Nuclear relaxation rate enhancement by a 14N quadrupole nucleus in a fluctuating electric-field gradient.

We consider the longitudinal quadrupole relaxation rate enhancement (QRE) of a 1H nucleus due to the time fluctuations of the local dipolar magnetic field created by a close quadrupole 14N nucleus, the electric-field gradient (EFG) Hamiltonian of which changes with time because of vibrations/distortions of its chemical environment. The QRE is analytically expressed as a linear combination of the cosine Fourier transforms of the three quantum time auto-correlation functions GAA(t) of the 14N spin components along the principal axes A = X, Y, and Z of the mean (time-averaged) EFG Hamiltonian. Denoting the three transition frequencies between the energy levels of this mean Hamiltonian by νA, the functions GAA(t) oscillate at frequencies νA + sA/(2π) with mono-exponential decays of relaxation times τA, where the frequency dynamic shifts sA and the relaxation times τA are closed expressions of the magnitude of the fluctuations of the instantaneous EFG Hamiltonian about its mean and of the characteristic fluctuation time. Thus, the theoretical QRE is the sum of three Lorentzian peaks centered at νA + sA/(2π) with full widths at half maxima 1/(πτA). The predicted peak widths are nearly equal. The predicted dynamic shifts of the peaks are much smaller than their widths and amazingly keep proportional to the transition frequencies νA for reasonably fast EFG fluctuations. The theory is further improved by correcting the transition frequencies by the 14N Zeeman effects of second order. It is successfully applied to reinterpret the QRE pattern measured by Broche, Ashcroft, and Lurie [Magn. Reson. Med. 68, 358 (2012)] in normal cartilage.

Simple expressions of the nuclear relaxation rate enhancement due to quadrupole nuclei in slowly tumbling molecules.

For slowly tumbling entities or quasi-rigid lattices, we derive very simple analytical expressions of the quadrupole relaxation enhancement (QRE) of the longitudinal relaxation rate R1 of nuclear spins I due to their intramolecular magnetic dipolar coupling with quadrupole nuclei of arbitrary spins S ≥ 1. These expressions are obtained by using the adiabatic approximation for evaluating the time evolution operator of the quantum states of the quadrupole nuclei S. They are valid when the gyromagnetic ratio of the spin S is much smaller than that of the spin I. The theory predicts quadrupole resonant peaks in the dispersion curve of R1 vs magnetic field. The number, positions, relative intensities, Lorentzian shapes, and widths of these peaks are explained in terms of the following properties: the magnitude of the quadrupole Hamiltonian and the asymmetry parameter of the electric field gradient (EFG) acting on the spin S, the S-I inter-spin orientation with respect to the EFG principal axes, the rotational correlation time of the entity carrying the S-I pair, and/or the proper relaxation time of the spin S. The theory is first applied to protein amide protons undergoing dipolar coupling with fast-relaxing quadrupole (14)N nuclei and mediating the QRE to the observed bulk water protons. The theoretical QRE agrees well with its experimental counterpart for various systems such as bovine pancreatic trypsin inhibitor and cartilages. The anomalous behaviour of the relaxation rate of protons in synthetic aluminium silicate imogolite nano-tubes due to the QRE of (27)Al (S = 5/2) nuclei is also explained.

Determination of the static zero-field splitting of Gd3+ complexes in solution from the shifts of the central magnetic fields of their EPR spectra.

In principle, the Redfield theory of EPR spectra applies only to fast-rotating complexes with rather small static zero-field splitting (ZFS) terms. However, at sufficiently high frequencies, typically of 35 GHz and above, it predicts values of the central magnetic fields which are surprisingly accurate well beyond its expected applicability range. This remarkable feature is demonstrated by showing that the Redfield EPR spectrum crosses its baseline at the same point as its "exact" simulated counterpart. It is shown that the shift of the central magnetic field with respect to its limiting value in the absence of ZFS terms is often simply proportional to the square of the magnitude of the static ZFS term divided by the spectrometer frequency. This property is used to determine the magnitude of the static ZFS term independently of its fluctuation dynamics and of the presence of the transient ZFS term.

Quantitative interpretation of the very fast electronic relaxation of most Ln3+ ions in dissolved complexes.

In a reference frame rigidly bound to the complex, we consider two Hamiltonians possibly at the origin of the very fast electronic relaxation of the paramagnetic lanthanide Ln(3+) ions (Ln = Ce to Nd, Tb to Yb), namely the mean (static) ligand-field Hamiltonian and the transient ligand-field Hamiltonian. In the laboratory frame, the bombardment of the complex by solvent molecules causes its Brownian rotation and its vibration-distorsion dynamics governing the fluctuations of the static and transient terms, respectively. These fluctuations are at the origin of electronic relaxation. The electronic relaxation of a Ln(3+) ion is defined by the decays of the time correlation functions (TCFs) of the longitudinal and transverse components of the total angular momentum J of its ground multiplet. The Brownian rotation of the complex and its vibration-distorsion dynamics are simulated by random walks, which enable us to compute the TCFs from first principles. It is shown that the electronic relaxation is governed mainly by the magnitude of the transient ligand-field, and not by its particular expression. The range of expected values of this ligand-field together with the lower limit of relaxation time enforced by the values of the vibration-distortion correlation time in liquids give rise to effective electronic relaxation times which are in satisfactory overall agreement with the experimental data. In particular, these considerations explain why the electronic relaxation times vary little with the coordinating ligand and are practically independent of the external field magnitude.

Enhancement of the water proton relaxivity by trapping Gd3+ complexes in nanovesicles.

We present a theoretical model for calculating the relaxivity of the water protons due to Gd(3+) complexes trapped inside nanovesicles, which are permeable to water. The formalism is applied to the characterization of apoferritin systems [S. Aime et al., Angew. Chem., Int. Ed. 41, 1017 (2002); O. Vasalatiy et al., Contrast Media Mol. Imaging 1, 10 (2006)]. The very high relaxivity due to these systems is attributed to an increase of the local viscosity of the aqueous solution inside the vesicles and to an outer-sphere mechanism which largely dominates the inner-sphere contribution. We discuss how to tailor the dynamic parameters of the trapped complexes in order to optimize the relaxivity. More generally, the potential of relaxivity studies for investigating the local dynamics and residence time of exchangeable molecules in nanovesicles is pointed out.

Almost ideal 1D water diffusion in imogolite nanotubes evidenced by NMR relaxometry.

The longitudinal proton relaxation rates R(1) of water diffusing inside synthetic aluminium silicate imogolite nanotubes are measured by fast field-cycling NMR for frequencies between 0.02 and 35 MHz at 25, 37 and 50 degrees C. We give analytical expressions of the dominant intermolecular dipolar spin-spin contribution to R(1) and to the transverse relaxation rate R(2). A remarkable variation of R(1) by more than two orders of magnitude is observed and shown to be close to the theoretical law, inversely proportional to the square root of the resonance frequency, which is characteristic of perfect molecular 1D diffusion. The physics of diffusion is discussed.

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.

Comparison of different methods for calculating the paramagnetic relaxation enhancement of nuclear spins as a function of the magnetic field.

The enhancement of the spin-lattice relaxation rate for nuclear spins in a ligand bound to a paramagnetic metal ion [known as the paramagnetic relaxation enhancement (PRE)] arises primarily through the dipole-dipole (DD) interaction between the nuclear spins and the electron spins. In solution, the DD interaction is modulated mostly by reorientation of the nuclear spin-electron spin axis and by electron spin relaxation. Calculations of the PRE are in general complicated, mainly because the electron spin interacts so strongly with the other degrees of freedom that its relaxation cannot be described by second-order perturbation theory or the Redfield theory. Three approaches to resolve this problem exist in the literature: The so-called slow-motion theory, originating from Swedish groups [Benetis et al., Mol. Phys. 48, 329 (1983); Kowalewski et al., Adv. Inorg. Chem. 57, (2005); Larsson et al., J. Chem. Phys. 101, 1116 (1994); T. Nilsson et al., J. Magn. Reson. 154, 269 (2002)] and two different methods based on simulations of the dynamics of electron spin in time domain, developed in Grenoble [Fries and Belorizky, J. Chem. Phys. 126, 204503 (2007); Rast et al., ibid. 115, 7554 (2001)] and Ann Arbor [Abernathy and Sharp, J. Chem. Phys. 106, 9032 (1997); Schaefle and Sharp, ibid. 121, 5387 (2004); Schaefle and Sharp, J. Magn. Reson. 176, 160 (2005)], respectively. In this paper, we report a numerical comparison of the three methods for a large variety of parameter sets, meant to correspond to large and small complexes of gadolinium(III) and of nickel(II). It is found that the agreement between the Swedish and the Grenoble approaches is very good for practically all parameter sets, while the predictions of the Ann Arbor model are similar in a number of the calculations but deviate significantly in others, reflecting in part differences in the treatment of electron spin relaxation. The origins of the discrepancies are discussed briefly.

Relaxation theory of the electronic spin of a complexed paramagnetic metal ion in solution beyond the Redfield limit.

The relaxation of the electronic spin S of a paramagnetic metal ion with fully quenched orbital angular momentum in its ground state is investigated in an external magnetic field through a systematic study of the time correlation functions governing the evolution of the statistical operator (density matrix). Let omega0 be the Larmor angular frequency of S. When the relaxation is induced by a time-fluctuating perturbing Hamiltonian hH1(t) of time correlation tauc, it is demonstrated that after a transient period the standard Redfield approximation is relevant to calculate the evolution of the populations of the spin states if parallelH1 parallel2tauc2/(1+omega0(2)tauc2)<<1 and that this transient period becomes shorter than tauc at sufficiently high field for a zero-field splitting perturbing Hamiltonian. This property, proven analytically and confirmed by numerical simulation, explains the surprising success of several simple expressions of the longitudinal electronic relaxation rate 1/T1e derived from the Redfield approximation well beyond its expected validity range parallelH1 paralleltauc<<1. It has favorable practical consequences on the interpretation of the paramagnetic relaxation enhancement of nuclei used for structural and dynamic studies.

Towards a better understanding of magnetic interactions within m-phenylene alpha-nitronyl nitroxide and imino nitroxide based radicals, part III: Magnetic exchange in a series of triradicals and tetraradicals based on the phenyl acetylene and biphenyl coupling units.

The present work completes and extends our previous reports on the determination of the magnetic ground state and on the strength of the through bond exchange coupling within series of biradicals. This knowledge was subsequently exploited for the analysis of the magnetic interactions in their crystals. We report here the studies of series of triradicals incorporating alpha-nitronyl nitroxides (NN) or alpha-imino nitroxides (IN) as terminal radical fragments connected through a m-phenylene coupling unit in one case and a phenyl acetylene unit in other case. Tetraradical derivatives have also been studied. The studies of isolated molecules (EPR in solution and DFT calculations) allow the assessment of the magnetic interactions through the magnetic coupling unit. All triradical derivatives are found to exhibit a quartet ground state, whereas a singlet ground state is determined for the tetraradical. This last result reinforces previous findings that the singlet ground state is favoured in related biradicals involving similar m-phenylene couplers. Moreover, the through bond magnetic exchange coupling for the ortho-meta connectivity could be demonstrated as being ferromagnetic, thus ascertaining our previous hypotheses. The magnetic properties of the triradicals and tetraradicals in their solid state have been rationalized by using a previously proposed methodology, allowing to identify the most relevant magnetic pathways.

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.

Aminomethyl-bipyridine bearing two flexible nitronyl-nitroxide arms: a new podand for complexation of transition metals in a facial or meridional conformation.

Transition metal complexes of 6-aminomethyl-bis[methyl-2-(4,5-dihydro-4,4,5,5- tetramethylimidazolinyl-3-oxide-l-oxy)]-2,2'-bipyridine, bpyN(NIT)(2), 1, have been synthesized and characterized by FAB-MS, UV-vis, FT-IR, and EPR spectroscopies, elemental analysis, and susceptibility measurements. Single-crystal X-ray diffraction studies have been performed on all compounds giving the following crystal data: bpyN(NIT)(2), 1, triclinic, P(-)1, Z = 2, a = 10.7224(4) A, b = 11.0995(4) A, c = 13.1134(3) A, alpha = 114.101(9) degrees, beta = 97.476(9) degrees, gamma = 99.667(9) degrees; ZnbpyN(NIT)(2), 2, hexagonal, P3(2), Z = 3, a = 15.4545(3) A, b = 15.4545(3) A, c = 13.5594(3) A; NibpyN(NIT)(2), 3, hexagonal, P3(2), Z = 3, a = 15.2867(1) A, b = 15.2867(1) A, c = 13.7160(1) A; CubpyN(NIT)(2), 4, triclinic, P(-)l, Z = 2, a = 11.8640(4) A, b = 13.2023(4) A, c = 13.2661(5) A, alpha = 90.539(9) degrees, beta = 104.983(9) degrees, gamma = 113.252(9) degrees. The two radicals of the free ligand 1 are almost perpendicular to one another in the solid state, favoring a weak ferromagnetic interaction (J/k(B) = 8.8 K). The complexes obtained by wrapping the ligand around a single metal center gave rise to two different coordination schemes where the two radicals of 1 adopt a ON(3)O meridional (with Ni and Zn) or a ON(3)O facial conformation (with Cu), which strongly affects the magnetic and electronic properties (O accounts for the coordinated oxygen atoms of the nitroxide radicals and N(3) accounts for the tertiary amine). For 2, a model of a dimer has been used giving rise to a weak antiferromagnetic interaction between the radicals (J/k(B) = -5.3 K). For 3, a very strong intramolecular antiferromagnetic coupling has been found and estimated at J/k(B) = -230 K and J'/k(B) = -110 K between the nickel and each radical using an asymmetric model of a trimer. For 4, an unusual magnetic behavior is observed, dominated by antiferromagnetic interactions with a residual plateau at chiT = 0.63 emu.K.mol(-)(1). Molecular modeling at the CASSCF level is in keeping with an antiferromagnetic coupling of the radical bound with the Cu(II) in the equatorial position. The combined structural, electronic, and magnetic characteristics suggest that the use of a flexible molecule provide an additional approach for fine-tuning magnetic interactions.

Synthesis, structures, and magnetic properties of a series of lanthanum(III) and gadolinium(III) complexes with chelating benzimidazole-substituted nitronyl nitroxide free radicals. Evidence for antiferromagnetic Gd(III)-radical interactions.

This paper reports the synthesis, crystal structures, and magnetic properties of a series of lanthanide complexes with nitronyl nitroxide radicals of general formula [[Ln(III)(radical)(4)] x (ClO(4))(3) x (H(2)O)(x) x (THF)(y)] (1-4) and [Ln(III)(radical)(2)(NO(3))(3)] (5, 6) [Ln = La (compounds 1, 3, 5) or Gd (compounds 2, 4, and 6); radical = 2-(2'-benzymidazolyl)-4,4,5,5-tetramethylimidazoline-1-oxyl-3-oxide (NITBzImH, compounds 1, 2, 5, 6) or 2-[2'-[(6'-methyl)benzymidazolyl]]-4,4,5,5-tetramethylimidazoline-1-oxyl-3-oxide (NITMeBzImH, compounds 3, 4)]. (1) C(64)H(88)Cl(3)LaN(16)O(24), fw = 1710.76, orthorhombic, Fddd, a = 11.0682(8) A, b = 34.240(3) A, c = 42.787(3) A, V = 16215(2) A(3), Z = 8, R = 0.0876, R(w) = 0.2336. (2) C(64)H(88)Cl(3)GdN(16)O(24), fw = 1729.10, tetragonal, P 4 macro 2c, a = 16.0682(4) A, b = 16.0682(4) A, c = 18.7190(6) A, V = 4833.0(2) A(3), R = 0.0732, R(w) = 0.2218. (3) C(68)H(94)Cl(3)LaN(16)O(23), fw = 1742.80, tetragonal, P 4 macro 2(1)m, a = 21.125(3) A, b = 21.125(3) A, c = 10.938(2) A, V = 4881.5(14) A(3), R = 0.1017, R(w) = 0.3126. (5) C(28)H(34)LaN(11)O(13), fw = 871.57, orthorhombic, Pna2(1), a = 19.5002(12) A, b = 13.0582(8) A, c = 14.5741(9) A, V = 3711.1(4) A(3), R = 0.0331, R(w) = 0.1146. (6) C(28)H(34)GdN(11)O(13), fw = 889.91, orthorhombic, Pna2(1), a = 19.1831(10) A, b = 13.1600(7) A, c = 14.4107(7) A, V = 3638.0(3) A(3), Z = 4, R = 0.0206, R(w) = 0.0625. Compounds 1-4 consist of [M(III)(radical)(4)](3+) cations, uncoordinated perchlorate anions, THF, and water crystallization molecules. In these complexes, the coordination number around the lanthanide ion is eight, and the polyhedron is either a distorted dodecahedron (1) or a distorted cube (2, 3). The crystal structures of 5 and 6 consist of independent [M(III)(radical)(2)(NO(3))(3)] entities in which the lanthanide is ten-coordinated and has a distorted bicapped square antiprism coordination polyhedron. For the lanthanum(III) complexes, the temperature dependence of the magnetic susceptibility indicates that radical-radical magnetic interactions are negligible either for compounds 1 and 3, while for compound 5 it is simulated considering dimers of weakly antiferromagnetically coupled radicals (J(rad-rad) = -1.1 cm(-1)). In the case of the gadolinium(III) compounds (2, 4, 6), each magnetic behavior gives unambiguous evidence of antiferromagnetic Gd(III)-radical interaction (2, J(Gd-rad) = -1.8 cm(-1); 4, J(Gd-rad) = -3.8 cm(-1); 6, J(Gd-rad1) = -4.05 cm(-1) and J(Gd-rad2) = -0.80 cm(-1)), in contrast to the ferromagnetic case generally observed. The nature of the Gd(III)-radical interaction is explained in relation to the donor strength of the free radical ligand.

Proximate Nitroxide Ligands in the Coordination Spheres of Manganese(II) and Nickel(II) Ions. Precursors for High-Dimensional Molecular Magnetic Materials.

The chelating nitroxide ligands 2-(2-pyridyl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazolyl-3-oxide-1-oxy (NITPy, 1), 2-(2-imidazolyl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazolyl-3-oxide-1-oxy (NITImH, 2), and 2-(2-benzimidazolyl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazolyl-3-oxide-1-oxy (NITBzImH, 3) and some of their transition metal complexes (Mn(II), Ni(II), Zn(II)) have been prepared and characterized by X-ray diffraction techniques and magnetic susceptibility measurements. All complexes are four- (or three-) spin systems where the metal coordination sphere is free of ancillary ligands because of the chelate effect which enforces the coordination of the oxyl group. The fac or mer nature of these species depends on the metal ions and on the steric demand of the ligand. It has been found that crystal packing is an important driving force toward the fac modification when steric requirements are not important. Crystal packing is probably also the cause of the noncentrosymmetric space group observed for the derivatives of NITPy. For the Zn(II) complex of NITImH, a moderate inter-nitroxide interaction within the metal coordination sphere of -14 cm(-)(1) is estimated. However, due to the modification of the spin distribution upon complexation, this interaction does not play a major role in the other complexes, where strong antiferromagnetic metal-nitroxide interactions (H = -2JS(i).S(j), -111 < J < -53 cm(-)(1)) are operative. The derivatives of NITImH are precursors of extended species which would be obtained by deprotonation of the ligand.

1D Manganese(II) Derivatives of an Imidazole-Substituted Nitronyl Nitroxide. An Approach toward Molecular Magnetic Materials of High Dimensionality.

Extended linear complexes of manganese(II) with a bis-chelating nitronyl nitroxide ligand, 2-(2-imidazolato)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazolyl-3-oxide-1-oxy (NITIm), have been prepared where metallic and organic spin carriers alternate. Depending on the deprotonating agent, the solvent, and the counteranion, the species [Mn(NITIm)(H(2)O)(2)]CH(3)COO, 1, [Mn(NITIm)(DMSO)(2)]BPh(4), 2, [Mn(NITIm)(H(2)O)(ImH)]NO(3), 3, and [Mn(NITIm)(NITImH)]ClO(4), 4, have been obtained, which differ by the additional ligands completing the metal coordination sphere. Complexes 1-3 are cis isomers and 4 is found as the mer modification; in all compounds, one observes a regular alternation of Lambda and Delta metal environments. Their magnetic properties are similar, with Mn(II)-nitroxide interactions J approximately -45 cm(-)(1) (H = -2JS(i)().S(j)()), and they display weak ferromagnetic properties below 5 K. Canting of the manganese ions is responsible for these properties. Relevant crystallographic parameters are as follows: 1, space group Fdd2, a = 16.713(1), b = 40.111(3), c = 9.735(1), Z = 16; 2, space group Pca2(1), a = 30.328(3), b = 13.422(1), c = 9.589(1), Z = 4; 3, space group P2(1)/c, a = 9.787(2), b = 22.973(5), c = 9.671(2), beta = 117.32(3) degrees, Z = 4; 4, space group P2(1)/c, a = 9.761(2), b = 28.668(5), c = 9.941(2), beta = 96.07(3) degrees, Z = 4.