Nuclear spin relaxation in paramagnetic systems: Electron spin relaxation effects under near-Redfield limit conditions and beyond

The analysis of experimental relaxometric profiles of paramagnetic complexes is usually performed using the Solomon-Bloembergen-Morgan (SBM) theory. The SBM theory is not valid for slowly rotating systems when the electronic levels are split at zero field, in which case a modified theory developed in Florence should be used. However, for many interesting systems, including Gd-based contrast agents for MRI, the electron spin relaxation is rather close to the Redfield limit, where none of these approaches is valid. In the present paper, the SBM theory and modified versions of the Florence model are compared against a general theory valid beyond the Redfield limit (the so-called slow-motion theory). Significant differences are found already for the cases where the electron spin relaxation is in a regime near the Redfield limit, but still within it. Indeed, the values of the parameters describing the electron spin relaxation are underestimated for the SBM theory relative to those used in calculating the slow-motion profiles. The present results are relevant for the interpretation of relaxometric profiles of paramagnetic complexes and proteins, and for the interpretation of the behavior of contrast agents used in MRI, and should be taken into account when planning the improvement of the relaxometric properties for the next generation of contrast agents based on theoretical predictions.