Coupling Tensors Research Articles

NMR interaction tensors of 51V and 207Pb in vanadinite, Pb5(VO4)3Cl, determined from DFT calculations and single-crystal NMR measurements, using only one general rotation axis

Orientation-dependent NMR spectra of a single crystal of the mineral vanadinite, Pb5(VO4)3Cl, were acquired using only one rotation axis with a general orientation in the hexagonal crystal lattice (space group P63/m). The chemical shift (CS) tensors for the 207Pb on Wyckoff positions 6h and 4f, and both CS and quadrupole coupling tensor Q for 51V at the positions 6h were determined by including the NMR response of symmetry-related atoms in the unit cell (and in case of 207Pb at 4f, also the isotropic shift from MAS NMR spectra). This previously suggested ’single rotation method’ greatly reduces the necessary amount of data acquisition and analysis. The precise orientation of the rotation axis could not be found by X-ray diffraction experiments because of the high linear absorption coefficient of vanadinite, which is chiefly due to its high lead content. The axis orientation was therefore included into the multi-parameter data fit routine. This NMR-based approach is widely applicable, and offers an alternative way of orienting single crystals. The NMR parameters derived from the tensor eigenvalues are δiso=(−1729±9) ppm, Δδ=(−1071±5) ppm, ηCS=0.362±0.008 for 207Pb at positions 6h, and δiso=(−1619±2) ppm, Δδ=(−780±58) ppm, ηCS=0.06±0.08 for positions 4f. For 51V, δiso=(−509±3) ppm, Δδ=(−37±2) ppm, ηCS=0.78±0.09, with the quadrupolar coupling described by χ=(2.52±0.01) MHz and ηQ=0.047±0.003. In contrast to the precisely determined tensor eigenvalues, the orientation of the eigenvectors in the crystal ab -plane of the vanadinite system could only be resolved by resorting to data obtained from density functional theory (DFT) calculations.

Relativistic DFT Calculations of Hyperfine Coupling Constants in 5d Hexafluorido Complexes: [ReF6 ]2- and [IrF6 ]2.

The performance of relativistic density functional theory (DFT) methods has been investigated for the calculation of the recently measured hyperfine coupling constants of hexafluorido complexes [ReF6]2− and [IrF6]2−. Three relativistic methods were employed at the DFT level of theory: the 2‐component zeroth‐order regular approximation (ZORA) method, in which the spin–orbit coupling was treated either variationally (EV ZORA) or as a perturbation (LR ZORA), and the 4‐component Dirac–Kohn–Sham (DKS) method. The dependence of the results on the basis set and the choice of exchange‐correlation functional was studied. Furthermore, the effect of varying the amount of Hartree–Fock exchange in the hybrid functionals was investigated. The LR ZORA and DKS methods combined with DFT led to very similar deviations (about 20 %) from the experimental values for the coupling constant of complex [ReF6]2− by using hybrid functionals. However, none of the methods were able to reproduce the large anisotropy of the hyperfine coupling tensor of complex [ReF6]2−. For [IrF6]2−, the EV ZORA and DKS methods reproduced the experimental tensor components with deviations of ≈10 and ≈5 % for the hybrid functionals, whereas the LR ZORA method predicted the coupling constant to be around one order of magnitude too large owing to the combination of large spin–orbit coupling and very low excitation energies.

Electromagnetic δ -function sphere

We develop a formalism to extend our previous work on the electromagnetic $\delta$-function plates to a spherical surface. The electric ($\lambda_e$) and magnetic ($\lambda_g$) couplings to the surface are through $\delta$-function potentials defining the dielectric permittivity and the diamagnetic permeability, with two anisotropic coupling tensors. The formalism incorporates dispersion. The electromagnetic Green's dyadic breaks up into transverse electric and transverse magnetic parts. We derive the Casimir interaction energy between two concentric $\delta$-function spheres in this formalism and show that it has the correct asymptotic flat plate limit. We systematically derive expressions for the Casimir self-energy and the total stress on a spherical shell using a $\delta$-function potential, properly regulated by temporal and spatial point-splitting, which are different from the conventional temporal point-splitting. In strong coupling, we recover the usual result for the perfectly conducting spherical shell but in addition, there is an integrated curvature-squared divergent contribution. For finite coupling, there are additional divergent contributions; in particular, there is a familiar logarithmic divergence occurring in the third order of the uniform asymptotic expansion that renders it impossible to extract a unique finite energy except in the case of an isorefractive sphere, which translates into $\lambda_g=-\lambda_e$.

The DFT Calculations of Structures and EPR Parameters for the Dinuclear Paddle-Wheel Copper(II) Complex {Cu2(μ2-O2CCH3)4}(OCNH2CH3) as Powder or Single Crystal

Abstract Density functional theory (DFT) calculations of the structures and the Cu2+ g factors (g x , g y and g z ) and hyperfine coupling tensor A (A x , A y and A z ) were performed for the paddle-wheel (PW)-type binuclear copper(II) complex {Cu2(μ2-O2CCH3)4}(OCNH2CH3) powder and single crystal. Calculations were carried out with the ORCA software using the functionals BHandHlyp, B3P86 and B3LYP with five different basis sets: 6-311g, 6-311g(d,p), VTZ, def-2 and def2-TZVP. Results were tested by the MPAD analysis to find the most suitable functional and basis sets. The electronic structure and covalency between copper and oxygen were investigated by the electron localisation function and the localised orbital locator as well as the Mayer bond order for the [CuO5] group. The optical spectra were theoretically calculated by the time-dependent DFT module and plotted by the Multiwfn program for the [CuO5] group and reasonably associated with the local structure in the vicinity of the central ion copper. In addition, the interactions between the OCNH2CH3, NH3 and H2O molecules and the uncoordinated PW copper(II) complex were studied, and the corresponding adsorption energies, the frequency shifts with respect to the free molecules and the changes of the Cu–Cu distances were calculated and compared with the relevant systems.

Origins of Willis coupling and acoustic bianisotropy in acoustic metamaterials through source-driven homogenization

In addition to conventional acoustic properties (mass density and compressibility), recent research has shown that inhomogeneous acoustic media may require coupling tensors between effective volume strain and momentum fields. These coupling tensors imply conversion between monopolar and dipolar motion in the effective material response. Intrinsic coupling between strain and momentum is known as Willis coupling in elastodynamics, and it is analogous to bianisotropy in electromagnetism. This paper investigates the microscale and mesoscale effects that lead to Willis coupling, studies the proper homogenization of acoustic metamaterials with non-negligible Willis coupling, and demonstrates the impact of Willis coupling on defining physically meaningful effective material parameters.

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.

Nuclear quadrupole coupling in SiH2I2 due to the presence of two iodine nuclei

The rotational spectrum of diiodosilane was measured with a jet-pulsed, cavity Fourier transform microwave (FTMW) spectrometer over the frequency range 8.8–15GHz and assigned for the first time. The complete nuclear quadrupole coupling (NQC) tensors for both iodine nuclei were obtained for the 28Si, 29Si, and 30Si isotopologues of diiodosilane. In addition to the nuclear quadrupole coupling constants (NQCCs), rotational constants, centrifugal distortion constants, and nuclear spin-rotation constants were determined for each silicon isotopologue. Subtle, yet unmistakable, changes in the NQCCs of iodine upon isotopic substitution were observed and will be discussed. A r0 structure of diiodosilane was also fit via isotopic substitution, which led to the determination of bond lengths and angles: r0(SiI)=2.4236(19)Å, r0(SiH)=1.475(21)Å, ∠(ISiI)=111.27(13)°, and ∠(ISiH)=105.9(19)°. These molecular parameters will be compared to the results of a previous gas electron diffraction study.

Charge Transfer Processes in OPV Materials as Revealed by EPR Spectroscopy

Understanding charge separation and charge transport at a molecular level is crucial for improving the efficiency of organic photovoltaic (OPV) cells. Under illumination of Bulk Heterojunction (BHJ) blends of polymers and fullerenes, various paramagnetic species are formed including polymer and fullerene radicals, radical pairs, and photoexcited triplet states. Light‐induced Electron Paramagnetic Resonance (EPR) spectroscopy is ideally suited to study these states in BHJ due to its selectivity in probing the paramagnetic intermediates. Advanced techniques like pulsed EPR and ENDOR spectroscopy allow the determination of hyperfine coupling tensors, while high‐frequency EPR allows the EPR signals of the individual species to be resolved and their g‐tensors to be determined. The magnetic resonance parameters of the various polymer donors reveal details about the delocalization of the positive polaron which is important for the efficient charge separation in BHJ systems. Time‐resolved EPR can contribute to the study of the dynamics of charge separation, charge transfer and recombination in BHJ by probing the unique spectral signatures of charge transfer and triplet states. EPR also has the potential to allow characterization of intermediates and products of BHJ degradation.

Paramagnetic Enhancement of Nuclear Spin-Spin Coupling.

We present a derivation and computations of the paramagnetic enhancement of the nuclear magnetic resonance (NMR) spin-spin coupling, which may be expressed in terms of the hyperfine coupling (HFC) and (for systems with multiple unpaired electrons) zero-field splitting (ZFS) tensors. This enhancement is formally analogous to the hyperfine contributions to the NMR shielding tensor as formulated by Kurland and McGarvey. The significance of the spin-spin coupling enhancement is demonstrated by using a combination of density-functional theory and correlated ab initio calculations, to determine the HFC and ZFS tensors, respectively, for two paramagnetic 3d metallocenes, a CrII(acac)2 complex, a Co(II) pyrazolylborate complex, and a lanthanide system, Gd-DOTA. Particular attention is paid to relativistic effects in HFC tensors, which are calculated using two methods: a nonrelativistic method supplemented by perturbational spin-orbit coupling corrections, and a fully relativistic, four-component matrix-Dirac-Kohn-Sham approach. The paramagnetic enhancement lacks a direct dependence on the distance between the coupled nuclei, and represents more the strength and orientation of the individual hyperfine couplings of the two nuclei to the spin density distribution. Therefore, the enhancement gains relative importance as compared to conventional coupling as the distance between the nuclei increases, or generally in the cases where the conventional coupling mechanisms result in a small value. With the development of the experimental techniques of paramagnetic NMR, the more significant enhancements, e.g., of the 13C13C couplings in the Gd-DOTA complex (as large as 9.4 Hz), may eventually become important.

Antisymmetric Couplings Enable Direct Observation of Chirality in Nuclear Magnetic Resonance Spectroscopy.

Here we demonstrate that a term in the nuclear spin Hamiltonian, the antisymmetric J-coupling, is fundamentally connected to molecular chirality. We propose and simulate a nuclear magnetic resonance (NMR) experiment to observe this interaction and differentiate between enantiomers without adding any additional chiral agent to the sample. The antisymmetric J-coupling may be observed in the presence of molecular orientation by an external electric field. The opposite parity of the antisymmetric coupling tensor and the molecular electric dipole moment yields a sign change of the observed coupling between enantiomers. We show how this sign change influences the phase of the NMR spectrum and may be used to discriminate between enantiomers.

Transparent anisotropy for the relaxed micromorphic model: Macroscopic consistency conditions and long wave length asymptotics

In this paper, we study the anisotropy classes of the fourth order elastic tensors of the relaxed micromorphic model, also introducing their second order counterpart by using a Voigt-type vector notation. In strong contrast with the usual micromorphic theories, in our relaxed micromorphic model only classical elasticity-tensors with at most 21 independent components are studied together with rotational coupling tensors with at most 6 independent components. We show that in the limit case Lc → 0 (which corresponds to considering very large specimens of a microstructured metamaterial) the meso- and micro-coefficients of the relaxed model can be put in direct relation with the macroscopic stiffness of the medium via a fundamental homogenization formula. We also show that a similar homogenization formula is not possible in the case of the standard Mindlin-Eringen-format of the anisotropic micromorphic model. Our results allow us to forecast the successful short term application of the relaxed micromorphic model to the characterization of anisotropic mechanical metamaterials.

Solid-state 17O NMR study of 2-acylbenzoic acids and warfarin

We report synthesis and solid-state 17O NMR characterization of four site-specifically 17O-labeled 2-acylbenzoic acids (2-RC(O)C6H4COOH) where R=H and CH3): 2-[3-17O]formylbenzoic acid, 2-[1,2-17O2]formylbenzoic acid, 2-[3-17O]acetylbenzoic acid, and 2-[1,2,3-17O3]acetylbenzoic acid. In the solid state, both 2-formyl- and 2-acetyl-benzoic acids exist as the cyclic phthalide form each containing a five-membered lactone ring and a cyclic hemiacetal/hemiketal group. Static and magic-angle-spinning 17O NMR spectra were recorded at 14.1 and 21.1T for these compounds, from which the 17O chemical shift and nuclear quadrupolar coupling tensors were determined for each oxygen site. These results represent the first time that 17O NMR tensors are fully characterized for lactone, cyclic hemiacetal, and cyclic hemiketal functional groups. We also report solid-state 17O NMR data for the cyclic hemiketal group an anticoagulant drug, warfarin. Experimental 17O NMR tensors in these compounds were compared with computational results obtained with a periodic DFT code BAND.

Hyperfine interactions and internal rotation in methanol.

We present a rigorous derivation of the nuclear spin-rotation and spin-torsion coupling terms in the hyperfine Hamiltonian for molecules with internal rotation. Our formulas differ from the expressions derived by Heuvel and Dymanus [J. Mol. Spectrosc. 47, 363 (1973)], which these authors used and which were also applied recently by others to interpret experimental hyperfine spectra of such molecules. In the present work, our theoretical results are applied to methanol. We calculate the nuclear spin-spin magnetic dipole-dipole interactions and the nuclear contribution to the spin-torsion coupling vectors from the nuclear coordinates as functions of the internal rotation angle γ, compute the spin-rotation coupling tensors by ab initio electronic structure methods also as functions of γ, and obtain the missing parameters for the electronic contribution to the spin-torsion coupling from a fit to measured spectra. The resulting hyperfine Hamiltonian is then used to compute hyperfine transition frequencies and intensities for twelve torsion-rotation transitions in methanol. With the use of the ab initio calculated spin-rotation coupling parameters without any modification, and physically reasonable values for the spin-torsion coupling parameters from the fit, we find good agreement with all of the measured spectra.

Chirality-sensitive nuclear magnetic resonance effects induced by indirect spin-spin coupling.

It is predicted that, for two spin-1/2 nuclei coupled by indirect spin-spin coupling in a chiral molecule, chirality-sensitive induced electric polarization can be observed at the frequencies equal to the sum and difference between the spin resonance frequencies. Also, an electric field oscillating at the difference frequency can induce spin coherences which allow the direct discrimination between enantiomers by nuclear magnetic resonance. The dominant contribution to the magnitude of these expected chiral effects is proportional to the permanent electric dipole moment and to the antisymmetric part of the indirect spin-spin coupling tensor of the chiral molecule. Promising compounds for experimental tests of the predictions are derivatives of 1,3-difluorocyclopropene.

Fourier-transform microwave spectroscopy of a halogen substituted Criegee intermediate ClCHOO.

Pure rotational spectra of the chloro-substituted Criegee intermediate (ClCHOO) were observed by Fourier-transform microwave spectroscopy. Two conformers (syn and anti) of the isolated molecule were identified from the rotational spectra of the parent and 37Cl and 13C isotopologues detected in natural abundance. Rotational constants, centrifugal distortion constants, and all components of the nuclear quadrupole coupling tensor were determined for both conformers. Structural features of the molecule have been rationalized with supporting ab initio calculations and the natural bond orbital analysis, which suggest that the conformational preferences are driven by hyperconjugative effects.

Probing nitrite ion dynamics in NaNO2 crystals by solid‐state 17O NMR

AbstractWe report a solid‐state 17O (I = 5/2) NMR study of the nitrite ion dynamics in crystalline NaNO2. Variable temperature (VT) 17O NMR spectra were recorded at 3 magnetic fields, 11.7, 14.1, and 21.1 T. The VT 17O NMR data suggest that the ion in the ferroelectric phase of NaNO2 undergoes 2‐fold flip motion about the crystallographic b axis and the corresponding rotational barrier is 68 ± 5 kJ mol−1. We also obtained a 2D 17O EXSY spectrum for a stationary sample of NaNO2 at 250 K, which, in combination with 1D 17O NMR spectral analyses, allowed precise determination of the relative orientation between the 17O quadrupolar coupling and chemical shift tensors in the molecular frame of reference. The experimentally determined 17O NMR tensors for NaNO2 were in agreement with quantum chemical calculations produced by a periodic DFT code BAND.

Symmetry Breaking Nuclear Quadrupole Coupling Tensor Orientation for Cesium‐133 Nuclei Located in a Mirror Plane

Simultaneous multiple data set fits of all transition peaks of 133Cs nuclei enabled us to obtain accurate cesium‐133 nuclear magnetic resonance (NMR) parameters and Euler angles between the principal axis systems of the chemical shift (CS) and quadrupole coupling (Q) tensors of 133Cs nuclei in Cs2CrO4 . Although in a previous study of Cs2CrO4 by Power et al. (W. P. Power, S. Mooibroek, R. E. Wasylishen, T. S. Cameron, J. Phys. Chem. 1994, 98, 1552), one central transition was observed for cesium sites 1 and 2 in the 133Cs NMR spectra and one Euler angle between the CS tensors and Q tensors was obtained as 52° and 7° for cesium sites 1 and 2, respectively, the present single‐crystal 133Cs NMR measurements found two Euler angles (10(2)°, 51.9(1)°, 0°) for site 1 and two central transition peaks for site 2. Three principal components of the CS tensor for Cs1 are oriented along the crystallographic a, b, and c axes, whereas none of the principal components of the Q tensor for Cs1 are oriented along the crystal axes. The principal component V 22 of the Q tensor for Cs1 is tilted 10° from the b axis in the bc plane, and the other two components are not located in the ac plane. Therefore, we have found that the requirement that “the quadrupole coupling tensor for a nucleus located in a mirror plane has one principal axis perpendicular to the mirror plane” cannot be applied to Cs1. On the other hand, δ11 and V 22 for Cs2 are aligned along the b axis, and the other components of the CS and Q tensors deviate at an angle of 1.4(1)° and 10.1(1)°, respectively, from the a and c axes in the ac plane. A distortion‐free powder 133Cs NMR spectrum of Cs2CrO4 was measured using a solid‐state spin echo technique.

A Study of 2-Iodobutane by Rotational Spectroscopy.

Rotational transitions belonging to 2-iodobutane (sec-butyl-iodide, CH3CHICH2CH3) were measured over the frequency range 5.5-16.5 GHz via jet-pulsed Fourier transform microwave spectroscopy. The complete nuclear quadrupole coupling tensor of iodine, χ, was obtained for the gauche (g)-, anti (a)-, and gauche' (g')-conformers as well as the four (13)C isotopologues of the gauche species. Rotational constants, centrifugal distortion constants, quadrupole coupling constants, and nuclear spin-rotation constants were determined for each species. Changes in χ of the iodine nucleus, resulting from conformational and isotopic differences, are discussed. Isotopic substitution of g-2-iodobutane allowed for an rs structure to be determined for the carbon backbone. Additionally, isotopic substitution in conjunction with an ab initio structure allowed for a fit of various r0 structural parameters belonging to g-2-iodobutane.

The magnetic structure on the ground state of the equilateral triangular spin tube

The ground state of the frustrated equilateral triangular spin tube CsCrF4 is still hidden behind a veil though NMR spectrum broaden into 2 T at low temperature. In order to investigate the spin structure in an ordered state by 19F-NMR, we have determined the anisotropic hyperfine coupling tensors for each three fluorine sites in the paramagnetic state. The measurement field was raised up to 10 T to achieve highest resolution. The preliminary analysis using the obtained hyperfine tensors has shown that the archetypal 120°-type structure in ab-plane does not accord with the NMR spectra of ordered state.

The effect of CuII ions in l-asparagine single crystals

We report the synthesis, crystal growth, and spectroscopic characterization of l-asparagine monohydrate (LAM) single crystals doped with CuII. The crystals were successfully grown by slow cooling from a supersaturated aqueous solution up to size of 16×12×2mm3;the effect of copper impurities in the crystals morphology was discussed. Electron Paramagnetic Resonance (EPR) was used to calculate the g and hyperfine coupling (A) tensors of the CuII ions (g1=2.044, g2=2.105, g3=2.383and A1≈0, A2=35, A3=108Gauss). The EPR spectra for certain orientations of the magnetic field suggest that CuII ions are coordinated to two 14N atoms. Correlating the EPR and optical absorption results, the crystal field and the CuII orbital bond parameters were calculated. The results indicate that the paramagnetic center occupies interstitial rhombic distorted site and the ground orbital state for the unpaired electron is the d(x2-y2).