13C–{1H} nuclear Overhauser enhancement and 13C spin lattice relaxation in molecules undergoing multiple internal rotations

The effects of multiple internal rotations on the 13C–{1H} nuclear Overhauser enhancement (NOE) and 13C spin lattice relaxation has been considered. It is shown that the 5×5 matrices which arise from a treatment using the Wigner rotation matrices of order 2 can be replaced by 3×3 matrices by making use of the inherent symmetry of the problem without any loss of generality. The cross correlations which arise in chains of methylene carbons are also taken into account. Calculations are given for the NOE values for carbons in a methylene chain for several values of the internal diffusion coefficients Di, assumed constant along the chain, as a function of D0. It is found that the effect of cross correlations on the NOE values is relatively small except in the region where the isotropic diffusion coefficient of the end of the chain satisfies the condition 6D0∼ωc. In this region the effect of cross correlations depends on the internal diffusion coefficient Di, being insignificant for Di=109 sec−1 and somewhat more important for Di=1010 and 1011 sec−1. The spin lattice relaxation is also most markedly nonexponential in the region where 6D0∼ωc. As D0 increases or decreases beyond this value the relaxation becomes more exponential. The effect of the isotropic D0 motion on both the NOE and the spin lattice relaxation decreases rapidly for carbons further from the isotropically tumbling end of the molecule. An example involving a galactolipid phospholipid suspension is briefly discussed.