Lineshape chemical shielding

Figure 1. Calculated absorption lineshapes and representative C-13 spectra for polycrystalline samples (a) an axially symmetric chemical shielding tensor (o. and

Since the intrinsic lineshape has finite width, the experimentally observed lineshape is the convolution of 1(f) with one of the lineshape functions g(f). A powder lineshape for an axially symmetric chemical shielding tensor is shown in Fig. 4 and a typical example of a general powder lineshape is shown in Fig. 5. Many systems yield lineshapes close to that of a powder pattern and the mathematical properties of these lineshapes are discussed in detail by Alexander et al.iA... 

In general, the Hamilton operator H applicable to an experimentally observed resonance is the sum (3.1.1) of operators Hx of different interactions. The lineshape, therefore, is the result of all spin interactions. For observation of just one dominant interaction, special techniques need to be applied such as isotope enrichment, homonuclear multipulse and heteronuclear high-power decoupling. Nevertheless, in C NMR, for instance, despite high-power H decoupling an overlap of chemical shielding powder spectra centred at different chemical shifts is observed in most cases without site-specific isotope enrichment. 

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. 

In many cases, not all these parameters are known for the specific spin system under investigation. Therefore, two techniques that may be employed when a lineshape simulation is desirable are (i) a simulation based on known chemical shielding tensors (a), /-coupling constants, and values, where... 

Fig. 7. The 13C powder lineshape calculated for the Cp ring hopping between chemically equivalent sites in [A1C14] [AlCp 2]+ using the 13C-shielding tensor determined from ab initio electronic structure calculations.12 The figure illustrates how the lineshape varies with the ring hopping rate k. The orientation of the principal axes of the 13C-shielding tensor determined from the ab initio calculations is shown in the inset.

Figure 16 Spectral lineshapes for powdered solids. (A) Peak doublet produced by dipole coupling between two spin 1/2 nuclei. The doublet is composed of two parts (shown dotted). They correspond to the observed proton flip occurring when its neighbor is spin up (left) or spin down (right). The indicated turning points correspond to the angle between the internuclear vector and 5b. (B) Chemical shift anisotropy pattern with shielding tensor components (Til, < 22. and (T33. (C) Combined DD and CSA spectrum. Note that this is not simply (A) -1- (B). (Reproduced with permission from Power WP and Wasylishen RE (1991) In Webb GA (ed.) Annual Reports in NMR Spectroscopy, vol. 23, p. 17. London Academic Press.)...

Shift anisotropy. If the chemical shift depends upon molecular orientation, as it does in an aromatic ring, then this will also contribute to V t) as a result of motionally induced fluctuations in the electron shielding field. The contribution increases with and typically contributes 0.02 Hz to 1/Ti, in high-field spectrometers. Again, if it arises in partially oriented molecules then it affects lineshape, this time asymmetrically. This is discussed further in chapters 5 and 7. 

In the past, this has been studied semi-quantitatively by means of NMR second moments and NMR quadrupole echoes (5,6,7). Here we show that at high temperatures ( -iyOK) and NMR lineshapes can be obtained with sharp, well-defined features, so that quadrupole coupling or nuclear shielding (chemical shift) tensor components can be measured directly to yield information on guest molecule orientation in the clathrate hydrate cages. 

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