General treatment of paramagnetic relaxation enhancement associated with translational diffusion.
A theory of nuclear spin relaxation in isotropic liquids for nuclear spins interacting with electron spins, residing in other molecules (the outer-sphere relaxation), is presented. The approach, valid outside of the Redfield limit for electron spin relaxation, is an extension of the Swedish slow motion theory [Benetis et al., Mol. Phys. 48, 329 (1983); Nilsson and Kowalewski, J. Magn. Reson. 146, 345 (2000)] for inner-sphere relaxation. It is demonstrated that the outer-sphere relaxation rate can be expressed as an integral of a product of a translational diffusion correlation function and a function analogous to the inner-sphere spectral density. A numerical implementation of the theory is described and applied to a large number of realistic parameter sets for S = 7/2 and S = 1, which may correspond to Gd(III) and Ni(II) systems. It is shown that the outer-sphere contribution is relevant and should be included into the analysis of nuclear magnetic relaxation dispersion relaxation profiles, especially for slow relative translational diffusion and fast molecular tumbling.
Intermolecular relaxation in glycerol as revealed by field cycling 1H NMR relaxometry dilution experiments.
(1)H spin-lattice relaxation rates R(1) = 1/T(1) have been measured for partly deuterated glycerol-h(5) diluted in fully deuterated glycerol-h(0) for progressively lower concentrations of glycerol-h(5). By means of the field cycling (FC) technique relaxation dispersion data, R(1)(ω), have been collected for several temperatures in the frequency range of 10 kHz-20 MHz. In order to disclose the spectral shape of the intra- and intermolecular relaxation, extrapolation of the relaxation data to the zero concentration limit has been performed. The paper confirms that the low frequency excess contribution to the total relaxation rate R(1)(ω) previously reported for several liquids is of intermolecular origin and reflects translational motion, whereas the high-frequency part is attributed to molecular rotation. Thus, intra- and intermolecular relaxation contributions are spectrally separated. The intermolecular relaxation itself contains also a contribution from rotational motion, which is due to non-central positions of the interacting nuclei in the molecule. This eccentricity effect is quantitatively reproduced by treating the intermolecular spectral density as a sum of translational-like (described by the free diffusion model) and rotational-like contributions (described by a Cole-Davidson function). Applying frequency-temperature superposition master curves as well as individual relaxation dispersion data, R(1)(ω), are analyzed. It is demonstrated that, in spite of the rotational influence, the translational diffusion coefficients, D(T), can be extracted from the (1)H relaxation dispersion which gives (1)H NMR relaxometry the potential to become a routine technique determining the diffusion coefficient in liquids.
INTERMOLECULAR INTERACTIONS OF HIGHLY STABLE PARAMAGNETIC LANTHANIDE(III) CHELATES AS STUDIED BY NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY
Abstract The paramagnetic 13 C NMR relaxation rate enhancements and the 1 H induced chemical shifts of a series of organic molecules, caused by various paramagnetic metal complexes and a nitroxide radical (TEMPOL), were measured in aqueous solution. These NMR perturbations were used to study and model the mechanisms of their non-covalent interactions. The paramagnetic metal complexes showed a varying degree of binding specificity, in contrast to the non-specific interactions of the nitroxide radical. Weak and basically non-specific binding was observed for the neutral DTPA–bis(amide) complexes, possibly due to hydrophobic interactions, whereas the single negatively charged DOTA and DOTP–MB complexes showed weak specific interactions with ammonium functions. The strongest and most specific interactions occurred between the negatively charged Ln(DOTP) chelates and the protonated linear and macrocyclic amines. In the case of Ln(DOTP)–ADA, the 1 H induced shifts and 13 C spin-lattice relaxation rates were fitted to the theoretical equations, yielding a geometry for the adduct where the ammonium group interacts with the Ln-unbound negatively charged oxygen(s) of one phosphonate group. Two Ln(DOTP) molecules appear to be able to sandwich the diprotonated tetraazamacrocyclic amine CY. In the polyhydroxyammonium compound MEG, the strong electrostatic interaction is assisted by hydrogen bonding of hydroxyl groups to the Ln-unbound phosphonate oxygens of DOTP. A comparison of the strong pH dependences found for the paramagnetic NMR effects of the Ln(DOTP) chelates on the 1 H and 13 C nuclei of CY and MEG clearly indicated the dominance of the electrostatic interactions in both cases. Considering the organic molecules used as good models of side-chains of amino-acid residues at the surface of proteins, the observed interactions allow specific probing of protein surfaces using NMR methods.