The rotational motion and electronic relaxation of the Gd(III) aqua complex in water revisited through a full proton relaxivity study of a probe solute

Recent advances in the design of fast field cycling (FFC) relaxometers make it now possible to explore the nuclear magnetic relaxation dispersion (NMRD) of semidilute nuclei with short relaxation times. The paramagnetic relaxation rate enhancement of the protons of the tetramethylammonium (CH3)4N+ cation due to the intermolecular magnetic dipolar coupling with the electronic spin S=7/2 of Gd(D2O)83+ in heavy water has been measured between 10 kHz and 800 MHz by combining FFC and standard relaxation techniques. In order to interpret the complete paramagnetic NMRD profile, particularly in the low field region, two previously neglected features are taken into account: (i) The evolution beyond the Redfield limit of the electronic relaxation of the spin S is obtained from accurate Monte Carlo simulations. (ii) The time fluctuation of the static zero field splitting (ZFS) is attributed not only to the usual global Brownian rotational diffusion of the complex, but also to the rearrangement of the water molecules in the first hydration shell of the Gd3+ ion via 90° pseudorotations Th. Kowall et al., J. Phys. Chem. 99, 13078 (1995). To calculate the longitudinal electronic relaxation function G∥(t) of the Gd3+ ion, its static and transient ZFS parameters in the aqua complex as well as the correlation times of the Brownian rotation and vibrations of this complex are needed. We use the values of these parameters derived from an independent multiple frequency and temperature study of the full electronic paramagnetic resonance spectra of Gd3+ in light water H2O, for magnetic fields where the Redfield limit applies. The predicted NMRD profile is in excellent global agreement with experiment over the whole proton frequency range, especially if the correlation times governing the rotational dynamics of the aqua complex are slightly increased to account for the higher viscosity of D2O with respect to H2O.