Relaxation of long-lived modes in NMR of deuterated methyl groups

Long-lived imbalances of spin state populations can circumvent fast quadrupolar relaxation by reducing effective longitudinal relaxation rates by about an order of magnitude. This opens new avenues for the study of dynamic processes in deuterated molecules. Here we present an analysis of the relaxation properties of deuterated methyl groups CD₃. The number of coupled equations that describe cross-relaxation between the 27 symmetry-adapted spin states of a D₃ system can be reduced to only 2 non-trivial "lumped modes" by (i) taking the sums of the populations of all states that equilibrate rapidly within each irreducible representation of the symmetry group, and (ii) by combining populations that have similar relaxation rates although they belong to different irreducible representations. The quadrupolar relaxation rates of the spin state imbalances in CD₃ groups are determined not by the correlation time of overall tumbling of the molecule, but by the frequency of jumps of methyl groups about their three-fold symmetry axis. We access these states via dissolution dynamic nuclear polarization (D-DNP), a method that allows one to populate the desired long-lived states at cryogenic temperatures and their subsequent detection at ambient temperatures after rapid dissolution. Experimental examples of DMSO-d₆ and ethanol-d₆ demonstrate that long-lived deuterium spin states are indeed accessible and that their lifetimes can be determined. Our analysis of the system via "lumped" modes allows us to visualize different possible spin-state populations of symmetry A, B, or E. Thus, we identify a long-lived spin state involving all three deuterons in a CD₃ group as an A/E imbalance that can be populated through DNP at low temperatures.