The effect of molecular motion on cross relaxation in the laboratory and rotating frames

The relative sensitivity of ROESY and NOESY cross-relaxation experiments has been investigated theoretically for AX and AX₃ spin systems in various motional regimes. It is found that ROESY will be more sensitive for moderate-sized molecules. For macromolecules, the sensitivity of ROESY relative to NOESY can be strongly affected by relaxation within a group of equivalent or nearly equivalent spins, e.g., a methyl or methylene group, where the spins have either very fast or no internal motion. Cross-relaxation rates for ROESY and NOESY are shown to have different dependences on molecular motion. Equations are derived for both cross-relaxation rates under conditions of anisotropic global motion, internal motion with one degree of freedom, and anisotropic global motion plus fast internal motion. The results indicate that the measurement of both cross-relaxation rates can be used to study molecular motion or, conversely, to indicate when assumption of isotropic, rigid-body motion is inappropriate for estimation of interatomic distances.