Determination of outer-sphere dipolar time correlation functions from high-field NMR measurements. Example of a Gd3+ complex in a viscous solvent

Abstract

We consider a diamagnetic species carrying a nuclear spin and having a purely outer-sphere dynamics with respect to a Gd(3+) complex. The maximal structural and dynamic information attainable from the paramagnetic relaxation (rate) enhancement (PRE) of this nuclear spin due to the Gd(3+) electronic spin is the outer-sphere dipolar time correlation function (OS-DTCF) of the relative position of these spins. We show how to determine this OS-DTCF by a model-free analysis of high-field PRE measurements, which accounts for the relative diffusion coefficient of the spin carrying species derived from pulsed-gradient spin-echo experiments. The method rests on the spectral characterization of the OS-DTCF through a PRE property, the "star" relaxivity, which can be measured over an unexpectedly large frequency range by combining multiple field and temperature NMR experiments. It is illustrated in the case of the (1)H spins on the three diamagnetic probes tert-butanol CHD(2)(CD(3))(2)COD and glycerol (CD(2)OD)(2)CHOD and CHDOD-CDOD-CD(2)OD interacting with Gddtpa(2-) (dtpa(5-)=diethylen triamin pentaacetate) in a viscous glycerol-d8/D(2)O solvent. The general usefulness of the OS-DTCF for the description of the liquid state and electronic spin relaxation is discussed.