Quadrupole coupling lineshapes

The difference between the Markov model lineshapes and those from the Smoluchowski model is particularly pronounced when the diffusion coefficient is of the order of the quadrupole coupling constant. In the limit of large diffusion coefficients, the two models converge, and in the limit of low diffusion coefficients, the spectra are dominated by small-amplitude oscillations within potential wells, which can be approximately modelled by a suitable Markov model. This work strongly suggests that there could well be cases where analysis of powder pattern lineshapes with a Markov model leads to a fit between experimental and simulated spectra but where the fit model does not necessarily describe the true dynamics in the system. 

In some cases, when a spin-1/2 nucleus such as P, or is coupled to a quadrupolar nucleus, the simulation by a computer program of the unusual lineshape of the spin-1/2 may provide information about the chemical shift anisotropy, the quadrupole coupling constant and the indirect scalar spin-spin coupling constant involving the metal atom. This method has been applied to the P spectra of phosphines bound to cobalt in heteronuclear clusters [17]. 

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. 

Fig. 29. Calculated central transition spectra48 for a single spin-3/2 nucleus undergoing (a) four-site tetrahedral jumps and (b) 12-site icosahedral jumps between equally populated sites in each case. The motional correlation times are given in the figure in seconds for each lineshape. The quadrupole coupling constant (axially symmetric) used in the simulations was 3 MHz.

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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