Methyl NMR relaxation due to dipolar interactions

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Abstract
The nuclear magnetic relaxation for the three equivalent spin one‐half nuclei of a methyl group relaxed by intramolecular dipolar interactions is calculated in terms of three spin systems, the identification of each system being in terms of the symmetry representation and z‐component magnetization of the spins. Preservation of the symmetry labels of each system is accomplished through symmetrization of the spin operators. The concepts of auto and cross correlation are shown to disappear in this formalism, to be replaced by spectral densities associated with symmetry‐preserving or symmetry‐crossing transitions. The relaxation equations become particularly simple in the limits of slow motion and rapid motion for the case of a methyl group attached to a spherical molecule in solution, and these limits are presented in terms of internal and overall rotational diffusion constants.