Anisotropy of the Chemical Shielding

In Chapter 4 we saw that chemical shielding arises primarily from induced currents in the vicinity of the nucleus but depends on the distribution of electrons within the molecule. Except for highly symmetric molecules the induced current varies with relative orientation of the molecule and the magnetic field B0 that induces the currents. As we saw in Section 4.1, the shielding tr is clearly a tensor, which can be expressed in terms of its principal components rn, cr22, and O33 along three mutually orthogonal coordinates in the molecules. The normal convention is to take 

If the molecule is in a solid, tr can also be described in terms of Cartesian space-fixed (laboratory) coordinates in which B0 is normally taken along the z axis, and it is the shielding along this axis that alters the resonance frequency. Within the secular approximation, it is only cra that contributes, and it may be related to the three principal components via their direction cosines relative to B0  

Equation 7.14 may readily be rewritten in terms of triso = / (cr, + cr22 + tr33)  

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Not only the isotropic chemical shift but also the anisotropy of the chemical shielding (CSA) tensor of the nucleus is another unique NMR parameter that could be generally measured. Such a tensor is a probe to the electron density distribution around the nucleus and provides structural information that is very difficult to obtain by other means. 

Here, ak is the isotropic chemical shift referenced in ppm from the carrier frequency co0, SkSA is the anisotropy and tfk SA the asymmetry of the chemical-shielding tensor, here also expressed in ppm. Note that for heteronuclear cases different reference frequencies co0 are chosen for different nuclei (doubly rotating frame of reference). The two Euler angles ak and pk describe the orientation of the chemical-shielding tensor with respect to the laboratory-fixed frame of reference. The anisotropy dkSA defines the width and the asymmetry t]kSA the shape of the powder line shape (see Fig. 11.1a). 

Under anisotropic conditions, NMR lineshapes for a quadrupolar nucleus are dominated by chemical shielding and (first and second order) quadrupolar interactions. Dipolar interaction is usually a minor contribution only. First-order quadrupole interaction lifts the degeneracy of the allowed 21 (i.e. seven in the case of V / = V2) Zeeman transitions as shown in Figure 3.7, giving rise to seven equidistant lines, viz. a central line (mj = + V2 -V2. unaffected by quadrupole interaction) and six satellite lines. The overall breadth of the spectrum is determined by the size of the nuclear quadrupole coupling constant Cq the deviations from axial symmetry and hence the shape of the spectral envelope are governed by the asymmetry parameter. Static solid-state NMR thus provides additional parameters, in particular the quadrupole coupling constant, which correlates with the electronic situation in a vanadium compound. [ 1 The central component reflects the anisotropy of the chemical shift. 

One potential problem with chemical shift anisotropy lineshape analysis (or indeed analysis of lineshapes arising from any nuclear spin interaction) is that the analysis results in a description of the angular reorientation of the chemical-shielding tensor during the motion, not the molecule. To convert this information into details of how the molecule moves, we need to know how the chemical-shielding tensor (or other interaction tensor) is oriented in the molecular frame. A further possible complication with the analysis is that it may not be possible to achieve an experiment temperature at which the motion is completely quenched, and thus it may not be possible to directly measure the principal values of the interaction tensor, i.e. anisotropy, asymmetry and isotropic component. If the motion is complex, lack of certainty about the input tensor parameters leads to an ambiguous lineshape analysis, with several (or even many) possible fits to the experimental data. 

These slow motions which induce a change in the orientation of the chemical shielding tensor of a particular spin can also be studied by spin echo spectroscopy [47]. The experiment consists of producing and digitizing a whole spin-echo train while simultaneously decoupling the protons in a static sample. The Fourier transform of the train gives a spectrum in which the powder pattern of the chemical shift anisotropy is split into a number... 

Up until this point, we have implicitly assumed time independence of the interactions and their corresponding Hamiltonian operators. This assumption is valid for a rigid stationary sample. However, when the sample is spun rapidly, each of the internal Hamiltonians becomes time-dependent. For example, Jfz,cs becomes time-dependent when there is chemical shielding anisotropy due to the fact that the orientations of the chemical shielding tensors relative to the applied magnetic field change as the sample... 

We describe here how the conformation of the phosphodiester backbone of DNA can be deduced from analysis of the chemical-shielding anisotropy of the nuclei and also show how the P-NMR spectral pattern is sensitive... 

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