Theory of nuclear magnetic resonance line shapes for spin systems containing several quadrupolar nuclei

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Abstract
The general method of calculating the high resolution nuclear magnetic resonance band shape of a group of spin -½ nuclei scalar coupled to more than one quadrupolar nucleus is described, the 2A3X3Y case considered in detail, and computed spectra presented. The detailed treatment is carried out with the assumption that molecular reorientation is sufficiently rapid for the extreme narrowing approximation to be applicable. The relationship between the relaxation matrix method of conducting such band-shape calculations and that based upon analogy with chemical exchange is investigated and it is concluded that the latter approach is inadequate. The band shapes resulting in the limit of rapid quadrupole relaxation are discussed and it is shown that these can be understood using a theory [6] of scalar relaxation of the second kind.