Rotating-Frame Proton Cross Relaxation in the Presence of Paramagnetic Metal Ions

Rotating-frame cross relaxation for a pair of protons rotating in a spherical molecule with external relaxation is examined theoretically. The results of this study allow us to model intensities in 1D ROE and 2D ROESY spectra of protons in the presence of a paramagnetic metal ion. External relaxation moves the threshold correlation time for spin diffusion to longer times. In contrast to the effect of external relaxation on longitudinal cross relaxation (NOESY), the range of observable transverse cross relaxation (ROESY) expands with increasing external relaxation. At the same time, external relaxation compresses the overall time scale for cross-peak evolution. The initial slopes of cross-peak evolution are unaffected by external relaxation, but are sensitive to the rotational correlation time of the proton pair. Very short mixing times are necessary for accurate estimation of the initial Slopes.