Axially symmetric chemical-shift tensor, powder

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. 1. Powder line shapes for an anisotropic chemical shift (a) arbitrary chemical shift tensor (tr, a22 <733).

Figure 1 Solid-state NMR powder patterns, dominated by chemical shift anisotropy effects (a) spherically symmetric chemical shift tensor, (b) axially symmetric chemical shift tensor, (c) asymmetric chemical shift tensor. Top traces theoretical powder patterns bottom traces powder patterns broadened by other anisotropic interactions or chemical shift distribution effects.

Fig. 8.6. The powder line shapes of an axially symmetric chemical-shift tensor. (Reproduced with permission from Ref. [26]. 1984 Pergamon Press, Inc.)...

Two theoretical [6] chemical shift tensor powder patterns are illustrated in Figure 5.4(a),(b). Principal values 022 and <733 are indicated, and their isotropic averages, o-j, are given as dotted lines. In the axially symmetric case (b), (7 and are the resonant frequencies observed when the principal-axis system is aligned and J. to the applied field. Molecular motion will narrow... 

Figure 5.4 Schematic chemical shift tensor powder pattern for an axially asymmetric (a) and axially symmetric (b) tensor. The isotropic chemical shift values

Chemical shift spectra of PTFE obtained at 259° are shown in Figure 1. These lineshapes, for three different samples of varying crystallinity, may be seen to be a linear combination of two lineshapes one is characteristic of an axially symmetric powder pattern and the other of an isotropic chemical shift tensor. At this temperature these two lineshapes differ greatly and may be numerically decomposed. 

Figure 3.2.10 Schematic representation of theoretical powder line shapes for the chemical-shift tensor, (a) - asymmetric shift anisotropy, (b) axially symmetric shift anisotropy.

Figure 7-16 and 7-17) [71]. This rotation averages both of the chemical shift and quadrupolar interactions, such that the NMR powder pattern becomes axially symmetrical (t)q = X]q = 0), the principal axes of the chemical shift tensor and quadrupolar tensor coincide, and the Cq value decreases from 4.7 MHz in the crystalline P2 phase to 1.7 MHz in the liquid crystalline region (Figure 7-15 and Table 7-3). 

Thus the chemical shift will have the same value for the field anywhere in the 2-3 plane but a different value when the field is perpendicular to the plane the chemical-shift tensor is axially symmetric. The chemical shift expected when the field is parallel to the unique axis is labeled a, whereas that expected for the field perpendicular to this axis is Figure 2B demonstrates this averaging and the resultant powder spectrum. Note the characteristic shape vwth the buildup of intensity at <7x- Both a, and individual components of the powder line shape (Seelig, 1978). 

This term is anisotropic and produces a powder pattern. It has been derived under the assumptions that first-order perturbation of the S-states is sufficient, that the J tensor is axially symmetric and that the unique axis of J is aligned with the intemuclear vector. Under MAS this term will be scaled but, as it is not proportional to P2(cos0), it cannot be completely removed. Hence the MAS spectrum will still have some residual width, but the most profound effect is to leave an isotropic term which can be calculated by averaging the powder lineshape. Hence for a J-coupled system with an axially symmetric quadrupole interaction, the spectrum is shifted from the isotropic chemical shift by ... 

Chemical-shift anisotropy is very sensitive to molecular structure and dynamics. Each nucleus can be pictured as being surrounded by an ellipsoidal chemical-shift field, A, arising from the influences of neighboring spins, as described by Eq. (4). If the molecules in the sample have no preferred orientational order, these tensors will be randomly distributed, and the line-shape is predictable. If the shielding is equivalent in all directions = (5yy = zi, A is spherical), a symmetric peak, like shown that in Fig. 29a, will be observed at qjso, which is defined in Eq. (5). Axial symmetry = Gyy A is, more or less, football-shaped) results in a powder pattern like that shown in Fig. 29b. In this case, the tensor elements may be labeled CTy ) and (g x and Gj ). If there is no symmetry in the chemical-shift field (gxx is a flattened football), then the... 

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