Nuclear Overhauser Effects and 13C Relaxation Times in 13C–{H} Double Resonance Spectra

The effect of proton decoupling upon carbon‐13 magnetic resonance spectra is treated in detail with the Solomon formulation for multiply irradiated spin systems. The factors affecting the nuclear Overhauser enhancement are discussed in terms of competition between the dipole–dipole relaxation mechanism essential to the Overhauser effect and other relaxation processes. Using a density matrix formulation, it is exhibited that the maximum Overhauser effect (achieved when the dipolar mechanism dominates) is independent of the number of hydrogen atoms interacting with a relaxing carbon‐13 nucleus. On the other hand, if the molecular tumbling motion is isotropic and the dipole–dipole mechanism dominates the relaxation process, then to a first approximation $T_1$ can be shown to depend inversely upon the number of directly bonded hydrogen atoms. Expressions for treating an AMX three‐spin system are given also, and the effect of the third spin is discussed. The highly symmetric adamantane molecule provides an excellent test case for the validity of the theoretical conclusions as it is an isotropic tumbler because of the rigidity and its tetrahedral symmetry. Furthermore, it has two nonequivalent carbon positions having different numbers of hydrogen atoms. The experimental Overhauser enhancement was found to be the same for both carbons and the $T_1\text{'}\mathrm{s}$ for these two carbons, measured with the adiabatic rapid passage technique, reflected the two‐to‐one factor expected for CH and CH₂ groups, respectively. Minor deviations are explained with small contributions from vicinal hydrogens. Having exhibited the validity of the theoretical treatment for adamantane, it becomes evident that exceptions may be interpreted in terms of deviations from isotropic tumbling motion. As most molecules lack the symmetry to be isotropic in rotational diffusional processes, this experimental technique offers an important way for studying anisotropic molecular motion in liquids.