The relative motion of a tetramethylammonium (CH3)(4)N+ ion with respect to a Gd3+ octoaqua complex, together with the quantum dynamics of the electronic spin of this lanthanide, is probed by the nuclear magnetic relaxation dispersion (NMRD) of the (CH3)(4)N+ proton spins. The measured proton resonance frequencies range between 10 and 800 MHz, A pronounced maximum is observed at around 90 MHz. This behavior is interpreted by assuming that the relative diffusion of (CH3)(4)N+ and Gd(D2O)(8)(3+) accounts for their repulsive potential of mean force, calculated with the help of the hypernetted chain approximation for two charged hard spheres in discrete, polar, and polarizable water, and by using a detailed picture of the Gd3+ electronic relaxation, based on an independent electronic paramagnetic resonance study. The standard dipolar nuclear relaxation formalism of Solomon-Bloembergen, valid for the above frequencies, leads to overall good agreement with the experimental data without any adjustable parameters. NMRD experiments using probe solutes of well-known spatial dynamics with respect to a Gd3+ complex, can be combined with the Solomon-Bloembergen theory to provide an indirect estimate of the longitudinal electronic relaxation time of this complex. This knowledge is useful in the theory of magnetic resonance imaging relaxivity.