Linewidths in High-Resolution NMR Spectra of Coupled Nuclear Systems. Broadening Mechanisms Induced by Molecular Reorientation

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Abstract
The perturbation theory of energy‐level widths in coupled nuclear systems is applied to the relaxation processes activated by molecular reorientation, i.e., to the dipolar relaxation, the quadrupolar relaxation, the relaxation due to the chemical shift anisotropy, the intermolecular relaxation, and the relaxation due to the spin–rotation interaction. The relaxation processes are divided into two groups with respect to their behavior under rotations of molecular coordinates; the first three are of tensor character while the last two are of vector character. For each of the two groups a theory is developed based on the properties of normed spherical operators. This sheds some new light on the two previously studied cases, i.e., the dipolar relaxation and the intermolecular relaxation, and leads to the solutions of the other cases. The theory of the quadrupolar relaxation is documented by two simple examples. It turns out that in the case of molecules containing quadrupolar nuclei useful information about the molecular structure can be obtained from the linewidth patterns. The same also holds, of course, for the other relaxation processes provided they lead to experimentally accessible effects. Explicit formulas are given for the cross‐term contributions due to simultaneous action of two different relaxation mechanisms.