| Abstract
| - The relaxation of electronic spins S of paramagnetic species is studied by the field-dependenceof the longitudinal, transverse, and longitudinal in the rotating frame relaxation rates R1, R2, and R1ρ ofnuclear spins I carried by dissolved probe solutes. The method rests on the model-independentlow-frequency dispersions of the outer-sphere (OS) paramagnetic relaxation enhancement (PRE) of theserates due to the three-dimensional relative diffusion of the complex with respect to the probe solute. Wepropose simple analytical formulas to calculate these enhancements in terms of the relative diffusioncoefficient D, the longitudinal electronic relaxation time T1e, and the time integral of the time correlationfunction of the I−S dipolar magnetic interaction. In the domain of vanishing magnetic field, these parameterscan be derived from the low-frequency dispersion of R1 thanks to sensitivity improvements of fast field-cycling nuclear relaxometers. At medium field, we present various approaches to obtain these parametersby combining the rates R1, R2, and R1ρ. The method is illustrated by a careful study of the proton PREs ofdeuterated water HOD, methanol CH3OD, and tert-butyl alcohol (CH3)3COD in heavy water in the presenceof a recently reported nonacoordinate Gd(III) complex. The exceptionnally slow electronic relaxation of theGd(III) spin in this complex is confirmed and used to test the accuracy of the method through the self-consistency of the low- and medium-field results. The study of molecular diffusion at a few nanometerscale and of the electronic spin relaxation of other complexed metal ions is discussed.
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