Analysis of spin diffusion and cross correlation on the net nuclear Overhauser effect in NMR

The effect of dipole-dipole cross correlations on the net nuclear Overhauser effect (NOE) has been analyzed here for realistic systems by extending the three-spin calculations to four and five spins in order to account for additional cross correlations and spin diffusion. These have been compared with the addition of leakage terms to the three-spin system. The additional spins enhance cross-correlation effects on one hand but on the other act as supplementary relaxation pathways for the magnetization to diffuse. This analysis shows that for a linear array of spins in the long-correlation limit, dipole-dipole cross correlations increase net NOE, while spin diffusion decreases it, and that the cumulative effect is a reduced effect of cross correlations. In other geometries and correlation limits, the effect of cross correlations on net NOE is generally small.