Electric Field Gradient Principal Axes Research Articles

Density Functional Theory Study on the 193Ir Mössbauer Spectroscopic Parameters of Vaska's Complexes and Their Oxidative Adducts.

In the present study, density functional theory (DFT) calculation was applied to Vaska's complexes of formula trans-[IrIX(CO)(PPh3)2] and their oxidative adducts with small molecules (YZ) including H2, i.e., trans-[IrIIIClYZ(CO)(PPh3)2], to successfully correlate the electronic states of the complexes with the corresponding 193Ir Mössbauer spectroscopic parameters. After confirming the reproducibility of the DFT methods for elucidating the equilibrium structures and 193Ir Mössbauer isomer shifts of the octahedral Ir complexes, the isomer shifts and quadrupole splitting values of Vaska's complexes and their oxidative adducts were calculated. A bond critical point analysis revealed that the tendency in the isomer shifts was correlated with the strength of the covalent interaction in the coordination bonds. In an electric field gradient (EFG) analysis of the oxidative adducts, the sign of the principal axis was found to be positive for the complex with YZ = Cl2 and negative for the complex with YZ = H2. This reversal of the sign of the EFG principal axis was caused by the difference in the electron density distribution for the coordination bonds between Ir and YZ, according to a density of states analysis.

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.

Solid-state NMR/NQR and first-principles study of two niobium halide cluster compounds

Two hexanuclear niobium halide cluster compounds with a [Nb6X12]2+ (X=Cl, Br) diamagnetic cluster core, have been studied by a combination of experimental solid-state NMR/NQR techniques and PAW/GIPAW calculations. For niobium sites the NMR parameters were determined by using variable Bo field static broadband NMR measurements and additional NQR measurements. It was found that they possess large positive chemical shifts, contrary to majority of niobium compounds studied so far by solid-state NMR, but in accordance with chemical shifts of 95Mo nuclei in structurally related compounds containing [Mo6Br8]4+ cluster cores. Experimentally determined δiso(93Nb) values are in the range from 2400 to 3000ppm. A detailed analysis of geometrical relations between computed electric field gradient (EFG) and chemical shift (CS) tensors with respect to structural features of cluster units was carried out. These tensors on niobium sites are almost axially symmetric with parallel orientation of the largest EFG and the smallest CS principal axes (Vzz and δ33) coinciding with the molecular four-fold axis of the [Nb6X12]2+ unit. Bridging halogen sites are characterized by large asymmetry of EFG and CS tensors, the largest EFG principal axis (Vzz) is perpendicular to the X-Nb bonds, while intermediate EFG principal axis (Vyy) and the largest CS principal axis (δ11) are oriented in the radial direction with respect to the center of the cluster unit. For more symmetrical bromide compound the PAW predictions for EFG parameters are in better correspondence with the NMR/NQR measurements than in the less symmetrical chlorine compound. Theoretically predicted NMR parameters of bridging halogen sites were checked by 79/81Br NQR and 35Cl solid-state NMR measurements.

Monte Carlo Simulations of PAC-Spectra as a General Approach to Dynamic Interactions

Time Dependent Perturbed Angular Correlations of γ-rays (PAC) can be used to study hyperfine interactions of a dynamic nature. However, the exact effect of the dynamic interaction on the PAC-spectrum is sometimes difficult to derive analytically. A new approach based on Monte Carlo simulations is therefore suggested, here implemented as a Fortran 90 program for simulating PAC spectra of dynamic electric field gradients of any origin. The program is designed for the most common experimental condition where the intermediate level has spin 5/2, but the approach can equally well be used for other spin states. Codes for 4 different situations have been developed: (1) Rotational diffusion by jumps; used as a test case. (2) Jumps between two states with different electric field gradients, different lifetimes and different orientations of the electric field gradient principal axes. (3) Relaxation of one state to another. (4) Molecules adhering to a surface with random rotational jumps around the axis perpendicular to the surface. To illustrate how this approach can be used to improve data-interpretation, previously published data on 111mCd-plastocyanin and 111Ag-plastocyanin are re-considered. The strength of this novel approach is its simplicity and generality so that other dynamic processes can easily be included by only adding new program units describing the random process behind the dynamics. The program is hereby made publicly available.

Halogen Nuclear Quadrupole Coupling Constants in Non-axially symmetric Molecules; Ab initio Calculations, which Include Correlation, Compared with Experiment

Abstract Ab initio determination of the electric field gradient (EFG) tensors at halogen and other centres ena-bled determination of the nuclear quadrupole coupling constants (NQCC) for a diverse set of C2v , C3v and other symmetry molecules of general formula MH2X2 and MHX3 , where the halogen atoms (X) are Cl, Br and I, and the heavy central atoms (M) are C and Si. The study presents results at a standardised level of calculation, triple-zeta in the valence space plus polarisation functions (TZVP) for the equilib-rium geometry stage; all-electron MP2 correlation is included in all these studies. For the bromo and iodo compounds, especially the latter, it is essential to allow core polarisation, by decontraction of the p,d-functions. This is conveniently done by initial optimization of the structure with a partly contract-ed basis, followed by reestablishment of the equilibrium structure with the decontracted basis. The NQCCs, derived from the EFGs, using the 'best' values for the atomic quadruple moments Cl, Br and I, lead to good agreement with the inertial axis (IA) data obtained from microwave spectroscopy. When the data from the present study is plotted against the values derived from the IA data, obtained by whatever approximations chosen by the MW authors, we obtain a linear regression for the data (85 points) with the slope 1.0365 and intercept -0.1737, with standard errors of 0.0042 and 0.2042, respectively; these are statistically identical results irrespective of whether the data is restricted to IA or EFG principal axis (PA) data. Since as in the C3v MH3X compounds studied previously, a close correlation of the microwave spectral data with the calculations was observed using the 'best' current values for Qz , there seems no need to postulate that the values of QBr for both 79Br and 81Br are seriously in error. A scaling downwards of Qz by about 5% for Br and I increases the agreement with experiment, but the contributions of relativistic effects are unknown, and could lead to further reassessment. Of the two common assumptions used in MW spectroscopy, to convert from IA to EFG-PA data, either (a) cylindrical symmetry of the NQCC along the bond direction, or (b) coincidence of the tensor principal element with the bond axis, the latter is found to be a much more realistic approximation.

Determination of the electric field gradient tensor by 2D NQR

For a full specification of the Electric Field Gradient (EFG) tensor, five independent parameters are necessary: the asymmetry parameter (η), the largest component of the EFG ( eq), and three angles which determine the orientation of the EFG principal axis with respect to the crystallographic frame. The parameters eq and η can be determined independently by pure Nuclear Quadrupole Resonance (NQR) (for nuclear spin I = 1 and I > 3 2 ). However, to determine the orientation angles one needs to use other methods such as X-ray Crystallography, Nuclear Magnetic Resonance (NMR), NQR with external field, EPR, Mössbauer spectroscopy or Perturbed Angular Correlations (PAC). In this paper we propose a new 2D NQR method which permits the full determination of the EFG tensor in a monocrystalline sample. It can be used to determine the preferential orientation of small monocrystals in a polycrystalline sample. The angular precision of the method is ± 2.5°.

Temperature dependence of the 57Fe Mössbauer parameters in riebeckite

Mossbauer spectra for two riebeckite minerals were collected at temperatures in the range 4.2 to 500 K. The magnetic-ordering temperatures were found to be 33±1 and 31±1 K respectively. Fitting the paramagnetic spectra with a discrete number of doublets (three or four) did not lead to consistent results. Instead, a superposition of an Fe3+ (M2) doublet and one distributed ferrous component was found to produce adequate fits with reasonable parameter values. For both samples, a minor fraction of ferrous ions was observed to be present at the M4 sites and for one of the samples at the M2 sites as well. The temperature variations of the center shifts were well reproduced using the Debye model of the lattice vibrational spectrum to evaluate the second-order Doppler shift. The characteristic Mossbauer temperatures were calculated to be in the range 340–390 K for Fe2+, and 520 K for Fe3+. The temperature dependences of the various ferrous quadrupole splittings could not be explained in terms of the point-charge model and assuming a temperature-independent energy-level scheme for the 5D term. It is suggested that a gradual change with temperature of the orbital-level splittings takes place. All calculations yielded a positive sign for the principal component of the electric field gradient (EFG). The spectrum recorded at 4.2 K for one of the riebeckites was fitted with a superposition of an Fe3+ and a Fe2+ hyperfine-field distribution, the latter one primarily characterizing the Fe2+ (M1) cations. The following relevant hyperfine data were calculated: Hhf=161 kOe, ΔEQ=3.11 mm/s, and Vzz<0, all referring to the maximum-propability values. For the second riebeckite at 4.2 K, an additional distributed ferrous component could independently be resolved. The two maximum-probability hyperfine fields were found to be 189 and 98 kOe and the corresponding ΔEQ values 3.10 and 2.67 mm/s. Both components exhibit a negative Vzz. The subspectra were attributed to M1 and M3 sites respectively. The Fe3+ hyperfine fields are 548+-2 kOe for both riebeckites. The different values found for the Fe3+ quadrupole shift 2ɛQ for the two samples is explained by a different angle between the hyperfine field and the EFG's principal axis. The magnetic spectra recorded at 15 K and higher, could not be reproduced adequately with reasonable parameter values.

Anharmonic Librations and the Temperature Dependence of NQR Frequencies

Abstract The temperature dependence of NQR frequencies of nuclei in molecules undergoing quasi-har-monic rotational oscillations is calculated. Following the model proposed by Bayer, the instanta-neous orientation of the electric field gradient principal axes is assumed to change from its average orientation as a result of rotational oscillations, while the EFG magnitude remains constant. The eigenstates and energy eigenvalues of a rotator in a potential of the form V(θ)= V2θ2 - K4θ4 are calculated by standard perturbation methods, followed by the evaluation of statistical averages of square angular amplitudes. For molecular crystals with more than one molecule in a unit cell the angular displacements are expressed in terms of normal coordinates, and the same procedure is followed. The final expression for the change in the NQR frequency consists of two terms, the first one being related to the harmonic part of the potential and the second one to the quartic term. At the absolute zero it yields a nonzero contribution to ⟨θ2⟩, and for high temperatures it reproduces the nonlinear character of νQ(T) observed experimentally. The model has been tested with measure-ments on solid Cl2 performed by Nakamura and Chihara, combined with libration mode frequencies measured in Raman spectroscopy by Cahill and Leroi and analysed according to our anharmonic libration picture. The fitting of our equation to experimental data supports Cahill and Leroi's hypothesis about the existence of an undetected libration mode in Cl2 Raman spectra of frequency near 60 cm- 1

Hyperfine Interaction Induced K-type Doubling in the mmw Spectrum of HS33SH

Abstract The rotational spectrum of the disulfane isotopomer HS33SH has been recorded and assigned between 70 and 300 GHz. In the analysis, rotational constants and 33S hyperfine parameters are derived, the latter accounting for nuclear electric quadrupole as well as nuclear spin -rotation hyperfine interactions. The quadrupole constants are in qualitative agreement with a published ab-initio calculation. The electric field gradient principal axes are considerably rotated against the principal inertial axes, giving rise to off-diagonal elements in the electric field gradient tensor. In combination with the very small inertial asymmetry of the molecule, this causes the A'-doubling in the lowest rotational levels to be dominated by the hyperfine structure rather than the inertial asymmetry contributions. By diagonalization of the quadrupole tensor, an estimate for the dihedral angle (η≈94°) can be obtained, in good agreement with a previous value.

The effects of H-bonding, change of state and molecular distortion on 2H and 17O nuclear quadrupole coupling constants: general theoretical considerations and specific application to formic acid

The major emphasis here is in analysing the effect of H-bonding on the nuclear quadrupole coupling behaviour of 2H and 17O nuclei. Using ab initio quantum mechanical methods on the test molecule formic acid, the coupling amplitudes (nuclear quadrupole coupling constants e 2 qQ/h) and, also, coupling anisotropies (asymmetry parameter η) and orientations of the electric field gradient principal axis system with respect to molecular axes have been calculated. As formic acid contains 2H and 17O nuclei in a variety of functional groups — alkyl ( 2H), hydroxyl ( 2H and 17O) and carboxyl ( 17O) — it is a particularly efficient molecule for theoretical study. In addition the structures of its H-bonded complexes vary as a function of phase from the cyclic H-bonded gaseous dimer through a probably chain-like association in the liquid to a regular chain H-bonded solid phase. Thus in this work the consequences of differing H-bond geometries on nuclear quadrupole coupling of the given nuclei are investigated, and also the relative contributions to the coupling changes of geometric and electronic disortions resulting from H-bonding and lattice field effects in the solid, are evaluated. The theoretical results are compared with the most up-to-date experimental data available. General problems in calculating molecular electric field gradients are outlined and, in particular, errors resulting from uncertainties in experimental input geometries are critically assessed. Differences in computational emphasis for 2H as compared with 17O and other “heavy” nuclei are pointed out.

Crystal structure and bond character study of 2,4-Dichloroacetanilide by NQR

Two NQR lines were observed in 2,4-dichloroacetanilide at liquid-nitrogen and room temperatures. The Zeeman spectrum of both lines was investigated using a single crystal of the compound. Analysis of the zero-splitting loci show two non-equivalent directions for the electric field gradient principal axes for each of the lines. The observations are in agreement with the C 2 h symmetry for the crystal as reported by Groth. The c axis is inclined at an angle of 13° to the growth axis. The two CCl bonds in the molecule make an angle of 123° with one another. The crystal contains two sets of benzene rings with their planes inclined at angle of 24° to one another. The unit cell contains a minimum of 4 molecules. The ionic, single-bond, and double-bond character for both chlorines in all of the molecules are in the ratio 25:72:3.

Relative Orientations of the Electric Field Gradient and Susceptibility Tensors in Monoclinic Symmetry

Using crystalline fields with local monoclinic symmetry and the spin-orbit interaction acting on those paramagnetic ions whose orbital state may be described by a linear combination of ${d}_{\ensuremath{\epsilon}}$ (or ${T}_{2g}$) orbitals, it is shown that the electric field gradient (EFG) and susceptibility ($\ensuremath{\chi}$) tensors have only one common axis for their respective principal-axis systems. Expressions for the EFG and the magnetic hyperfine interactions referred to the magnetic axes are presented to include the effects of monoclinic symmetry. The reorientation of the magnetic and EFG principal axes may have marked effects on the M\"ossbauer and NMR spectra where the nuclear probe is sensitive to both magnetic and electric hyperfine interactions. Some examples are presented and M\"ossbauer spectra calculated to show the effects of monoclinic symmetry.

Determination of Spin Directions and Electric Field Gradient Axes in Vivianite by Polarized Recoil‐Free γ‐Rays

AbstractNon‐polarized and linearly polarized recoil‐free γ‐rays (Mössbauer effect) have been used to determine spin directions and the orientation of the electric field gradient (EFG) principal axes for the two iron sites in vivianite. The values obtained for the internal fields, quadrupole splittings, isomer shifts, and the relative orientations of the internal fields and EFG principal axes with respect to the crystal axes are tabulated.