The viscosity and temperature dependence of X-band ESR lineshapes of Gd(III) aqueous complex

X-band ESR spectra of Gd-aqua complex in various weight concentration of glycerol have been recorded at four temperatures. The interpretation of the ESR linewidth is preformed using both the stochastic Liouville approach (SLA) and a perturbation theory. The SLA uses a one dynamic model of the zero-field splitting whereas the perturbation approach uses a two dynamic model. Both models can reproduce the variation of the linewidth with respect to viscosity. In the SLA model, both the zero-field splitting (ZFS) interaction and the correlation time vary with the glycerol content. In the two dynamic perturbation model, only the correlation times are viscosity dependent. The two models give different NMRD profiles.     

Direct calculation of (1)H(2)O T(1) NMRD profiles and EPR lineshapes for the electron spin quantum numbers S = 1, 3/2, 2, 5/2, 3, 7/2, based on the stochastic Liouville equation combined with Brownian dynamics simulation

Direct calculation of electron spin relaxation and EPR lineshapes, based on Brownian dynamics simulation techniques and the stochastic Liouville equation approach (SLE-L) [Mol. Phys., 2004, 102, 1085-1093], is here generalized to high spin systems with spin quantum number S = 3/2, 2, 5/2, 3 and 7/2. A direct calculation method is demonstrated for electron spin-spin and spin-lattice relaxation, S-, X- and Q-band EPR-lineshapes and paramagnetic enhanced water proton T(1)- NMRD profiles. The main relaxation mechanism for the electron spin system is a stochastic second rank zero field splitting (ZFS). Brownian dynamics simulation techniques are used in describing a fluctuating ZFS interaction which comprises two parts namely the "permanent" part which is modulated by isotropic reorientation diffusion, and the transient part which is modulated by fast local distortion, which is also modelled by the isotropic rotation diffusion model. The SLE-L approach present is applicable both in the perturbation (Redfield) regime as well as outside the perturbation regime, in the so called slow motion regime.     

A high-frequency EPR study of frozen solutions of Gd(III) complexes: straightforward determination of the zero-field splitting parameters and simulation of the NMRD profiles

Gd(III) (S = 7/2) polyaminocarboxylates, used as contrast agents for Magnetic Resonance Imaging (MRI), were studied in frozen solutions by High-Frequency-High-Field Electron Paramagnetic Resonance (HF-EPR). EPR spectra recorded at 240 GHz and temperatures below 150 K allowed the direct and straightforward determination of parameters governing the strength of zero-field splitting (ZFS). For the first time, a correlation has been established between the sign of the axial ZFS parameter, D, and the nature of the chelating ligand in Gd(III) complexes: positive and negative signs have been observed for acyclic and macrocyclic complexes, respectively. Furthermore, it has been shown that complexes of the less symmetric acyclic DTPA derivatives possess a substantial rhombicity, E, in contrast to the more symmetric macrocyclic DOTA derivatives, where E is negligible. The results obtained are compatible with recent results of liquid-state EPR and allowed to simulate 1H Nuclear Magnetic Relaxation Dispersion (NMRD) profiles with more directly physically meaningful EPR and NMR parameters over the full frequency range from 0.01 to 50 MHz.     

Stochastic Liouville equation treatment of the electron paramagnetic resonance line shape of an S-state ion in solution

The current approaches used for the analysis of electron paramagnetic resonance spectra of Gd3+ complexes suffer from a number of drawbacks. Even the elaborate model of [Rast et al., J. Chem. Phys. 113, 8724 (2000)] where the electron spin relaxation is explained by the modulation of the zero-field splitting (ZFS), by molecular tumbling (the so called static contribution), and deformations (transient contribution), is only readily applicable within the validity range of the Redfield theory [Advances in Magnetic Resonance, edited by J.-S. Waugh (Academic, New York, 1965), Vol. 1, p. 1], that is, when the ZFS is small compared to the Zeeman energy and the rotational and vibrational modulations are fast compared to the relaxation time. Spin labels (nitroxides and transition metal complexes) have been studied for years in systems that violate these conditions. The theoretical framework commonly used in such studies is the stochastic Liouville equation (SLE). The authors shall show how the physical model of Rast et al. can be cast into the SLE formalism, paying special attention to the specific problems introduced by the [Uhlenbeck and Ornstein, Phys. Rev. 36, 823 (1930)] process used to model the transient ZFS. The resulting equations are very general and valid for arbitrary correlation times, magnetic field strength, electron spin S, or symmetry. The authors demonstrate the equivalence of the SLE approach with the Redfield approximation for two well-known Gd3+ complexes.     

Molecular dynamics simulations of MRI-relevant GdIII chelates: direct access to outer-sphere relaxivity

The structure and dynamics of the surrounding water were studied through molecular dynamics (MD) simulations for several GdIII polyaminocarboxylate and polyaminophosphonate complexes in aqueous solution. The radial distribution functions (rdf) show that a few water molecules are bonded to the ligand through hydrogen bonds to hydrophilic groups such as carboxylates and phosphonates. Residence times are of the order of 20-25 ps for the polyaminocarboxylate and 56ps for the polyaminophosphonate chelates. No preferred orientation or bonding of water molecules is observed in the hydrophobic region of the anisotropic macrocyclic complexes. Our rdf allow calculation of the outer-sphere contribution to the nuclear magnetic resonance dispersion (NMRD) profiles using Freed's finite differences method, including electronic relaxation. The results show that the commonly used analytical force-free model is only an empirical relationship. When experimental outer-sphere NMRD profiles are available ([Gd(teta)]- and [Gd(dotp)]5-(teta=N,N',N",N"'-tetracarboxymethyl-1,4,8,11- tetraazacyclotetradecane; dotp = N,N',N",N"'-tetraphosphonatomethyl-1,4,7,10-tetraazacyclododecane) the calculated curves are in good agreement. In the case of [Gd(teta)]-, the comparison with the experimental NMRD profile has led us to predict a very fast electronic relaxation, which has been confirmed by the EPR spectrum.     

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.     

"Through-space" nuclear spin-spin J(PP) coupling in tetraphosphine ferrocenyl derivatives: a (31)P NMR and X-ray structure correlation study for coordination complexes

Herein, we report on (31)P(31)P solution-phase "through-space" nuclear spin-spin coupling constants (J(PP)) from a novel family of organometallic tetraphosphine nickel and palladium complexes. These J(PP) constants were accurately determined through NMR iterative simulation based on the second-order spectra obtained for the compounds. The corresponding solid-state X-ray structures of the complexes were determined, and the "through-space" P.P distances are reported. Due to the blocked conformation of the species in solution, a qualitative and semiquantitative experimental correlation is obtained, which links the geometric parameters and the intensity of the corresponding P.P coupling constant. The lone-pair overlap theory developed for (19)F(19)F and (15)N(19)F "through-space" couplings in organic compounds [J. Am. Chem. Soc. 1973, 95, 7747-7752; 2000, 122, 4108-4116] appears to be a reliable foundation on which to account for our results. Based on the reported observations, the lone-pair overlap model is extended to "through-space" (31)P(31)P coupling, and the model is broadened to encompass metal orbital contributions for coordination complexes. Some of the predictions and consequences of the proposed theory are discussed.     

Lanthanide(III) complexes with ligands derived from a cyclen framework containing pyridinecarboxylate pendants. The effect of steric hindrance on the hydration number

Two new macrocyclic ligands, 6,6′-((1,4,7,10-tetraazacyclododecane-1,7-diyl)bis(methylene))dipicolinic acid (H2DODPA) and 6,6′-((4,10-dimethyl-1,4,7,10-tetraazacyclododecane-1,7-diyl)bis(methylene))dipicolinic acid (H2Me-DODPA), designed for complexation of lanthanide ions in aqueous solution, have been synthesized and studied. The X-ray crystal structure of [Yb(DODPA)](PF6)·H2O shows that the metal ion is directly bound to the eight donor atoms of the ligand, which results in a square-antiprismatic coordination around the metal ion. The hydration numbers (q) obtained from luminescence lifetime measurements in aqueous solution of the Eu(III) and Tb(III) complexes indicate that the DODPA complexes contain one inner-sphere water molecule, while those of the methylated analogue H2Me-DODPA are q = 0. The structure of the complexes in solution has been investigated by 1H and 13C NMR spectroscopy, as well as by theoretical calculations performed at the density functional theory (DFT; mPWB95) level. The minimum energy conformation calculated for the Yb(III) complex [Λ(λλλλ)] is in good agreement with the experimental structure in solution, as demonstrated by the analysis of the Yb(III)-induced paramagnetic 1H shifts. The nuclear magnetic relaxation dispersion (NMRD) profiles recorded for [Gd(Me-DODPA)]+ are typical of a complex with q = 0, where the observed relaxivity can be accounted for by the outer-sphere mechanism. However, [Gd(DODPA)]+ shows NMRD profiles consistent with the presence of both inner- and outer-sphere contributions to relaxivity. A simultaneous fitting of the NMRD profiles and variable temperature 17O NMR chemical shifts and transversal relaxation rates provided the parameters governing the relaxivity in [Gd(DODPA)]+. The results show that this system is endowed with a relatively fast water exchange rate k(ex)(298) = 58 × 10(6) s(–1).     

First-principle computation of zero-field splittings: application to a high valent Fe(IV)-oxo model of nonheme iron proteins

We report the computational implementation of a combined spin-density-functional theory and perturbation theory (SDFT-PT) methodology for the accurate calculation of zero-field splittings (ZFS) in complexes of the most diverse nature including metal centers in proteins. We have applied the SDFT-PT methodology to study the cation of the recently synthesized complex [Fe(IV)(O)-(TMC)(NCCH(3))](OTf)(2), [J. Rohde et al., Science 299, 1037 (2003)] which is an important structural and functional analog of high-valent intermediates in catalytic cycles of nonheme iron enzymes. The calculated value (D(Theory)=28.67 cm(-1)) is in excellent agreement with the unusually large ZFS reported by experiment (D(Exp)=29+/-3 cm(-1)). The principal component D(zz) of the ZFS tensor is oriented along the Fe(IV)=oxo bond indicating that the oxo ligand dominates the electronic structure of the complex.     

Design of Gd(III)-based magnetic resonance imaging contrast agents: static and transient zero-field splitting contributions to the electronic relaxation and their impact on relaxivity

A multiple-frequency (9.4-325 GHz) and variable-temperature (276-320 K) electron paramagnetic resonance (EPR) study on low molecular weight gadolinium(III) complexes for potential use as magnetic resonance imaging (MRI) contrast agents has been performed. Peak-to-peak linewidths Delta Hpp and central magnetic fields have been analyzed within the Redfield approximation taking into account the static zero-field splitting (ZFS) up to the sixth order and the transient ZFS up to the second order. Longitudinal electronic relaxation is dominated by the static ZFS contribution at low magnetic fields (B < 0.3 T) and by the transient ZFS at high magnetic fields (B > 1.5 T). Whereas the static ZFS clearly depends on the nature of the chelating ligand, the transient ZFS does not. For the relatively fast rotating molecules studied water proton relaxivity is mainly limited by the fast rotation and electronic relaxation has only a marked influence at frequencies below 30 MHz. From our EPR results we can conclude that electronic relaxation will have no influence on the efficiency of Gd(III)-based MRI contrast agents designed for studies at very high magnetic fields (B > 3T).     

Ab initio and coupled-perturbed density functional theory estimation of zero-field splittings in MnII transition metal complexes

The paper presents a method comparison for the prediction of zero-field splitting (ZFS) parameters in a series of Mn (II) coordination complexes. The test set consists of Mn (II) complexes that are experimentally well-characterized by X-ray diffraction and high-field electron paramagnetic resonance. Their ZFS parameters have been calculated using density functional theory (DFT) as well as complete active space self-consistent field (CASSCF) methods. It is shown that the recently introduced coupled-perturbed spin-orbit coupling (CP-SOC) approach [ Neese, F. J. Chem. Phys. 2007, 127, 164112 ] together with hybrid-DFT functionals leads to a slope of the correlation line (plot of experimental vs calculated D values) that is essentially unity provided that the direct spin-spin interaction is properly included in the treatment. This is different from our previous DFT study on the same series of complexes where a severe overestimation of the D parameter has been found [ Zein, S. ; Duboc, C. ; Lubitz, W. ; Neese, F. Inorg. Chem. 2008, 47, 134 ]. CASSCF methods have been used to evaluate the ZFS in an "ab initio ligand-field" type treatment. The study demonstrates that a substantial part of the relevant physics is lost in such a treatment since only excitations within the manganese d-manifold are accounted for. Thus, a severe underestimation of the D parameter has been found. Because the CASSCF calculations in combination with quasidegenerate perturbation theory treats the SOC to all orders, we have nevertheless verified that second-order perturbation theory is an adequate approximation in the case of the high-spin d (5) configuration.     

Dynamics of hyaluronan aqueous solutions as assessed by fast field cycling NMR relaxometry

Fast field cycling (FFC) NMR relaxometry has been used to study the conformational properties of aqueous solutions of hyaluronan (HYA) at three concentrations in the range 10 to 25 mg mL^–1. Results revealed that, irrespective of the solution concentration, three different hydration layers surround hyaluronan. The inner layer consists of water molecules strongly retained in the proximity of the HYA surface. Because of their strong interactions with HYA, water molecules in this inner hydration layer are subject to very slow dynamics and have the largest correlation times. The other two hydration layers are made of water molecules which are located progressively further from the HYA surface. As a result, decreasing correlation times caused by faster molecular motion were measured. The NMRD profiles obtained by FFC-NMR relaxometry also showed peaks attributable to ¹H–¹⁴N quadrupole interactions. Changes in intensity and position of the quadrupolar peaks in the NMRD profiles suggested that with increasing concentration the amido group is progressively involved in the formation of weak and transient intramolecular water bridging adjacent hyaluronan chains. In this work, FFC-NMR was used for the first time to obtain deeper insight into HYA–water interactions and proved itself a powerful and promising tool in hyaluronan chemistry.     

Relaxometric and solution NMR structural studies on ditopic lanthanide(III) complexes of a phosphinate analogue of DOTA with a fast rate of water exchange

A novel "ditopic" ligand containing two monophosphinate triacetate DOTA-like units linked by a thiourea bridge has been synthesized and its complexes with Ln3+ ions (Ln = Y, Eu, Gd, Dy) investigated by NMR spectroscopy and relaxometry. The presence of one water molecule in the first coordination sphere has been determined by the measurement of the dysprosium(III)-induced 17O NMR shifts. The 1H and 31P NMR spectra of the Eu(III) derivative indicate a higher abundance of the fast-exchanging twisted square antiprismatic (m) isomer than the isomeric square antiprismatic (M; m/M = 3:2) complex. The analysis of the 89Y and 13C T1 NMR relaxation times in the Gd(III)/Y(III) mixed complex have provided useful structural information. Values of ca. 6.3 and 8.2 A for the Gd...Y and Gd...C distances, respectively, have been estimated which indicate a rather compact solution structure. This result finds support in the value of the relaxivity whose increase (at 20 MHz and 298 K) on passing from the monomeric (5.7 s(-1) mM(-1)) to the ditopic complex (8.2 s(-1) mM(-1)) can be attributed to the doubling of the inner-sphere term following the doubling of the molecular size. The structural and dynamic relaxivity-controlling parameters were assessed by a simultaneous fitting of the variable temperature 17O NMR and 1H NMRD relaxometric data. The mean water residence lifetime (298tauM) has been found to be 53 ns, one of the shortest values reported for ditopic complexes. The reorientational correlation time is two times longer (298tauR = 183 ps) than the corresponding value of the parent monomeric Gd(III) complex, thus supporting the view of a limited degree of internal rotation. The possible influence of magnetic Gd-Gd coupling has been excluded by a comparison of the 1H NMRD profiles of the homodinuclear Gd(III)/Gd(III) and the heterodinuclear Gd(III)/Y(III) complexes.     

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.     

High relaxivity gadolinium hydroxypyridonate-viral capsid conjugates: nanosized MRI contrast agents

High relaxivity macromolecular contrast agents based on the conjugation of gadolinium chelates to the interior and exterior surfaces of MS2 viral capsids are assessed. The proton nuclear magnetic relaxation dispersion (NMRD) profiles of the conjugates show up to a 5-fold increase in relaxivity, leading to a peak relaxivity (per Gd3+ ion) of 41.6 mM(-1) s(-1) at 30 MHz for the internally modified capsids. Modification of the exterior was achieved through conjugation to flexible lysines, while internal modification was accomplished by conjugation to relatively rigid tyrosines. Higher relaxivities were obtained for the internally modified capsids, showing that (i) there is facile diffusion of water to the interior of capsids and (ii) the rigidity of the linker attaching the complex to the macromolecule is important for obtaining high relaxivity enhancements. The viral capsid conjugated gadolinium hydroxypyridonate complexes appear to possess two inner-sphere water molecules (q = 2), and the NMRD fittings highlight the differences in the local motion for the internal (tauRl = 440 ps) and external (tauRl = 310 ps) conjugates. These results indicate that there are significant advantages of using the internal surface of the capsids for contrast agent attachment, leaving the exterior surface available for the installation of tissue targeting groups.     

Ab initio studies on the zero-field splitting parameters of manganese porphyrin complexes

The magnetic property of a one-dimensional magnetic chain, 5,10,15,20-tetrakis(4-bromophenyl)porphyrinatomanganese(III) tetracyanoethenide ([MnTBrPP]⁺[TCNE]⁻), is investigated by using model complexes and ab initio calculations. In these models, MnTBrPP is reduced to a manganese porphyrin complex (MnP). The spin-polarized density functional theory (UDFT) and the hybrid UDFT were used to calculate the complexes, and Pederson’s scheme was used to calculate their zero-field splitting (ZFS) parameters. We found from the model calculations that the TCNE coordination hardly affects the magnetic anisotropy of MnP.     

Relaxometric study of copper [15]metallacrown-5 gadolinium complexes derived from alpha-aminohydroxamic acids

Proton nuclear magnetic relaxation dispersion (NMRD) profiles were recorded between 0.24 mT and 1.4 T for lanthanum(III)- and gadolinium(III)-containing [15]metallacrown-5 complexes derived from alpha-aminohydroxamic acids and with copper(II) as the ring metal. The influence of the different R-groups on the proton relaxivity was investigated, and a linear relationship between the relaxivity and the molecular mass of the metallacrown complex was found. The selectivity of the metallacrown complexes was tested by transmetalation experiments with zinc(II) ions. The crystal structure of the copper [15]metallacrown-5 gadolinium complex with glycine hydroximate ligands is reported.     

Matrix isolation ESR spectroscopy and quantum chemical calculations on 5-methylhexa-1,2,4-triene-1,3-diyl, a highly delocalized triplet "hybrid" carbene

The ESR spectrum of 5-methylhexa-1,2,4-triene-1,3-diyl (1) was recorded in an argon matrix at 15 K. The derived zero-field splitting (ZFS) parameters (D = 0.5054 ± 0.0006 cm(-1) and E = 0.0045 ± 0.0002 cm(-1)) fall between those determined previously for propargylene (2) and vinylcarbene (3). DFT and ab initio (CAS and MRCI) quantum-chemical calculations of the ZFS parameters of 1, 2, and 3 were performed. These calculations indicate that multireference methods are needed to successfully predict ZFS parameters of delocalized carbenes/biradicals such as 1-3. The calculated singly occupied MOs and spin density distributions show that the spin is more delocalized in 1 than in 2 and 3, indicating that 1 is a "hybrid" of the constituent ethynyl- and vinylcarbenes, 2 and 3, respectively. The dominant contribution to the D-value in 1 and 2 is found to result from spin-spin interactions on the C atoms of the propylidene moiety, which is strongly affected by spin polarization. Accurate values for the D-parameter are also predicted for other types of delocalized triplet carbenes such as HC(5)H and HCCN.