(1)H relaxation dispersion in solutions of nitroxide radicals: Effects of hyperfine interactions with (14)N and (15)N nuclei

(1)H relaxation dispersion of decalin and glycerol solutions of nitroxide radicals, 4-oxo-TEMPO-d(16)-(15)N and 4-oxo-TEMPO-d(16)-(14)N was measured in the frequency range of 10 kHz-20 MHz (for (1)H) using STELAR Field Cycling spectrometer. The purpose of the studies is to reveal how the spin dynamics of the free electron of the nitroxide radical affects the proton spin relaxation of the solvent molecules, depending on dynamical properties of the solvent. Combining the results for both solvents, the range of translational diffusion coefficients, 10(-9)-10(-11) m(2)∕s, was covered (these values refer to the relative diffusion of the solvent and solute molecules). The data were analyzed in terms of relaxation formulas including the isotropic part of the electron spin - nitrogen spin hyperfine coupling (for the case of (14)N and (15)N) and therefore valid for an arbitrary magnetic field. The influence of the hyperfine coupling on (1)H relaxation of solvent molecules depending on frequency and time-scale of the translational dynamics was discussed in detail. Special attention was given to the effect of isotope substitution ((14)N∕(15)N). In parallel, the influence of rotational dynamics on the inter-molecular (radical - solvent) electron spin - proton spin dipole-dipole coupling (which is the relaxation mechanism of solvent protons) was investigated. The rotational dynamics is of importance as the interacting spins are not placed in the molecular centers. It was demonstrated that the role of the isotropic hyperfine coupling increases for slower dynamics, but it is of importance already in the fast motion range (10(-9)m(2)∕s). The isotope effects is small, however clearly visible; the (1)H relaxation rate for the case of (15)N is larger (in the range of lower frequencies) than for (14)N. It was shown that when the diffusion coefficient decreases below 5 × 10(-11) m(2)∕s electron spin relaxation becomes of importance and its role becomes progressively more significant when the dynamics slows done. As far as the influence of the rotational dynamics is concerned, it was show that this process is of importance not only in the range of higher frequencies (like for diamagnetic solutions) but also at low and intermediate frequencies.     

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.     

Applying Unconventional Spectroscopies to the Single-Molecule Magnets,Co(PPh3)2X2 (X=Cl,Br, I): Unveiling Magnetic Transitions and Spin-Phonon Coupling

Large separation of magnetic levels and slow relaxation in metal complexes are desirable properties of single-molecule magnets (SMMs). Spin-phonon coupling (interactions of magnetic levels with phonons) is ubiquitous, leading to magnetic relaxation and loss of memory in SMMs and quantum coherence in qubits. Direct observation of magnetic transitions and spin-phonon coupling in molecules is challenging. We have found that far-IR magnetic spectra (FIRMS) of Co(PPh₃)₂X₂ ( Co-X ; X=Cl, Br, I) reveal rarely observed spin-phonon coupling as avoided crossings between magnetic and u-symmetry phonon transitions. Inelastic neutron scattering (INS) gives phonon spectra. Calculations using VASP and phonopy programs gave phonon symmetries and movies. Magnetic transitions among zero-field split (ZFS) levels of the S=3/2 electronic ground state were probed by INS, high-frequency and -field EPR (HFEPR), FIRMS, and frequency-domain FT terahertz EPR (FD-FT THz-EPR), giving magnetic excitation spectra and determining ZFS parameters (D, E) and g values. Ligand-field theory (LFT) was used to analyze earlier electronic absorption spectra and give calculated ZFS parameters matching those from the experiments. DFT calculations also gave spin densities in Co-X , showing that the larger Co(II) spin density in a molecule, the larger its ZFS magnitude. The current work reveals dynamics of magnetic and phonon excitations in SMMs. Studies of such couplings in the future would help to understand how spin-phonon coupling may lead to magnetic relaxation and develop guidance to control such coupling.     

Electron spin relaxation of N@C60 in CS2 in CS2

We examine the temperature dependence of the electron spin relaxation times of the molecules N@C60 and N@C70 (which comprise atomic nitrogen trapped within a carbon cage) in liquid CS2 solution. The results are inconsistent with the fluctuating zero-field splitting (ZFS) mechanism, which is commonly invoked to explain electron spin relaxation for S> or =1 spins in liquid solution, and is the mechanism postulated in the literature for these systems. Instead, we find an Arrhenius temperature dependence for N@C60 , indicating the spin relaxation is driven primarily by an Orbach process. For the asymmetric N@C70 molecule, which has a permanent ZFS, we resolve an additional relaxation mechanism caused by the rapid reorientation of its ZFS. We also report the longest coherence time (T2) ever observed for a molecular electron spin, being 0.25 ms at 170 K.     

NMR paramagnetic relaxation of the spin 2 complex Mn(III)TSPP: a unique mechanism

The S = 2 complex, manganese(III) meso-tetra(4-sulfonatophenyl)porphine chloride (Mn(III)TSPP) is a highly efficient relaxation agent with respect to water protons and has been studied extensively as a possible MRI contrast agent. The NMR relaxation mechanism has several unique aspects, key among which is the unusual role of zero-field splitting (zfs) interactions and the effect of these interactions on the electron spin dynamics. The principal determinant of the shape of the R1 magnetic relaxation dispersion (MRD) profile is the tetragonal 4th-order zfs tensor component, B4(4), which splits the levels of the m(S) = +/-2 non-Kramers doublet. When the splitting due to B4(4) exceeds the Zeeman splitting, the matrix elements of (S(z)) are driven into coherent oscillation, with the result that the NMR paramagnetic relaxation enhancement is suppressed. To confirm the fundamental aspects of this mechanism, proton R1 MRD data have been collected on polyacrylamide gel samples in which Mn(III)TSPP is reorientationally immobilized. Solute immobilization suppresses time-dependence in the electron spin Hamiltonian that is caused by Brownian motion, simplifying the theoretical analysis. Simultaneous fits of both gel and solution data were achieved using a single set of parameters, all of which were known or tightly constrained from prior experiments except the 4th-order zfs parameter, B4(4), and the electron spin relaxation times, which were found to differ in the m(S) = +/-1 and m(S) = +/-2 doublet manifolds. In liquid samples, but not in the gels, the B4(4)-induced splitting of the m(S) = +/-2 non-Kramers doublet is partially collapsed due to Brownian motion. This phenomenon affects the magnitudes of both B4(4) and electron spin relaxation times in the liquid samples.     

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.     

三角晶场中4A2(3d3)态离子全组态EPR理论研究

在中间场耦合图像中,建立了4A2(3d3)态离子全组态EPR理论;研究了EPR参量随三角晶场参量V、V′及立方晶场参量Dq变化关系;用完全对角化方法验证了MacfarlaneEPR参量的三阶微扰公式,结果表明,在较大的晶场范围内微扰公式的收敛性很好;研究了EPR参量的微观起源及自旋二重态对EPR参量的贡献,指出自旋二重态对零场分裂参量的贡献不可忽略,二重态对g因子的贡献甚微.     

Spin-frustrated trinuclear Cu(II) clusters with mixing of 2(S = 1/2) and S = 3/2 states by antisymmetric exchange. 1. Dzialoshinsky-Moriya exchange contribution to zero-field splitting of the S = 3/2 state

The mixing of the spin-frustrated 2(S = 1/2) and S = 3/2 states by the Dzialoshinsky-Moriya (DM) exchange is considered for the Cu 3(II) clusters with strong DM exchange coupling. In the antiferromagnetic Cu 3 clusters with strong DM interaction, the 2(S = 1/2)-S = 3/2 mixing by the in-plane DM exchange ( G x ) results in the large positive contribution 2 D DM > 0 to the axial zero-field splitting (ZFS) 2 D of the S = 3/2 state. The correlations between the ZFS 2 D DM of the excited S = 3/2 state, sign of G z and chirality of the ground-state were obtained. In the isosceles Cu 3 clusters, the in-plane DM exchange mixing results in the rhombic magnetic anisotropy of the S = 3/2 state. Large distortions result in an inequality of the pair DM parameters, that leads to an additional magnetic anisotropy of the S = 3/2 state. In the {Cu 3} nanomagnet, the in-plane DM exchange (Gx, Gy) mixing results in the 58% contribution 2 D DM to the observed ZFS 2 D of the S = 3/2 state. The DM exchange and distortions explain the experimental observation that the intensities of the electron paramagnetic resonance (EPR) transitions arising from the 2(S = 1/2) group of levels of the {Cu 3} nanomagnet are comparable to each other and are 1 order of magnitude weaker than that of the S = 3/2 state. In the ferromagnetic Cu 3 clusters, the in-plane DM exchange mixing of the excited 2(S = 1/2) and the ground S = 3/2 states results in the large negative DM exchange contribution 2 D DM' < 0 to the axial ZFS 2 D of the ground S = 3/2 state.     

Joint analysis of ESR lineshapes and 1H NMRD profiles of DOTA-Gd derivatives by means of the slow motion theory

The "Swedish slow motion theory" [Nilsson and Kowalewski, J. Magn. Reson. 146, 345 (2000)] applied so far to Nuclear Magnetic Relaxation Dispersion (NMRD) profiles for solutions of transition metal ion complexes has been extended to ESR spectral analysis, including in addition g-tensor anisotropy effects. The extended theory has been applied to interpret in a consistent way (within one set of parameters) NMRD profiles and ESR spectra at 95 and 237 GHz for two Gd(III) complexes denoted as P760 and P792 (hydrophilic derivatives of DOTA-Gd, with molecular masses of 5.6 and 6.5 kDa, respectively). The goal is to verify the applicability of the commonly used pseudorotational model of the transient zero field splitting (ZFS). According to this model the transient ZFS is described by a tensor of a constant amplitude, defined in its own principal axes system, which changes its orientation with respect to the laboratory frame according to the isotropic diffusion equation with a characteristic time constant (correlation time) reflecting the time scale of the distortional motion. This unified interpretation of the ESR and NMRD leads to reasonable agreement with the experimental data, indicating that the pseudorotational model indeed captures the essential features of the electron spin dynamics.     

Explanation of spin-lattice relaxation rates of spin labels obtained with multifrequency saturation recovery EPR

Electron paramagnetic resonance (EPR) pulsed saturation recovery (pSR) measurements of spin-lattice relaxation rates have been made on nitroxide-containing fatty acids embedded in lipid bilayers by Hyde and co-workers. The data have been collected for a number of spin-labeled fatty acids at several microwave spectrometer frequencies (from 2 to 35 GHz). We compare these spin-lattice relaxation rates to those predicted by the Redfield theory incorporating several mechanisms. The dominant relaxation mechanism at low spectrometer frequencies is the electron-nuclear dipolar (END) process, with spin rotation (SR), chemical shift anisotropy (CSA), and a generalized spin diffusion (GSD) mechanism all contributing. The use of a wide range of spectrometer frequencies makes clear that the dynamics cannot be modeled adequately by rigid-body isotropic rotational motion. The dynamics of rigid-body anisotropic rotational motion is sufficient to explain the experimental relaxation rates within the experimental error. More refined models of the motion could have been considered, and our analysis does not rule them out. However, the results demonstrate that measurements at only two suitably chosen spectrometer frequencies are sufficient to distinguish anisotropic from isotropic motion. The results presented demonstrate that the principal mechanisms responsible for anisotropically driven spin-lattice relaxation are well understood in the liquids regime.     

Simulating electron spin resonance spectra of nitroxide spin labels from molecular dynamics and stochastic trajectories

Simulating electron spin resonance spectra of nitroxide spin labels from motional models is necessary for the quantitative analysis of experimental spectra. We present a framework for modeling the spin label dynamics by using trajectories such as those from molecular dynamics (MD) simulations combined with stochastic treatment of the global protein tumbling. This is achieved in the time domain after two efficient numerical integrators are developed: One for the quantal dynamics of the spins and the other for the classical rotational diffusion. For the quantal dynamics, we propagate the relevant part of the spin density matrix in Hilbert space. For the diffusional tumbling, we work with quaternions, which enables the treatment of anisotropic diffusion in a potential expanded as a sum of spherical harmonics. Time-averaging arguments are invoked to bridge the gap between the smaller time step of the MD trajectories and the larger time steps appropriate for the rotational diffusion and/or quantal spin dynamics.     

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.     

Electronic fine structure calculation of [Gd(DOTA)(H2O)]– using LF-DFT: The zero field splitting

Zerfo field splitting plays an important role in determining the electron spin relaxation of Gd(III) in solution. We understand the ZFS as an effect depending on the f electron structure and treat it in the framework of ligand field-density functional theory (LF-DFT). We apply this theory to calculate the ZFS of [Gd(DOTA)(H₂O)]^? from first principles, having an insight concerning the contributions determining the ZFS.     

On the interpretation of continuous wave electron spin resonance spectra of tempo-palmitate in 5-cyanobiphenyl

Electron spin resonance (ESR) measurements are highly informative on the dynamic behavior of molecules, which is of fundamental importance to understand their stability, biological functions and activities, and catalytic action. The wealth of dynamic information which can be extracted from a continuous wave electron spin resonance (cw-ESR) spectrum can be inferred by a basic theoretical approach defined within the stochastic Liouville equation formalism, i.e., the direct inclusion of motional dynamics in the form of stochastic (Fokker-Planck/diffusive) operators in the super Hamiltonian H governing the time evolution of the system. Modeling requires the characterization of magnetic parameters (e.g., hyperfine and Zeeman tensors) and the calculation of ESR observables in terms of spectral densities. The magnetic observables can be pursued by the employment of density functional theory which is apt, provided that hybrid functionals are employed, for the accurate computation of structural properties of molecular systems. Recently, an ab initio integrated computational approach to the in silico interpretation of cw-ESR spectra of multilabeled systems in isotropic fluids has been discussed. In this work we present the extension to the case of nematic liquid crystalline environments by performing simulations of the ESR spectra of the prototypical nitroxide probe 4-(hexadecanoyloxy)-2,2,6,6-tetramethylpiperidine-1-oxy in isotropic and nematic phases of 5-cyanobiphenyl. We first discuss the basic ingredients of the integrated approach, i.e., (1) determination of geometric and local magnetic parameters by quantum-mechanical calculations, taking into account the solvent and, when needed, the vibrational averaging contributions; (2) numerical solution of a stochastic Liouville equation in the presence of diffusive rotational dynamics, based on (3) parameterization of diffusion rotational tensor provided by a hydrodynamic model. Next we present simulated spectra with minimal resorting to fitting procedures, proving that the combination of sensitive ESR spectroscopy and sophisticated modeling can be highly helpful in providing three-dimensional structural and dynamic information on molecular systems in anisotropic environments.     

Molecular structure and dynamics of off-center Cu(2+) ions and strongly coupled Cu(2+)-Cu(2+) pairs in BaF(2) crystals: electron paramagnetic resonance and electron spin relaxation studies

X-band and Q-band electron paramagnetic resonance (EPR) spectra of Cu(2+) in BaF(2) crystal were recorded in the temperature range of 4.2-200 K. Spin-Hamiltonian parameters of single Cu(2+) complexes and of Cu(2+)-Cu(2+) pairs were derived and discussed. A special attention was paid to the dimeric species. Their molecular ground state configuration was found as having antiferromagnetic intradimer coupling with the singlet-triplet splitting J=-35 cm(-1). The zero-field splitting being D=0.0365 cm(-1) at 4.2 K increases with temperature as an effect of thermal population of excited dimer configurations. Electron spin echo (ESE) method was used for measurements of electron spin lattice and phase relaxation. The spin-lattice relaxation data show that except for coupling to the host lattice phonons the Cu(2+) ions are involved in local mode motions with energy of 82 cm(-1). Phase relaxation (ESE dephasing) of single Cu(2+) ions is due to spin diffusion at low temperatures. This relaxation is hampered for temperatures higher than 30 K due to the triplet state population of neighboring Cu(2+)-Cu(2+) dimers, which disturb dipolar coupling between Cu(2+) ions. For higher temperatures the relaxation is dominated by Raman T(1) processes. Fourier transform ESE spectrum displays dipolar Cu-F splitting which allowed determination of the off-center shift of Cu(2+) as delta(s)=0.132 nm. The dynamical effects observed in EPR spectra and in electron spin relaxation both for single Cu(2+) ions and Cu(2+)-Cu(2+) pairs are discussed as due to jumps between six off-center positions in the crystal unit cell and jumps between various dimer configurations.     

Two‐Step Thermal Spin Transition and LIESST Relaxation of the Polymeric Spin‐Crossover Compounds Fe(X‐py)2[Ag(CN)2]2 (X=H, 3‐methyl, 4‐methyl, 3,4‐dimethyl, 3‐Cl)

In the series of polymeric spin‐crossover compounds Fe(X‐py)₂[Ag(CN)₂)]₂ (py=pyridine, X=H, 3‐Cl, 3‐methyl, 4‐methyl, 3,4‐dimethyl), magnetic and calorimetric measurements have revealed that the conversion from the high‐spin (HS) to the low‐spin (LS) state occurs by two‐step transitions for three out of five members of the family (X=H, 4‐methyl, and X=3,4‐dimethyl). The two other compounds (X=3‐Cl and 3‐methyl) show respectively an incomplete spin transition and no transition at all, the latter remaining in the HS state in the whole temperature range. The spin‐crossover behaviour of the compound undergoing two‐step transitions is well described by a thermodynamic model that considers both steps. Calculations with this model show low cooperativity in this type of systems. Reflectivity and photomagnetic experiments reveal that all of the compounds except that with X=3‐methyl undergo light‐induced excited spin state trapping (LIESST) at low temperatures. Isothermal HS‐to‐LS relaxation curves at different temperatures support the low‐cooperativity character by following an exponential decay law, although in the thermally activated regime and for aX=H and X=3,4‐dimethyl the behaviour is well described by a double exponential function in accordance with the two‐step thermal spin transition. The thermodynamic parameters determined from this isothermal analysis were used for simulation of thermal relaxation curves, which nicely reproduce the experimental data.