Zero-field Splitting Interaction Research Articles

A novel non-adiabatic spin relaxation mechanism in molecular qubits.

The interaction of electronic spin and molecular vibrations mediated by spin-orbit coupling governs spin relaxation in molecular qubits. We derive an extended molecular spin Hamiltonian that includes both adiabatic and non-adiabatic spin-dependent interactions, and we implement the computation of its matrix elements using state-of-the-art density functional theory. The new molecular spin Hamiltonian contains a novel spin-vibrational orbit interaction with a non-adiabatic origin, together with the traditional molecular Zeeman and zero-field splitting interactions with an adiabatic origin. The spin-vibrational orbit interaction represents a non-Abelian Berry curvature on the ground-state electronic manifold and corresponds to an effective magnetic field in the electronic spin dynamics. We further develop a spin relaxation rate model that estimates the spin relaxation time via the two-phonon Raman process. An application of the extended molecular spin Hamiltonian together with the spin relaxation rate model to Cu(II) porphyrin, a prototypical S = 1/2 molecular qubit, demonstrates that the spin relaxation time at elevated temperatures is dominated by the non-adiabatic spin-vibrational orbit interaction. The computed spin relaxation rate and its magnetic field orientation dependence are in excellent agreement with experimental measurements.

High-Frequency EPR Studies of New 2p-3d Complexes Based on a Triazolyl-Substituted Nitronyl Nitroxide Radical: The Role of Exchange Anisotropy in a Cu-Radical System.

Using the 1-(m-tolyl)-1H-1,2,3-triazole-4-(4,4,5,5-tetramethylimidazoline-1-oxyl-3-oxide) (TlTrzNIT) radical and metal β-diketonate complexes [M(hfac)2(H2O)2], where hfac is hexafluoroacetylacetonato, three new 2p-3d heterospin complexes were synthesized. Their structures were solved using single crystal X-ray diffraction data, and magnetic investigation was performed by DC and AC measurements and multifrequency EPR spectroscopy. Compounds 1 and 2 are isostructural complexes with molecular formula [M3(TlTrzNIT)2(hfac)6] (MII = Mn or Cu) while compound 3 is the mononuclear [Co(TlTrzNIT)(hfac)2] complex. In all complexes, the radical acts as a bidentate ligand through the oxygen atom of the nitroxide moiety and the nitrogen atom from the triazole group. Furthermore, in compounds 1 and 2, the TlTrzNIT is bridge-coordinated between two metal centers, leading to the formation of trinuclear complexes. The fitting of the static magnetic behavior reveals antiferromagnetic and ferromagnetic intramolecular interactions for complexes 1 and 2, respectively. The EPR spectra of 1 are well described by an isolated ferrimagnetic S = 13/2 (= 5/2 - 1/2 + 5/2 - 1/2 + 5/2) ground state with a biaxial zero-field splitting (ZFS) interaction characterized, respectively, by 2nd order axial and rhombic parameters, D and E, such that E/D is close to the maximum of 0.33. Meanwhile, EPR spectra for 2 are explained in terms of a ferromagnetic model with weakly anisotropic Cu-radical exchange interactions, giving rise to an isolated S = 5/2 (= 5 × 1/2) ground state with both an anisotropic g tensor and a weak ZFS interaction. Complex 2 represents one of only a few examples of Cu-radical moieties with measurable exchange anisotropy.

Improved modelling of magnetic splitting in a chrome alum below 300 mK

Chrome-Caesium Alum (CCA) is a paramagnetic salt that can be used to achieve ultra-low temperature refrigeration through adiabatic demagnetization. Cooling capacity measurements of CCA show a significant reduction below the isolated paramagnetic spin model for temperatures below 100 mK. A more complete understanding of the thermodynamic properties of CCA could improve model accuracy, vital for meeting cooling requirements at subKelvin temperatures. Modelling effort was undertaken to understand the physical origin of this reduction in heat and refrigeration capacity, and measurements from two separate CCA salt pills between 50 mK and 300 mK were used for model validation. Both the model and the experimental design and results are discussed in this work. The model uses exact eigenvalues for the Cr3+ ions from the spin Hamiltonian. Two interactions of interest are the zero-field splitting and hyperfine splitting, as these are not standard in presently used models.We found that, though hyperfine interactions were not significant at temperatures above 50 mK, the inclusion of the zero-field splitting interaction resulted in qualitative agreement with the data. We optimized this model using a nonlinear least square regression to find the best fit to the two experimental data sets with two independent fitting parameters. Measured data at 50 mK still show a significant reduction below the fitted model prediction. Conductance measurements and thermal relaxation times were used to characterize addenda heat capacity and entropy loss due to non-adiabatic effects, which were not found to be significant. Accordingly, cooling capacity reduction below 50 mK cannot be accounted for by these effects. CCA is in the same chemical family as Chrome-Potassium Alum (CPA) which used widely in adiabatic demagnetization refrigerators. Thus, this modelling work described here is applicable to CPA. New measurements are planned to understand if the remaining discrepancy between the model and data is a systematic effect or a more fundamental feature of the salt.

EPR of Photoexcited Triplet-State Acceptor Porphyrins.

The photoexcited triplet states of porphyrin architectures are of significant interest in a wide range of fields including molecular wires, nonlinear optics, and molecular spintronics. Electron paramagnetic resonance (EPR) is a key spectroscopic tool in the characterization of these transient paramagnetic states singularly well suited to quantify spin delocalization. Previous work proposed a means of extracting the absolute signs of the zero-field splitting (ZFS) parameters, D and E, and triplet sublevel populations by transient continuous wave, hyperfine measurements, and magnetophotoselection. Here, we present challenges of this methodology for a series of meso-perfluoroalkyl-substituted zinc porphyrin monomers with orthorhombic symmetries, where interpretation of experimental data must proceed with caution and the validity of the assumptions used in the analysis must be scrutinized. The EPR data are discussed alongside quantum chemical calculations, employing both DFT and CASSCF methodologies. Despite some success of the latter in quantifying the magnitude of the ZFS interaction, the results clearly provide motivation to develop improved methods for ZFS calculations of highly delocalized organic triplet states.

Parallel-Mode EPR of Atomic Hydrogen Encapsulated in POSS Cages

In a typical EPR experiment, the transitions require that the static magnetic field $$B_0$$ is oriented perpendicular to the microwave field $$B_1$$ (perpendicular mode). This is determined by the transition rules either in the classical or in the quantum mechanical description. However, there are cases where EPR transitions are observed when $$B_0$$ is oriented parallel to $$B_1$$ (parallel mode). Quite numerous studies can be found in the literature where EPR transitions in both modes (dual-mode EPR) are feasible. In the majority of cases, dual-mode EPR studies are typically applied in $$S>1/2$$ systems where non-zero transition probabilities for the parallel mode are the result of the state mixing provided by the zero-field splitting interaction. On the other hand, the observation of parallel-mode EPR signals in $$S=1/2$$ systems becomes feasible when strong hyperfine interaction between the electronic and nuclear spin is present, as has been theoretically predicted for the hydrogen atom having a hyperfine coupling constant of $$A_0=1420$$ MHz (Weil in Concepts Magn Reson Part A 28:331, 2006). Herein, we report the first dual-mode X-band EPR experiments of hydrogen atom (both isotopes $$^1$$ H and $$^2$$ H) encapsulated in polyhedral oligomeric silsesquioxane cages. We extend the theory to the case of deuterium and we extract analytical formulas for transition probabilities. For the forbidden transitions, this study revealed a first-order dependence of resonance fields on the nuclear g-factor, $$g_{\mathrm{n}}$$ , and the existence of a clock transition with $$f=307$$ MHz.

Comprehensive investigation of the triplet state electronic structure of free-base 5,10,15,20-tetrakis(4-sulfonatophenyl)porphyrin by a combined advanced EPR and theoretical approach.

The nature of the photoexcited triplet state of free-base 5,10,15,20-tetrakis(4-sulfonatophenyl)porphyrin (H2TPPS4-) has been investigated by advanced Electron Paramagnetic Resonance (EPR) techniques combined with quantum chemical calculations. The zero-field splitting (ZFS) parameters, D and E, the orientation of the transition dipole moment in the ZFS tensor frame, and the proton hyperfine couplings have been determined by magnetophotoselection-EPR and pulse electron-nuclear double resonance spectroscopy. Both time-resolved and pulse experiments exploit the electron spin polarization of the photoexcited triplet state. Comparison of the magnetic observables with computational results, including CASSCF calculations of the ZFS interaction tensor, provides an accurate picture of the triplet-state electronic structure. The theoretical investigation has been integrated with a systematic analysis on the parent free-base porphyrin molecule to assess the effect of the sulfonatophenyl substituents on the magnetic tensors. Additionally, the magnetophotoselection effects are discussed in terms of tautomerization in the excited singlet state of H2TPPS4-.

Electrochemical Studies on Vanadyl Complex with meso-5,10,15,20-tetrakis(2,5-Dimethoxyphenyl) porphyrin using Electron Paramagnetic Resonance and Cyclic Voltammetry

The oxidation products of transition metal complexes with porphyrin are being examined currently by many research groups. meso- 5,10,15,20-tetrakis(2,5-Dimethoxyphenyl)porphyrin [T(2,5-(OCH3)2)PP] and its coordination compound with oxovanadium(IV) resulting in VO[T(2,5-(OCH3)2)PP] were prepared by the standard procedures. The resulting complex was characterized with or without the addition of antimony pentachloride by infrared (IR) spectroscopy, electron paramagnetic resonance (EPR) spectroscopy and cyclic voltammetry (CV). The UV-visible absorption spectrum of porphyrin ligand-based oxidation of vanadyl porphyrin VO[T(2,5-(OCH3)2)PP] in the presence of 0.5 mM SbCl5 has shown bands at 425, 540 and 650 nm. The final electro-oxidation product has a broad absorption band centered at 650 nm. It is characteristic of a porphyrin mono- cation which is seen due to oxidation at 0.0995V of ΔE value in the cyclic voltammogram of VO[T(2,5-(OCH3)2)PP]. These spectral features observed during the oxidation are in good agreement with the stepwise formation of mono-cation radical and di-cation. The EPR spectrum of VO[T(2,5-(OCH3)2)PP] suggests that it could be oxidized to the radical cation by oxidation with SbCl5 in dichloromethane. A radical cation is observed at low temperature and this spectrum corresponds to monomeric π-cation radical. A spectrum of fifteen lines is observed on the further addition of SbCl5 in dichloromethane. Thus, monomeric π-cation radical is recognized as [VO(TPP)]+. It is confirmed by the appearance of a new band at 1275 cm-1 in the IR spectrum. Zero field splitting (ZFS) was calculated from the triplet state on the EPR spectrum. It is suggested that ZFS interaction occurs from the dipolar coupling between the two electrons. Keywords: meso-Vanadyl porphyri

Synthesis and electron paramagnetic resonance studies of seven coordinated Mn(II) complexes with tridentate N-donor ligands

The reactions of Mn(NO3)2·4H2O with the heterocyclic aromatic ligands 2,3,5,6-tetrakis(2-pyridyl)pyrazine (tppz), 2,4,6-tri(2-pyridyl)-1,3,5-triazine (tptz) and 2,6-bis(pyrazol-1-yl)pyridine (bppy) in MeOH gave the cationic complexes [Mn(L)(NO3)(MeOH)2](NO3) (L = tppz (1), tptz (3), bppy (5)) and the neutral complexes [Mn(L)(NO3)2(S)] (L = tppz, S = H2O (2); L = tptz, S = MeOH (4); L = bppy, S = MeOH (6)), all of which contain the MnII ion in the rare seven-coordinate pentagonal bipyramidal geometry (the crystal structure of 6 contains also a MnII complex showing the rare eight-coordinate triangular dodecahedron geometry). The reactions of Mn(ClO4)2·6H2O with tptz and bppy in MeCN gave [Mn(tptz)(H2O)2(MeCN)](ClO4)2 (7) and [Mn(bppy)2](ClO4)2 (8), in which the MnII ion exhibits six-coordination. Electron Paramagnetic Resonance spectroscopy at X- and Q-band on powder samples was used in order to determine the zero field splitting (ZFS) parameters for 1–4 and 7, 8. All complexes exhibit ZFS parameter, |D| in the range 0.08–0.11 cm−1. The experimentally determined values are in agreement with theoretical calculations which reveal the contribution of each mechanism responsible for the ZFS interaction. The present results add further evidence that for seven-coordinated MnII complexes comprising N/O ligands ZFS is comparable to this found in six-coordinated MnII complexes.

Relativistic Approximations to Paramagnetic NMR Chemical Shift and Shielding Anisotropy in Transition Metal Systems.

We apply approximate relativistic methods to calculate the magnetic property tensors, i.e., the g-tensor, zero-field splitting (ZFS) tensor (D), and hyperfine coupling (HFC) tensors, for the purpose of constructing paramagnetic nuclear magnetic resonance (pNMR) shielding tensors. The chemical shift and shielding anisotropy are calculated by applying a modern implementation of the classic Kurland-McGarvey theory ( J. Magn. Reson. 1970 , 2 , 286 ), which formulates the shielding tensor in terms of the g- and HFC tensors obtained for the ground multiplet, in the case of higher than doublet multiplicity defined by the ZFS interaction. The g- and ZFS tensors are calculated by ab initio complete active space self-consistent field and N-electron valence-state perturbation theory methods with spin-orbit (SO) effects treated via quasidegenerate perturbation theory. Results obtained with the scalar relativistic (SR) Douglas-Kroll-Hess Hamiltonian used for the g- and ZFS tensor calculations are compared with nonrelativistically based computations. The HFC tensors computed using the fully relativistic four-component matrix Dirac-Kohn-Sham approach are contrasted against perturbationally SO-corrected nonrelativistic results in the density functional theory framework. These approximations are applied on paramagnetic metallocenes (MCp2) (M = Ni, Cr, V, Mn, Co, Rh, Ir), a Co(II) pyrazolylborate complex, and a Cr(III) complex. SR effects are found to be small for g and D in these systems. The HFCs are found to be more influenced by relativistic effects for the 3d systems. However, for some of the 3d complexes, nonrelativistic calculations give a reasonable agreement with the experimental chemical shift and shielding anisotropy. The influence of scalar relativity is strong for the 5d IrCp2 system. This mixed ab initio/DFT technique, with a fully relativistic method used for the critical HFC tensor, should be useful for the treatment of both electron correlation and relativistic effects at a reasonable computational cost to compute the pNMR shielding tensors in transition metal systems.

Möbius–Hückel Topology Switching in Expanded Porphyrins: EPR, ENDOR, and DFT Studies of Doublet and Triplet Open-Shell Systems

The one-sided Mobius band topology with its characteristic 180° twist has fascinated and inspired philosophers, artists and scientists since a long time. On the molecular level, only in the last 13 years a few chemistry groups succeeded to artificially create novel compounds with Mobius symmetry by theory-based molecular design and elaborate chemical synthesis. The interest in molecules with Mobius band symmetry was greatly stimulated in 1964 by a theoretical paper by Edgar Heilbronner from the ETH Zurich. He predicted that sufficiently large [n]annulenes with a closed-shell electron configuration of 4n π-electrons should allow for sufficient π-overlap stabilization to be synthesizable by twisting them into the Mobius topology of their hydrocarbon skeleton. In 2003, the first synthesis of an aromatic Mobius annulene was accomplished by Rainer Herges and co-workers in Kiel. In 2007, Lechoslaw Latos-Grazynski and co-workers in Wroclaw succeeded in synthesizing free-base di-p-benzi (Yoneda et al., Angew Chem Int Ed 53: 13169–13173, 2014) hexaphyrin (1.1.1.1.1.1), compound 1, an expanded porphyrin which can dynamically switch between Huckel and Mobius conjugation upon changes of solvent and temperature. Shortly thereafter, in 2008, Atsuhiro Osuka and his co-workers from Kyoto, Seoul and Hyogo published the synthesis of an expanded porphyrin in which metalation triggered the production of molecular twisting and Mobius aromaticity. In this minireview, among other studies also our recent EPR, ENDOR and DFT studies on open-shell states of 1, i.e., on the ground-state radical cation doublet state (total electron spin S = 1/2) and the first excited triplet state (S = 1) are summarized. The review is largely based on a previous joint publication of the current authors with the Latos-Grazynski group on radical cations of 1 (Mobius et al., Phys Chem Chem Phys 17:6644–6652, 2015). The radical cation study was the first one of an open-shell π-system with Mobius topology. In the doublet state, the hyperfine interactions of the unpaired electron spin with specific magnetic nuclei in the molecule was used as a sensitive probe for the electronic structure of the molecule and its symmetry properties. This work has now been extended to state-of-the-art DFT theory studies on photo-excited triplet states of 1. In the open-shell triplet state, besides hyperfine couplings, a change of the zero-field splitting interaction between the two unpaired electron spins is predicted to be a viable sensor for electronic structure changes upon Mobius-to-Huckel topology switching.

Construction of Giant-Spin Hamiltonians from Many-Spin Hamiltonians by Third-Order Perturbation Theory and Application to an Fe3 Cr Single-Molecule Magnet.

A general giant-spin Hamiltonian (GSH) describing an effective spin multiplet of an exchange-coupled metal cluster with dominant Heisenberg interactions was derived from a many-spin Hamiltonian (MSH) by treating anisotropic interactions at the third order of perturbation theory. Going beyond the existing second-order perturbation treatment allows irreducible tensor operators of rank six (or corresponding Stevens operator equivalents) in the GSH to be obtained. Such terms were found to be of crucial importance for the fitting of high-field EPR spectra of a number of single-molecule magnets (SMMs). Also, recent magnetization measurements on trigonal and tetragonal SMMs have found the inclusion of such high-rank axial and transverse terms to be necessary to account for experimental data in terms of giant-spin models. While mixing of spin multiplets by local zero-field splitting interactions was identified as the major origin of these contributions to the GSH, a direct and efficient microscopic explanation had been lacking. The third-order approach developed in this work is used to illustrate the mapping of an MSH onto a GSH for an S=6 trigonal Fe3 Cr complex that was recently investigated by high-field EPR spectroscopy. Comparisons between MSH and GSH consider the simulation of EPR data with both Hamiltonians, as well as locations of diabolical points (conical intersections) in magnetic-field space. The results question the ability of present high-field EPR techniques to determine high-rank zero-field splitting terms uniquely, and lead to a revision of the experimental GSH parameters of the Fe3 Cr SMM. Indeed, a bidirectional mapping between MSH and GSH effectively constrains the number of free parameters in the GSH. This notion may in the future facilitate spectral fitting for highly symmetric SMMs.

Folding process of silk fibroin induced by ferric and ferrous ions

Bombyx mori silk fiber has useful mechanical properties largely due to a high content of ordered β-sheet crystallites separated by non-crystalline spacers. Metallic ions present in the silk dope in nature could affect the β-sheet content. In this work, we used solid-state 13C NMR, EPR and Raman spectroscopy to investigate how the ferric/ferrous ions affect the folding process of the silk fibroin. NMR and Raman results indicate that ferric and ferrous ions have different effects on the secondary structure of silk fibroin. Ferric ions can induce a conformation change from helix to β-sheet form in silk fibroin when their concentration exceeds a critical value, while ferrous ions cannot. EPR results indicate that the ferric ions bound with silk fibroin have a high-spin state ( S = 5/2) with g-value of g 1 = 1.950, g 2 = 1.990 and g 3 = 1.995, zero-field splitting interaction D of 1.2–2 cm −1, and symmetric character of E/ D = 1/3, resulting in an effective g-value of g′ = 4.25. The hydrophilic spacer GTGSSGFGPYVAN(H)GGYSGYEYAWSSESDFGT in the heavy chain of silk fibroin is likely to be involved in the binding of ferric ions, and His, Asn and Tyr residues are considered as the potential binding sites.

Magnetic quantum tunneling: key insights from multi-dimensional high-field EPR

Multi-dimensional high-field/frequency electron paramagnetic resonance (HFEPR) spectroscopy is performed on single-crystals of the high-symmetry spin S = 4 tetranuclear single-molecule magnet (SMM) [Ni(hmp)(dmb)Cl](4), where hmp(-) is the anion of 2-hydroxymethylpyridine and dmb is 3,3-dimethyl-1-butanol. Measurements performed as a function of the applied magnetic field strength and its orientation within the hard-plane reveal the four-fold behavior associated with the fourth order transverse zero-field splitting (ZFS) interaction, (1/2)B(S + S), within the framework of a rigid spin approximation (with S = 4). This ZFS interaction mixes the m(s) = +/-4 ground states in second order of perturbation, generating a sizeable (12 MHz) tunnel splitting, which explains the fast magnetic quantum tunneling in this SMM. Meanwhile, multi-frequency measurements performed with the field parallel to the easy-axis reveal HFEPR transitions associated with excited spin multiplets (S < 4). Analysis of the temperature dependence of the intensities of these transitions enables determination of the isotropic Heisenberg exchange constant, J = -6.0 cm(-1), which couples the four spin s = 1 Ni(II) ions within the cluster, as well as a characterization of the ZFS within excited states. The combined experimental studies support recent work indicating that the fourth order anisotropy associated with the S = 4 state originates from second order ZFS interactions associated with the individual Ni(II) centers, but only as a result of higher-order processes that occur via S-mixing between the ground state and higher-lying (S < 4) spin multiplets. We argue that this S-mixing plays an important role in the low-temperature quantum dynamics associated with many other well known SMMs.

A theoretical spin relaxation and molecular dynamics simulation study of the Gd(H2O)93+ complex

A theoretical analysis of the paramagnetically enhanced water proton spin-lattice relaxation of a hydrated Gd(3+) ion is combined with Molecular Dynamics (MD) simulations. The electron-proton dipole-dipole correlation function, C(p)(DD)(tau), as well as the pseudo-rotation (PR) model of the transient zero-field splitting (ZFS) are evaluated with the help of the data from MD simulations. The fast local water motion in the first hydration shell, i.e. the wagging and rocking motions, is found not to change the mono exponential character of the dipole correlation function C(p)(DD)(tau), but is important in the time dependence of the transient ZFS interaction. The dynamics of the transient ZFS interaction is modeled as the water-induced electric field gradient tensor at the site of the metal ion. This approach follows the ideas of the pseudo-rotation model, describing the fluctuating zero-field interaction as a constant amplitude in the principal frame but reorienting according to a rotational diffusion equation of motion. The MD results indicate that the pseudo-rotation model gives a multi-exponential correlation function which oscillates at short times and is described by three exponential terms. The time scale is shorter than previously assumed but contain an intermediate time constant (1-2 ps). The electron spin resonance (ESR) spectral width at half height at frequencies of X-band, Q-band, 75 MHz, 150 MHz and 225 MHz can be reproduced at 320 K without any contributions from 4th or 6th rank ZFS interactions. Consequently, there are two mutually inconsistent dynamic models of the ZFS interaction which can describe the water proton T(1)-NMRD (nuclear magnetic resonance dispersion) profile and the field dependent ESR spectra of the hydrated Gd(III) complex equally well.

Origin of magnetization tunneling in single-molecule magnets as determined by single-crystal high-frequency EPR

We review an extensive body of single-crystal high-frequency electron paramagnetic resonance (HFEPR) data in order to determine the transverse spin Hamiltonian parameters that control the tunneling of the direction of magnetization in a variety of integer and half-integer-spin single-molecule magnets (SMMs). The SMMs studied are members of the following families: S = 9/2 [Mn 4O 3Cl] 6+; S = 5 [Mn 3NiO 4] 6+; S = 6 [Mn 3ZnO 4] 6+; and S = 4 [Ni 4(OR) 4] 4+. HFEPR spectra for the half-integer S = 9/2 Mn 4 complexes that have C 3 symmetry do not provide measurable evidence for transverse spin Hamiltonian terms. This finding is consistent with the relatively large coercive field seen in the magnetization hysteresis loops for these complexes. On the other hand, a low symmetry S = 9/2 complex exhibits a much faster rate of ground-state magnetization tunneling, in agreement with HFEPR spectra for a powder sample that gives a rhombic zero-field splitting (ZFS) parameter of E = 0.140 cm −1. The S = 5 Mn 3Ni systems exhibit magnetization tunneling that is much faster than seen for the high-symmetry S = 9/2 Mn 4 complexes. This can be attributed to their integer-spin ground states. Like the C 3 symmetry Mn 4 SMMs, the HFEPR spectra for high-symmetry Mn 3Ni complexes do not provide measurable evidence for transverse ZFS terms. However, the spectra exhibit broad peaks, suggesting distributions in the local molecular environments brought about by disordered solvate molecules. This disorder likely explains the fast tunneling in the high-symmetry S = 5 Mn 3Ni systems, though one cannot rule out fourth- (and higher-) order interactions that cannot be detected by HFEPR due to the broad resonances. The one S = 6 Mn 3Zn complex shows an even faster rate of tunneling compared to the isostructural S = 5 Mn 3Ni complex. Finally, the S = 4 [Ni(hmp)(dmb)Cl] 4 complex provides unique insights into the origin of fourth- (and higher-) order interactions found for many SMMs on the basis of analysis using a giant spin Hamiltonian (GSH) approximation. We conclude that the fourth-order anisotropy found for the S = 4 ground state of [Ni(hmp)(dmb)Cl] 4 originates from the second-order ZFS interactions associated with the individual Ni II ions, but only as a result of higher-order processes that occur via S-mixing between the ground state and higher-lying ( S < 4) spin-multiplets. The S-mixing is relatively strong in this system because of comparable exchange and anisotropy energy scales. The relatively fast tunneling is a direct consequence of this S-mixing, as opposed to any intrinsic fourth-order (spin–orbit) anisotropy associated with Ni II.

Single Crystal 55Mn ENDOR of Concanavalin A: Detection of Two Mn2+ Sites with Different 55Mn Quadrupole Tensors

Concanavalin A is a member of the plant hemeagglutinin (or plant lectin) family that contains two metal binding sites; one, called S1, is occupied by Mn2+ and the other, S2, by Ca2+. 55Mn electron-nuclear double resonance (ENDOR) measurements were performed on a single crystal of concanavalin A at W-band (95 GHz, ~3.5 T) to determine the 55Mn nuclear quadrupole interaction in a protein binding site and its relation to structural parameters. Such measurements are easier at a high field because of the high sensitivity for size-limited samples and the reduction of second-order effects on the spectrum which simplifies spectral analysis. The analysis of the 55Mn ENDOR rotation patterns showed that two chemically inequivalent Mn2+ types are present at low temperatures, although the high-resolution X-ray structure reported only one site. Their quadrupole coupling constants, e2Qq/h, are significantly different; 10.7 +/- 0.6 MHz for Mand only -2.7 +/-0.6 MHz for M. The ENDOR data also refined the hyperfine coupling determined earlier by single-crystal EPR measurements, yielding a small but significant difference between the two: -262.5 MHz for M and -263.5 MHz for M. The principal z-axis for M is not aligned with any of the Mn-ligand directions, but is 25 off the Mn-asp10 direction, and its orientation is different than that of the zero-field splitting (ZFS) interaction. Because of the small quadrupole interaction of M the orientation dependence was very mild, leading to larger uncertainties in the asymmetry parameter. Nonetheless, there too z is not along the Mn-ligand bonds and is rotated 90 with respect to MnA. These results show, that similar to the ZFS, the quadrupolar interaction is highly sensitive to small differences in the coordination sphere of the Mn2+, and the resolution of the two types is in agreement with the earlier observation of a two-site conformational dynamic detected through the ZFS interaction, which is frozen out at low temperatures and averaged at room temperature. To account for the structural origin of the different e2Qq/h values, the electric field gradient tensor was calculated using the point-charge model. The calculations showed that a relatively small displacement of the oxygen ligand of asp10 can lead to differences on the order observed experimentally.

Direct calculation of1H2O T1NMRD 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 multifrequency EPR approach to travertine characterisation

The understanding of processes that give rise to travertine deposits is important. This is so because of its widespread use as decorative material, but more so in environmental studies due to the significance, by proxy, of travertine in climatology. In this paper, a multifrequency EPR spectroscopy study of the behaviour of an ubiquitary vicariant of Ca in calcite, Mn(II), is presented. EPR spectra were obtained from a natural sample at 9.5 (X-band), 95, 190, and 285 GHz, and interpreted through numerical simulation. An analysis of the distribution of the zero-field splitting interaction revealed the source of some unexpected spectral features in the width of the lines in the X-band. By contrast, the homogeneous broadening plays only a minor role. Moreover, field-dependent anisotropies of the Zeeman and hyperfine tensors were observed at higher frequency. On the basis of results garnered in this study, the ZFS interaction of Mn(II) has been ascribed to the microstructural anomalies of the Mn(II) distribution in calcite. This may be considered as the fingerprint of the physical–chemical conditions at the time of travertine deposition. As a consequence, X-band EPR spectroscopy represents a specific tool to investigate the genesis, and to check the homogeneity of Mn(II) distribution in travertines as well as in other calcite-based materials.

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.

The viscosity and temperature dependence of 1H T1-NMRD of the Gd(H 2O) 83+ complex

Water proton T 1-NMRD profiles of the Gd(H 2O) 8 3+ complex have been recorded at three temperatures and at four concentrations of glycerol. The analysis is performed using both the generalized Solomon–Bloembergen–Morgan (GSBM) theory [J. Magn. Reson. 167(2004), 147–160], and the stochastic Liouville approach (SLA). The GSBM approach uses a two processes dynamic model of the zero-field splitting (ZFS) correlation function whereas SLA uses a single process model. Both models reproduce the proton T 1-NMRD profiles well. However, the model parameters extracted from the two analyses, yield different ESR X-band spectra which moreover do not reproduce the experimental ESR spectra. It is shown that the analyses of the proton T 1-NMRD profiles recorded for a solution Gd(H 2O) 8 3+ ions are relatively insensitive to the slow modulation part of dynamic model of the ZFS interaction correlation function. The description of the electron spin system results in a very small static ZFS, while recent ESR lineshape analysis indicates that the contribution from the static ZFS is important. Analysis of proton T 1-NMRD profiles of Gd(H 2O) 8 3+ complex do result in a description of the electron spin system but these microscopic parameters are uncertain unless they also are tested in a ESR-lineshape analysis.