dynamics prohibitively complicated or, if neglected, introduces an error whose magnitude has not yet been evaluated. 

Figure 15.9. Chemical shift tensor expansion in spherical harmonics (atomic orbitals) top second-rank tensor with no special symmetry bottom axially symmetric tensor.

Figure 15.11. Hexamethylbenzene l3C spectra at various spinning speeds. The rotation of the molecule about its sixfold axis imposes axial symmetry on its chemical shift tensors. The double rotation of the methyl group (first about its own C3 axis and then about the molecular D6 axis) averages its chemical shift anisotropy to an exceedingly small value.

The chemical shift tensor in the CO molecule is anisotropic with zero asymmetry, reflecting the axial symmetry of the molecule. The isotropic shift with respect to TMS is 185 ppm, and the anisotropy in the solid is 408 ppm. There is no known carbonyl based on zerovalent Pt or Pd, but for such carbonyls of other metals the shift tensor elements change by a few tens of ppm with respect to the free molecule. In most discussions of chemisorbed CO, the orbital Knight shift is taken comparable to the isotropic shift in the corresponding carbonyls. For CO on Pt, it has been proposed to take the calculated value for a PtyCO cluster, 160 + 20 ppm [7]. 

The chemical shift anisotropies for the carbonyl and aromatic carbons of Hytrel were reconstructed from a Herzfeld-Beiger analysis (24) of the intensities of the sidebands from NMR magic angle spinning experiments. The results in Table III indicate that the carbonyl carbon chemical shift anisotropy is axially symmetric for each terephthalate ester. We attribute this axial symmetry to a general property of terephthalate esters, rather than as a consequence of molecular motion, as the highly crystalline dimethyl terephthalate also has an axially symmetric carbonyl carbon chemical shift tensor. 

Powder as well as MAS studies are available for several r/ -bonded olefins. The spans of the chemical-shift tensors are reduced with respect to the free olefins, which is discussed in terms of the Dewar-Chatt-Duncanson model of fx-donation and tt- back-bonding." " " The bond lengths and the orientations of the shielding tensor elements are available from dipolar-chemical shift methods and 2-D spin-echo experiments on the doubly labelled oleflns." " 77 -cyclopentadienyl and 77 -benzene ligands of transition-metal complexes, but also some derivatives of alkali or main-group elements," exhibit single resonances and shielding tensors of axial symmetry at room temperature. Both observations point to relatively fast rotations around the respective 5- and 6-fold local rotor axis. ... 

Mean NMR chemical shift Principal values of the chemical shift tensor Principal values of a chemical shift tensor of axial symmetry NMR chemical shift of non-acidic SiOH Extrapolated value of S Line widths (in ppm)... 

Our investigation on Py-Cd-TPP represents a special case of Cd solid state NMR studies in general. The Cd chemical shift tensor elements are axially symmetric and can be easily assigned to a molecule fixed coordinate system because of the molecular symmetry. Hence, one can envision a study with dif-... 

While it is possible for the spin-rotation mechanism to be present in the solid state, (1) can be reduced to R1=R1CSA at high magnetic fields and at moderate temperatures. Under extreme narrowing arguments, and assuming axial symmetry of the chemical shift tensor (CST), the CSA relaxation process is described by [18]... 

Slow-spinning Si NMR CPMAS solid-state NMR spectroscopy for silylium borates 28[HCBnMe5Br6] and 452[Bi2Cli2] (see Fig. 3 for an example) revealed within the limits of accuracy an almost axial symmetric Si NMR chemical shift tensor (8n = 622 > 833 and skew k close to +1) in agreement with the local molecular C3-symmetry of silylium ions 28 and 45 (see Table 3) [20, 22]. A very large anisotropy of the Si NMR chemical shift tensor is indicated by the determined span ii = 811-833. Therefore, the anisotropy of the Si chemical shift tensor is significantly larger for triarylsilylium ions than for tetrahedral... 

Fig. 2. Various possible motional states of the phosphodiester moiety of a membrane lipid and the expected ip-NMR spectra (A) static phosphodiester (B) ordered phosphodiester, rapid axial rotation (C) disordered phosphodiester, rapid axial rotation. In the case of motional averaging of the chemical-shift tensor to axial symmetry,

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