Half second-order quadrupolar broadening

For the half-integer quadrupolar nuclei, the sateUite transitions (STs) are severely broadened by the first-order quadrupolar interaction to such an extent that they are often very difficult to observe. The CT, on the other hand, is not affected by the quadrupolar interaction to the first-order and is observable in most cases. But it is broadened by the second-order quadrupolar interaction. Figure 1.1 A illustrates the effect of r/q on the second-order line shape of the CT in static spectra. 

There is a redeeming instance that often makes partial spectra of quadrupolar nuclei observable. For odd-half integral nuclei, such as 23Na (7=2), the mz = to m. = -2 transition is not affected by the quadrupolar interaction to first order and remains relatively sharp, while the satellite transitions, such as mz = to mz = 2 and m. = —2 to mz = -2, are broadened by the powder distribution. There is a substantial second-order effect of the quadrupole coupling that broadens even the central transition, but this broadening is often only a few kilohertz to a few tens of kilohertz—large but much smaller than Megahertz. 

As an example, quadrupole nutation NMR of nuclei with half-integer quadrupolar spin in zeolitic materials can distinguish between nuclei of the same chemical element subjected to different quadrupole interactions, the signals of which overlap in conventional spectra. The situation is favourable for half-integer quadrupolar spins since the m=l/2 <-> m= -1/2 transition for these nuclei is broadened by the quadrupole interaction only in second-order perturbation theory. The technique can be usefully applied for the determination of the local environment of A1 in zeolitic catalysts (28). It allows discrimination between species of similar chemical shift but different quadrupolar coupling constants (see Figure 5). The main difficulty in the interpretation is the complex spectmm that results from a nutation experiment since it can consist of many overlapping powder patterns (29). 

In the last two equations the upper line is for the hetero- and the lower line for the homonuclear case. There are two specialities for quadrupolar nuclei (I> 1/2) (i) for strong quadrupolar interactions there are additional non-diagonal terms in the quadrupolar Hamiltonian which influence the spectra (ii) for half-integer quadrupolar nuclei, there exists a central transition (—1/2<-> +1/2) which is only in second order influenced by the quadrupolar interaction and thus an important observable for the chemical characterization of these nuclei. Details of these second order broadening are beyond the scope of this review and can be found for example in the recent reviews by Jerschow or Wimperis et alP ... 

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