Chemical-shift anisotropy

The first four chapters of this book make abundantly clear the power of high-resolution, liquid-state NMR. Resonance frequencies or chemical shifts are highly sensitive to the local microstructures of polymers, and their analyses lead to a detailed structural characterization. We seek comparable information concerning solid polymers, but to achieve this we must be able to observe high-resolution NMR spectra of solid samples to fully exploit the sensitivity of the magnetic resonance phenomenon to the local structural environment of the observed nucleus. 

The external applied magnetic field Bq produces electronic currents in a molecule, and these currents in turn produce local magnetic fields at the various constituent nuclei. Because the electronic environment about a nucleus is not uniform, i.e. the distribution of electrons is directionally sensitive or anisotropic, the local magnetic field experienced by a nucleus is three-dimensional, and its magnitude and molecular orientation may be described [5] by the chemical shift tensor a, given by 

The principal values of the chemical shift tensor (or, 722, 0 33) give the magnitude of the tensor 7 in three mutually perpendicular directions (Cartesian coordinates), and the As are direction cosines specifying the orientation of the molecular principal coordinate system with respect to the applied field Bq. The rapid molecular motion experienced by polymer segments in solution results in the observation of their isotropic chemical shifts, 7j, obtained by averaging the chemical shift tensor 7 over all orientations  

It is apparent from equation (5.3) that in a rigid, solid sample the chemical shift of a particular nucleus will depend on its orientation with respect to the applied field. A sample having all carbon nuclei with the same orientation, as in a single crystal, will exhibit a chemical shift that varies as the crystal is rotated in the applied magnetic field. In a powdered sample, all possible crystalline orientations are present, and the NMR spectrum will consist of the chemical shift tensor powder pattern. 

When the angle j between the axis of sample rotation and the applied magnetic field is 54.7° (the magic angle), sin jS = 2/3, 3 cos jS —1=0, and thus a = 1/3 ( 11 22 22) = isotropic chemical shift. Magic-angle spinning 

For simplicity, the spectrum in Fig. 7.8 assumes an isotropic chemical shift. As it turns out, all known alkyne sites have highly anisotropic chemical shifts which are best described by tensors. This is a nice lead-in to a discussion of chemical shift anisotropy. 

The chemical shift at a nucleus is due to the core and valence electrons near that nucleus. The bonding electrons in the axially-symmetric unit (Fig. 7.7B) 

The chemical shift anisotropy is usually described in a principal axis system, which is usually not the molecular axis system. In the principal axis system, the chemical shift tensor is diagonal. The elements of this tensor contribute to the NMR spectrum via these two equations  

In summary, orientation of R— C=C—molecules (Fig. 7.7B) chemisorbed on gold surfaces can be obtained from NMR of a stack of gold-coated glass 

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Chemical shift anisotropy (CSA) 2 Reorientation of the CSA principal axis Increases with the square of the magnetic field [13]... 

Pervushin K, Riek R, Wider G and Wuthrich K 1997 Attenuated T relaxation by mutual cancellation of dipole-dipole coupling and chemical shift anisotropy indicates an avenue to NMR structures of very... 

Tjandra N, Szabo A and Bax A 1996 Protein backbone dynamics and N-15 chemical shift anisotropy from quantitative measurement of relaxation interference effected. Am. Chem. Soc. 118 6986-91... 

Tjandra N and Bax A 1997 Solution NMR measurement of amide proton chemical shift anisotropy in N-15-enriched proteins. Correlation with hydrogen bond length J. Am. Chem. Soc. 119 8076-82... 

Chemical shift anisotropy 5.5,5 xxr yy zz Line-shape analysis MAS-sidebands Coordination symmetry... 

Figure 3 Characteristic solid state NMR line shapes, dominated by the chemical shift anisotropy. The spatial distribution of the chemical shift is assumed to be spherically symmetric (a), axially symmetric (b), and completely asymmetric (c). The top trace shows theoretical line shapes, while the bottom trace shows rear spectra influenced by broadening effects due to dipole-dipole couplings.

An Example Chemical Shift Anisotropy in Solid Vanadium Compounds... 

The measurement of correlation times in molten salts and ionic liquids has recently been reviewed [11] (for more recent references refer to Carper et al. [12]). We have measured the spin-lattice relaxation rates l/Tj and nuclear Overhauser factors p in temperature ranges in and outside the extreme narrowing region for the neat ionic liquid [BMIM][PFg], in order to observe the temperature dependence of the spectral density. Subsequently, the models for the description of the reorientation-al dynamics introduced in the theoretical section (Section 4.5.3) were fitted to the experimental relaxation data. The nuclei of the aliphatic chains can be assumed to relax only through the dipolar mechanism. This is in contrast to the aromatic nuclei, which can also relax to some extent through the chemical-shift anisotropy mechanism. The latter mechanism has to be taken into account to fit the models to the experimental relaxation data (cf [1] or [3] for more details). Preliminary results are shown in Figures 4.5-1 and 4.5-2, together with the curves for the fitted functions. 

Chemical Shift Anisotropy and Magic Angle Spinning... 

At low rotation rates, less than the chemical shifts anisotropy, however, the powder spectra contained disturbing side bands dispersed among the isotropic chemical shifts. In order to discriminate between sidebands and isotropic resonances two spectra obtained at different spinning speeds were multiplied together or the differentiation was made by visual inspection. 

From the NMR data of the polymers and low-molecular models, it was inferred that the central C—H carbons in the aliphatic chain in polymer A undergo motions which do not involve the OCH2 carbons to a great extent. At ambiet temperatures, the chemical shift anisotropy of the 0(CH2)4 carbons of polymer A are partially averaged by molecular motion and move between lattice positions at a rate which is fast compared to the methylene chemical shift interaction. 

The results also indicate that there is a significant descrease in the chemical shift anisotropy in going from the segmented polymer B (which contains very few soft segments, 0(CH2)4 to the polymer C (which contains 6 times more soft segments). The difference also seems to reflect increased molecular motion of the phenyl rings in the softer of the two segmented polymers. A similar conclusion may be drawn from the Tl-values, which for polymer B is 3 s. as oposed to 0.25 s. for the C polymer. 

The process of spin-lattice relaxation involves the transfer of magnetization between the magnetic nuclei (spins) and their environment (the lattice). The rate at which this transfer of energy occurs is the spin-lattice relaxation-rate (/ , in s ). The inverse of this quantity is the spin-lattice relaxation-time (Ti, in s), which is the experimentally determinable parameter. In principle, this energy interchange can be mediated by several different mechanisms, including dipole-dipole interactions, chemical-shift anisotropy, and spin-rotation interactions. For protons, as will be seen later, the dominant relaxation-mechanism for energy transfer is usually the intramolecular dipole-dipole interaction. 

When other relaxation mechanisms are involved, such as chemical-shift anisotropy or spin-rotation interactions, they cannot be separated by application of the foregoing relaxation theory. Then, the full density-matrix formalism should be employed. 

Figure 3 shows 13c MAS spectra of acetone-2-13c on various materials. Two isotropic peaks at 231 and 227 ppm were observed for acetone on ZnCl2 powder, and appreciable chemical shift anisotropy was reflected in the sideband patterns at 193 K. The 231 ppm peak was in complete agreement with the shift observed for acetone diffused into ZnY zeolite. A much greater shift, 245 ppm, was observed on AICI3 powder. For comparison, acetone has chemical shifts of 205 ppm in CDCI3 solution, 244 ppm in concentrated H2SO4 and 249 ppm in superacid solutions. The resonance structures 5 for acetone on metal halide salts underscore the similarity of the acetone complex to carbenium ions. The relative contributions of the two canonical forms rationalizes the dependence of the observed isotropic 13c shift on the Lewis acidity of the metal halide. 

Instead of measuring only the time-dependent dipolar interaction via NOE, it is also possible to determine dipolar couplings directly if the solute molecule is partially aligned in so-called alignment media. The most important resulting anisotropic parameters are RDCs, but residual quadrupolar couplings (RQCs), residual chemical shift anisotropy (RCSA) and pseudo-contact shifts (PCSs) can also be used for structure determination if applicable. 

In the light of what we have said above, we might expect that satellites due to platinum-element coupling would be useful in structure determination. However, because of chemical shift anisotropy they are in fact often not visible, and experience (and theory) suggest that the chance of seeing them decreases as the magnetic field of the spectrometer increases. 

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