Local diffusion in paramagnetic solutions by NMR relaxometry at one frequency

The relative diffusion coefficient D of a paramagnetic species and a diamagnetic probe molecule bearing nuclear spins is obtained from their measured relaxation times T1 and T2 (or T1rho). This is achieved by introducing the longitudinal relaxivity, r1, a linear expression of 1/T1, and the mixed relaxivity, rmix, a linear expression of 1/T1 and 1/T2 (or 1/T1rho). Under weak assumptions, D is proportional to (rmix - r1) to the power -2/3 and to rmix to the power -1, with easy-to-determine proportionality factors. The method is noninvasive and easy to use on standard NMR spectrometers and imagers. It is validated through the study of various solutions of a Gd(III)-based contrast agent for magnetic resonance imaging.     

Intermolecular nuclear relaxation in paramagnetic solutions: from free radicals to rare earths

The principles of the intermolecular relaxation of a nuclear spin by its fluctuating magnetic dipolar interactions with the electronic spins of the paramagnetic surrounding species in solution are briefly recalled. It is shown that a very high dynamic nuclear polarization (DNP) of solvent protons is obtained by saturating allowed transitions of free radicals with a hyperfine structure, and that this effect can be used in efficient Earth field magnetometers. Recent work on trivalent lanthanide Ln³⁺ aqua complexes in heavy water solutions is discussed, including paramagnetic shift and relaxation rate measurements of the ¹H NMR lines of probe solutes. This allows a determination of the effective electronic magnetic moments of the various Ln³⁺ ions in these complexes, and an estimation of their longitudinal and transverse electronic relaxation times T_1e and T_2e. Particular attention is given to Gd(III) hydrated chelates which can serve as contrast agents in magnetic resonance imaging (MRI). The full experimental electronic paramagnetic resonance (EPR) spectra of these complexes can be interpreted within the Redfield relaxation theory. Monte-Carlo simulations are used to explore situations beyond the validity of the Redfield approximation. For each Gd(III) complex, the EPR study leads to an accurate prediction of T_1e, which can be also derived from an independent relaxation dispersion study of the protons of the probe solutes.     

Electronic relaxation of paramagnetic metal ions and NMR relaxivity in solution: critical analysis of various approaches and application to a Gd(III)-based contrast agent

The time correlation functions (TCFs) G(alphaalpha(t)[triple bond](Salpha(t)Salpha(0)) (alpha = x,y,z) of the electronic spin components of a complexed paramagnetic metal ion give information about the time fluctuations of its zero-field splitting (ZFS) Hamiltonian due to the random dynamics of the coordination polyhedron. These TCFs reflect the electronic spin relaxation which plays an essential role in the inner- and outer-sphere paramagnetic relaxation enhancements of the various nuclear spins in solution. When a static ZFS Hamiltonian is allowed by symmetry, its modulation by the random rotational motion of the complex has a great influence on the TCFs. We discuss several attempts to describe this mechanism and show that subtle mathematical pitfalls should be avoided in order to obtain a theoretical framework, within which reliable adjustable parameters can be fitted through the interpretation of nuclear-magnetic relaxation dispersion experimental results. We underline the advantage of the numerical simulation of the TCFs, which avoids the above difficulties and allows one to include the effect of the transient ZFS for all the relative magnitudes of the various terms in the electron-spin Hamiltonian and arbitrary correlation times. This method is applied for various values of the magnetic field taken to be along the z direction. At low field, contrary to previous theoretical expectations, if the transient ZFS has negligible influence, the longitudinal TCF GII(t) [triple bond] G(zz)(t) has a monoexponential decay with an electronic relaxation time T1e different from 1/(2D(r)), D(r) being the rotational diffusion coefficient of the complex. At intermediate and high field, the simulation results show that GII (t) still has a monoexponential decay with a characteristic time T1e, which is surprisingly well approximated by a simple analytical expression derived from the Redfield perturbation approximation of the time-independent Zeeman Hamiltonian, even in the case of a strong ZFS where this approximation is expected to fail. These results are illustrated for spins S = 1, 3/2, and 5/2 in axial and rhombic symmetries. Finally, the simulation method is applied to the reinterpretation of the water-proton relaxivity profile due to P760-Gd(III), an efficient blood pool contrast agent for magnetic-resonance imaging.     

Model-free nuclear magnetic resonance study of intermolecular free energy landscapes in liquids with paramagnetic Ln3+ spotlights: theory and application to Arg-Gly-Asp

We propose an easily applicable method for investigating the pair distribution function of a lanthanide Ln(3+) complex LnL (L = ligand) with respect to any solvent or solute molecule A carrying observable nuclear spins. Let r be the distance of Ln(3+) to the observed nuclear spin I. We derive a simple expression of the experimental value of the configurational average of 1/r(6) in terms of longitudinal paramagnetic relaxation (rate) enhancements (PREs) of the spin I measured on a standard high-resolution NMR spectrometer and due to well-chosen concentrations of LnL complexes in which Ln(3+) is a fast-relaxing paramagnetic lanthanide or the slowly-relaxing gadolinium Gd(3+). The derivation is justified in the general case of a molecule A which is by turns in a bound state where it follows the complex and a free state where it moves independently. It rests on the expression of the underlying PRE theory in terms of the angle-dependent pair distribution function of LnL and A. The simplifications of this theory in the high-field regime and under the condition of fast exchange between bound and free states are carefully discussed. We also show that original information on the angle dependence of the molecular pair distribution function can be gained from the measured paramagnetic dipolar shifts induced by complexed fast-relaxing Ln(3+) ions. The method is illustrated by the case study of the anionic Lnttha(3-) = [Ln(3+)(ttha)](3-) (ttha(6-) = triethylene tetraamine hexacetate) complex interacting with the biologically important tripeptide Arg-Gly-Asp (RGD) which carries peripheral ionic groups. The usefulness of an auxiliary reference outer sphere probe solute is emphasized.     

Determination of the rate of a fast exchanging coordinated molecule in a lanthanide(III) complex by proton NMR

An elementary procedure is proposed and applied to study the exchange rate of a solvent or solute molecule bound to a complexed paramagnetic Ln(III) ion, other than Gd(III), from the measured longitudinal and transverse relaxation rates and paramagnetic resonance frequency shift at a given temperature.     

NMR paramagnetic relaxation due to the S=5/2 complex, Fe(III)-(tetra-p-sulfonatophenyl)porphyrin: central role of the tetragonal fourth-order zero-field splitting interaction

The metalloporphyrins, Me-TSPP [Me=Cr(III), Mn(III), Mn(II), Fe(III), and TSPP=meso-(tetra-p-sulfonatophenyl)porphyrin], which possess electron spins S=3/2, 2, 5/2, and 5/2, respectively, comprise an important series of model systems for mechanistic studies of NMR paramagnetic relaxation enhancement (NMR-PRE). For these S>1/2 spin systems, the NMR-PRE depends critically on the detailed form of the zero-field splitting (zfs) tensor. We report the results of experimental and theoretical studies of the NMR relaxation mechanism associated with Fe(III)-TSPP, a spin 5/2 complex for which the overall zfs is relatively large (D approximately = 10 cm(-1)). A comparison of experimental data with spin dynamics simulations shows that the primary determinant of the shape of the magnetic relaxation dispersion profile of the water proton R1 is the tetragonal fourth-order component of the zfs tensor. The relaxation mechanism, which has not previously been described, is a consequence of zfs-induced mixing of the spin eigenfunctions of adjacent Kramers doublets. We have also investigated the magnetic-field dependence of electron-spin relaxation for S=5/2 in the presence of a large zfs, such as occurs in Fe(III)-TSPP. Calculations show that field dependence of this kind is suppressed in the vicinity of the zfs limit, in agreement with observation.     

Water Exchange and Rotational Dynamics of the Dimeric Gadolinium(III) Complex [BO{Gd(DO3A)(H(2)O)}(2)]: A Variable-Temperature and -Pressure (17)O NMR Study(1)

Rapid water exchange and slow rotation are essential for high relaxivity MRI contrast agents. A variable-temperature and -pressure (17)O NMR study at 14.1, 9.4, and 1.4 T has been performed on the dimeric BO(DO3A)(2), 2,11-dihydroxy-4,9-dioxa-1,12-bis[1,4,7,10-tetraaza-4,7,10-tris(carboxymethyl)cyclododecyl]dodecane, complex of Gd(III). This complex is of relevance to MRI as an attempt to gain higher (1)H relaxivity by slowing down the rotation of the molecule compared to monomeric Gd(III) complexes used as contrast agents. From the (17)O NMR longitudinal and transverse relaxation rates and chemical shifts we determined the parameters characterizing water exchange kinetics and the rotational motion of the complex, both of which influence (1)H relaxivity. The rate constant and the activation enthalpy for the water exchange, k(ex) and DeltaH(), are (1.0 +/- 0.1) x 10(6) s(-)(1)and (30.0 +/- 0.2) kJ mol(-)(1), respectively, and the activation volume, DeltaV(), of the process is (+0.5 +/- 0.2) cm(3) mol(-)(1), indicating an interchange mechanism. The rotational correlation time becomes about three times longer compared to monomeric Gd(III) polyamino-polyacetate complexes studied so far: tau(R) = (250 +/- 5) ps, which results in an enhanced proton relaxivity by raising the correlation time for the paramagnetic interaction.     

An NMR experiment for the accurate measurement of heteronuclear spin-lock relaxation rates

Rotating-frame relaxation rates, R(1)(rho), are often measured in NMR studies of protein dynamics. We show here that large systematic errors can be introduced into measured values of heteronuclear R(1)(rho) rates using schemes which are usually employed to suppress cross-correlation between dipole-dipole and CSA relaxation mechanisms. For example, in a scalar-coupled two-spin X-H spin system the use of (1)H WALTZ16 decoupling or (1)H pulses applied at regularly spaced intervals leads to a significant overestimation of heteronuclear R(1)(rho) values. The problem is studied experimentally and theoretically for (15)N-(1)H and (13)C-(1)H spin pairs, and simple schemes are described which eliminate the artifacts. The approaches suggested are essential replacements of existing methodology if accurate dynamics parameters are to be extracted from spin-lock relaxation data sets.     

Structure and magnetism in Fe-Gd based dinuclear and chain systems. The interplay of weak exchange coupling and zero field splitting effects

The synthesis and characterization of two Fe-Gd systems based on bpca(-) (Hbpca = bis(2-pyridilcarbonyl)amine) as bridging ligand is presented, taking the systems as a case study for structure-property correlations. Compound 1, [Fe(LS)(II)(μ-bpca)(2)Gd(NO(3))(2)(H(2)O)]NO(3)·2CH(3)NO(2), is a zigzag polymer, incorporating the diamagnetic low spin Fe(LS)(II) ion. The magnetism of 1 is entirely determined by the weak zero field splitting (ZFS) effect on the Gd(III) ion. Compound 2 is a Fe(III)-Gd(III) dinuclear compound, [Fe(LS)(III)(bpca)(μ-bpca)Gd(NO(3))(4)]·4CH(3)NO(2)·CH(3)OH, its magnetism being interpreted as due to the antiferromagnetic coupling between the S(Fe) = ? and S(Gd) = 7/2 spins, interplayed with the local ZFS on the lanthanide center. In both systems, the d-f assembly is determined by the bridging capabilities of the ambidentate bpca(-) ligand, which binds the d ion by a tridentate moiety with nitrogen donors and the f center by the diketonate side. We propose a spin delocalization and polarization mechanism that rationalizes the factors leading to the antiferromagnetic d-f coupling. Although conceived for compound 2, the scheme can be proposed as a general mechanism. The rationalization of the weak ZFS effects on Gd(III) by multiconfiguration and spin-orbit ab initio calculations allowed us to determine the details of the small but still significant anisotropy of Gd(III) ion in the coordination sites of compounds 1 and 2. The outlined methodologies and generalized conclusions shed new light on the field of gadolinium coordination magnetochemistry.     

Paramagnetic NMR relaxation in polymeric matrixes: sensitivity enhancement and selective suppression of embedded species (1H and 13C PSR filter)

A study of the practical applications of the addition of paramagnetic spin relaxation (PSR) ions to a variety of polymers (PLL, PAA, PGA, PVP, and polysaccharides such as hyaluronic acid, chitosan, mannan, and dextran) in solution (D2O and DMSO-d6) is described. Use of Gd(III), Cu(II), and Mn(II) allows a reduction of up to 500% in the 1H longitudinal relaxation times (T1), and so in the time necessary for recording quantitative NMR spectra (sensitivity enhancement) neither an increase of the spectral line width nor chemical shift changes resulted from addition of any of the PSR agents tested. Selective suppression of the 1H and 13C NMR signals of certain components (low MW molecules and polymers) in the spectrum of a mixture was attained thanks to their different sensitivity [transverse relaxation times (T2)] to Gd(III) (PSR filter). Illustration of this strategy with block copolymers (PGA-g-PEG) and mixtures of polymers and low MW molecules (i.e., lactose-hyaluronic acid, dextran-PAA, PVP-glutamic acid) in 1D and 2D NMR experiments (COSY and HMQC) is presented. In those mixtures where PSR and CPMG filters alone failed in the suppression of certain components (i.e., PVP-mannan-hyaluronic acid) due to their similarity of 1H T2 values and sensitivities to Gd(III), use of the PSR filter in combination with CPMG sequences (PSR-CPMG filter) successfully resulted in the sequential suppression of the components (hyaluronic acid first and then mannan).     

Synthesis,Relaxivity and MRI Enhancement of Linear Oligo‐Gd(III) Complexes with Poly (DTPA‐ester) Ligands Derived from Amino Acids

Six linear oligo‐DTPA‐ester Gd(III) complexes being used for potential MRI contrast agents were synthesized from amino adds and characterized. Their longitudinal relaxation rates were measured. One of them, die phenylalanine derivative, with high relaxivity, was chosen for the acute toxicity and T₁,‐weighted imaging test. The results indicated that there was no obvious toxicity for this new oligomeric Gd(III) complex, and it exhibits the highly enhanced MRI signal intensity and the increasing signal duration in the liver tissue compared to Gd‐DTPA.     

Relationship between the longitudinal relaxation rates of water protons and of well defined paramagnetic centers at low temperature in hydrated vermiculite

A good agreement has been observed between the proton longitudinal relaxation rate in the two and one layer hydrate of the Na-Llano vermiculite, the location of the Fe³⁺ paramagnetic centers within the octahedral and tetrahedral layers of the lattice and the electronic longitudinal relaxation rate using the dipolar electronic—proton spin interaction. The water content influences noticeably the electronic longitudinal relaxation time.     

Bis‐Gadolinium Complexes for Solid Effect and Cross Effect Dynamic Nuclear Polarization

High‐spin complexes act as polarizing agents (PAs) for dynamic nuclear polarization (DNP) in solid‐state NMR spectroscopy and feature promising aspects towards biomolecular DNP. We present a study on bis(Gd‐chelate)s which enable cross effect (CE) DNP owing to spatial confinement of two dipolar‐coupled electron spins. Their well‐defined Gd⋅⋅⋅Gd distances in the range of 1.2–3.4 nm allowed us to elucidate the Gd⋅⋅⋅Gd distance dependence of the DNP mechanism and NMR signal enhancement. We found that Gd⋅⋅⋅Gd distances above 2.1 nm result in solid effect DNP while distances between 1.2 and 2.1 nm enable CE for ¹H, ¹³C, and ¹⁵N nuclear spins. We compare 263 GHz electron paramagnetic resonance (EPR) spectra with the obtained DNP field profiles and discuss possible CE matching conditions within the high‐spin system and the influence of dipolar broadening of the EPR signal. Our findings foster the understanding of the CE mechanism and the design of high‐spin PAs for specific applications of DNP.     

Half-integer spin heptanuclear single-molecule magnet with an unusual Mn(III)6Mn(II) exchange-coupled core

The synthesis, X-ray crystallography, magnetic properties, and high-field electron paramagnetic resonance (HFEPR) of a new heptanuclear manganese complex [Mn(7)(heamp)(6)](ClO(4))(2)·4CH(2)Cl(2)·H(2)O (complex 2), in which heampH(3) is 2-[N,N-di(2-hydroxyethyl)aminomethyl]phenol (compound 1), is reported. Complex 2 has a hexagonal, disk-shaped topology and contains six Mn(III) ions and a central Mn(II) ion. It crystallizes in the monoclinic space group P2(1)/c with two molecular orientations. Consideration of the cluster topology, together with variable-temperature and variable-field DC magnetic susceptibility data, suggest that complex 2 exists in a half-integer, S = (19)/(2) ± 1 spin ground state, with appreciable uniaxial zero-field splitting (D = -0.16 cm(-1)). AC magnetic susceptibility measurements clearly show out-of-phase signals, which are frequency- and temperature-dependent, indicating slow magnetization relaxation behavior. An analysis of the relaxation data employing the Arrhenius formula yielded an effective relaxation barrier of 12.9 cm(-1). Simulations of HFEPR studies agree with the assignment of an S ≈ (19)/(2) spin ground state, with g = 1.96, D = -4.71 GHz (-0.16 cm(-1)), and a longitudinal fourth-order zero-field splitting parameter B(4)(0) = -2.7 × 10(-4) GHz (-9.0 × 10(-6) cm(-1)).     

Multiexponential electronic spin relaxation and Redfield's limit in Gd(III) complexes in solution: consequences for 17O/1H NMR and EPR simultaneous analysis

Multiple experiments (17O NMR, 1H NMR, and EPR) have been performed in the past to understand the microscopic parameters that control the magnetic relaxation rate enhancement induced by paramagnetic molecules on neighboring water protons, the so-called relaxivity. The generally accepted theories of the electron spin relaxation of S = 7/2 ions such as Gd3+ (Solomon-Bloembergen-Morgan or simplified Hudson-Lewis) are unsatisfactory for a simultaneous analysis. Recently, an improved theory, where the electron spin relaxation is due to the combination of a static (thus explicitly linked to the molecular structure) and a dynamic zero field splitting, has been developed and tested on experimental EPR data. The model has also been extended beyond the electronic Redfield limit using Monte Carlo simulations. Using the aqua ion [Gd(H2O)8]3+ as a test case, we present here the first simultaneous analysis of 17O NMR, 1H NMR, and EPR relaxation data using this rigorous approach of the electron spin relaxation. We discuss the physical meaning of the calculated parameters. The consequences on future experiments are also considered, especially regarding the analysis of nuclear magnetic relaxation dispersion (NMRD) profiles in the study of Gd3+ complexes.     

Ligand protons in a frozen solution of copper histidine relax via a T1e -driven three-spin mechanism

Davies electron-nuclear double resonance spectra can exhibit strong asymmetries for long mixing times, short repetition times, and large thermal polarizations. These asymmetries can be used to determine nuclear relaxation rates in paramagnetic systems. Measurements of frozen solutions of copper(L-histidine)(2) reveal a strong field dependence of the relaxation rates of the protons in the histidine ligand, increasing from low (g( parallel)) to high (g( perpendicular)) field. It is shown that this can be attributed to a concentration-dependent T(1e)-driven relaxation process involving strongly mixed states of three spins: the histidine proton, the Cu(II) electron spin of the same complex, and another distant electron spin with a resonance frequency differing from the spectrometer frequency approximately by the proton Larmor frequency. The protons relax more efficiently in the g( perpendicular) region, since the number of distant electrons able to participate in this relaxation mechanism is higher than in the g( parallel) region. Analytical expressions for the associated nuclear polarization decay rate Tau(een) (-1) are developed and Monte Carlo simulations are carried out, reproducing both the field and the concentration dependences of the nuclear relaxation.     

Surface nuclear spin relaxation of 199Hg

We report the results of a detailed study of surface relaxation of 199Hg nuclear spins in paraffin coated cells. From measurements of the magnetic field and temperature dependence of the spin relaxation rates we determine the correlation time for magnetic fluctuations and the surface adsorption energy. The data indicate that surface relaxation is caused by dipolar coupling to paramagnetic sites on the surface. We also observe changes in the spin relaxation rate caused by ultraviolet radiation resonant with the 254 nm transition in Hg.