Practical route to relative diffusion coefficients and electronic relaxation rates of paramagnetic metal complexes in...

The relaxation of electronic spins S of paramagnetic species is studied by the field-dependence of the longitudinal, transverse, and longitudinal in the rotating frame relaxation rates R1, R2, and R1rho of nuclear spins I carried by dissolved probe solutes. The method rests on the model-independent low-frequency dispersions of the outer-sphere (OS) paramagnetic relaxation enhancement (PRE) of these rates due to the three-dimensional relative diffusion of the complex with respect to the probe solute. We propose simple analytical formulas to calculate these enhancements in terms of the relative diffusion coefficient D, the longitudinal electronic relaxation time T1e, and the time integral of the time correlation function of the I-S dipolar magnetic interaction. In the domain of vanishing magnetic field, these parameters can 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 parameters by combining the rates R1, R2, and R1rho. The method is illustrated by a careful study of the proton PREs of deuterated water HOD, methanol CH3OD, and tert-butyl alcohol (CH3)3COD in heavy water in the presence of a recently reported nonacoordinate Gd(III) complex. The exceptionally slow electronic relaxation of the Gd(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 nanometer scale and of the electronic spin relaxation of other complexed metal ions is discussed.