Through-space MP-CPMAS experiments between spin-1/2 and half-integer quadrupolar nuclei in solid-state NMR

We present a new CPMAS method that allows the acquisition of through-space 2D HETCOR spectra between spin-1/2 nuclei and half-integer quadrupolar nuclei in the solid state. It uses rotor-synchronized selective pulses on the quadrupolar nucleus and continuous-wave RF irradiation on the spin-1/2 nucleus to create hetero-nuclear dipolar coherences. The method is more robust, more efficient, and easier to set up than the standard CPMAS transfer.     

Potassium tetracyanoplatinate (II) trihydrate (K2Pt(CN)4·3H2O) studied by high resolution solid state C MAS NMR

Prudent analysis of the solid state ¹³C MAS NMR spectra of polycrystalline K₂Pt(CN)₄ · 3H₂O (KTCP)⁻ reveals that in crystals of this compound there are two types of carbon nuclei with slightly different ¹³C chemical shift tensors, contrary to what is found for the solution NMR spectrum and previous static powder NMR studies on this compound and the high resolution solid state NMR studies on other similar compounds. The ¹³C MAS spectra measured at different rotor spinning speeds are satisfactorily simulated though the use of a newly developed computer program based on a novel density matrix formulation. The present method is eminently successful even though the spectra are rather complicated because of (1) the relatively large anisotropies of the chemical shift tensors; (2) the high-order dipolar interactions between ¹³C and ¹⁴N nuclei because of the strong quadrupolar coupling constants of ¹⁴N nuclei; and (3) the indirect J-coupling between the ¹³C and ¹⁹⁵Pt. The principal elements as well as their orientations of the two ¹³C chemical shift tensors are evaluated from the spectral simulations.     

Generalized biaxial shearing of MQMAS NMR spectra

Two dimensional multiple quantum (MQ) MAS NMR experiments have become popular due to the wide applicability of this technique to structural questions in materials science, the abundance of half-integer spin nuclei in the periodic table, and the ease of implementation on typical solid state NMR instruments. In spite of the high-resolution theoretically possible from such experiments, the homogeneous and inhomogeneous broadening factors inherent in many samples of interest can make spectral analysis challenging. We present several possible spectral shearing schemes that may be useful for spectral analysis, and in particular we introduce shearing in the directly detected dimension. We suggest that for amorphous or disordered samples that give broad spectral features, shearing may be used as a general tool for optimal positioning of these features relative to one another and for the characterization of isotropic chemical and quadrupolar shifts.     

Geometry of kinked protein helices from NMR data

Residual dipolar couplings between spin-1/2 and quadrupolar nuclei are often observed and exploited in the magic-angle spinning (MAS) NMR spectra of spin-1/2 nuclei. These orientation-dependent splittings contain information on the dipolar interaction, which can be translated into structural information. The same type of splittings may also be observed for pairs of quadrupolar nuclei, although information is often difficult to extract from the quadrupolar-broadened lineshapes. Here, the complete theory for describing the dipolar coupling between two quadrupolar nuclei in the frequency domain by Hamiltonian diagonalization is given. The theory is developed under MAS and double-rotation (DOR) conditions, and is valid for any spin quantum numbers, quadrupolar coupling constants, asymmetry parameters, and tensor orientations at both nuclei. All terms in the dipolar Hamiltonian become partially secular and contribute to the NMR spectrum. The theory is validated using experimental 11B and 35/37Cl NMR experiments carried out on powdered B-chlorocatecholborane, where both MAS and DOR are used to help separate effects of the quadrupolar interaction from those of the dipolar interaction. It is shown that the lineshapes are sensitive to the quadrupolar coupling constant of both nuclei and to the J coupling (including its sign). From these experiments, the dipolar coupling constant for a heteronuclear spin pair of quadrupolar nuclei may be obtained as well as the sign of the quadrupolar coupling constant of the perturbing nucleus; these are two parameters that are difficult to obtain experimentally otherwise.     

Computation of Orientational Averages in Solid-State NMR by Gaussian Spherical Quadrature

We investigate Gaussian spherical quadrature as a method for calculating orientational averages in solid-state NMR. For the case of magic-angle-spinning sideband amplitudes of isolated spins-1/2, we demonstrate the superiority of Gaussian spherical quadrature over other orientational averaging methods. Depending on the shift anisotropy parameters and the desired accuracy, the computation speed is enhanced by a large factor (between two and many hundreds). In addition, a method for improving any present sampling scheme is devised. Such schemes are called SHREWD (Spherical Harmonic Reduction or Elimination by a Weighted Distribution). The role of orientational symmetry in solid-state NMR is explored. We also discuss the limitations of the Gaussian spherical quadrature methods.     

Solid state (47,49)Ti, (87)Sr and (137)Ba NMR characterisation of mixed barium/strontium titanate perovskites

Solid state ^47,49Ti, ¹³⁷Ba, ⁸⁷Sr NMR spectra have been recorded on Ba_xSr_1−xTiO₃ (0 x 1) perovskite samples prepared by the powder sintering method. Multinuclear solid state NMR shows great potential for characterising such systems since the quadrupolar parameters are very sensitive to any geometric deformation around the studied nucleus. ^47,49Ti NMR powder lineshapes appear strongly influenced by the presence of even a small amount of barium (or strontium) in the coordination second sphere of the probed titanium site: substitution of strontium by barium induces the broadening of the peaks, due to quadrupolar effects, while the isotropic chemical shift increases. ¹³⁷Ba NMR spectra exhibit a distribution of the quadrupolar interaction, that could be tentatively quantified, C_Q increasing with the amount of strontium. Preliminary results were also obtained on ⁸⁷Sr NMR showing behaviour comparable to ¹³⁷Ba NMR, i.e. a broadening of the peaks due to an increasing quadrupolar interaction with the amount of barium distorting the environment of the strontium sites.     

Solid state and solution 43Ca NMR of calcium peroxides involved in the disproportionation of hydrogen peroxide by calcium hydroxide

In order to get some insight into the mechanism of the disproportionation of hydrogen peroxide catalyzed by calcium hydroxide, 43Ca NMR spectra of enriched samples of calcium peroxides and of their precursors have been studied in both solution and solid state. This study demonstrates that no well-defined peroxidized calcium species are formed in solution, showing that the catalytic role of calcium is likely restricted to the solid state. Most of the calcium compounds that could be involved in the catalytic process have been investigated with solid state NMR. The shift and quadrupolar parameters of Ca(OH)2, CaO2.8H2O and CaO2.2H2O2 are reported for the first time. These parameters are different enough to allow the quantitative analysis of a complex mixture of these compounds by NMR.     

Signal enhancement in solid-state NMR of quadrupolar nuclei

Recent progress in the development and application of signal enhancement methods for NMR of quadrupolar nuclei in solids is presented. First, various pulse schemes for manipulating the populations of the satellite transitions in order to increase the signal of the central transition (CT) in stationary and rotating solids are evaluated (e.g., double-frequency sweeps, hyperbolic secant pulses). Second, the utility of the quadrupolar Carr–Purcell–Meiboom–Gill (QCPMG) and WURST-QCPMG pulse sequences for the rapid and efficient acquisition of particularly broad CT powder patterns is discussed. Third, less frequently used experiments involving polarization transfer from abundant nuclear spins (cross-polarization) or from unpaired electrons (dynamic nuclear polarization) are assessed in the context of recent examples. Advantages and disadvantages of particular enhancement schemes are highlighted and an outlook on possible future directions for the signal enhancement of quadrupolar nuclei in solids is offered.     

A simple theoretical treatment of quadrupolar effects on magic-angle-spinning solid-state NMR spectra of spin-1/2 nuclei in the limit of large quadrupole coupling constants

A simple approach is discussed for studying the effect of quadrupolar nuclei on the magic-angle-spinning solid-state NMR lines of spin-1/2 nuclei in the limit of large quadrupole coupling constants. Equations are derived both for the isotropic shifts and the Pake-like powder patterns for any quadrupolar spin and for arbitrary orientations of the internuclear vector with respect to the unique axis of an axially symmetric quadrupole tensor. First-order effects due to a small Zeeman perturbation on these lines are explored, as well as deviations from axial symmetry in the electric field gradient when S = 3/2 quadrupolar nuclei are involved. Spectral parameters likely to be observed in the case of coupling between ³¹P and ²⁰¹Hg are also discussed.     

Electron localization in a disordered insulating host

Transport of excess electrons has been studied in solid N2-Ar mixtures between 5 and 60 K using muon spin rotation in magnetic and electric fields. At low temperatures, orientational frustration of N2 molecular quadrupoles by a sufficiently high concentration of Ar atoms leads to formation of a quadrupolar glass phase in which electrons are found to be strongly localized. This feature is in marked contrast to the electron delocalization observed in the low-temperature alpha phase of pure solid nitrogen, which shows long-range orientational order.     

75As, 63Cu NMR and NQR characterization of selected arsenic minerals

The direct measurement and identification of solid state arsenic phases using ⁷⁵As NMR is made difficult by the simultaneous conditions of large quadrupole moment and low coordination symmetry in many compounds. However, specific arsenic minerals can efficiently be detected and discriminated via nuclear quadrupolar resonance (NQR). We report on the first NMR and NQR measurements in the natural minerals enargite (Cu₃AsS₄), niccolite (NiAs), arsenopyrite (FeAsS) and loellingite (FeAs₂). The NQR frequencies have been determined from both high-field NMR powder patterns and via zero-field frequency sweeps. Density functional theory (DFT) based ab initio calculations support the experimental results. The compounds studied here are common in terms of the known set of As-containing minerals. They are sometimes encountered in the context of base metal or gold mining. The study represents a significant addition to the list of arsenic minerals that can now be detected with NQR techniques.     

Deuteron NMR relaxometry applied to confined liquid crystals

We discuss the capability of deuteron nuclear magnetic resonance (NMR) spectroscopy and relaxometry to reveal molecular ordering and dynamics in confined liquid crystals. The attention is focused on the high-temperature phase above the nematic-isotropic transition, which is — in the absence of the long-range orientational order — very suitable for the study of surface interactions. Deuteron NMR spectra and relaxation rates are presented for two representatives of confined liquidcrystal systems: 8CB in cylindrical cavities of Anopore membranes and 5CB with an embedded polymer network. A substantial increase in the transverse spin relaxation rate, stimulated by the surface-induced order in enclosures, has been observed. In cylindrical cavities, it exhibits a strong temperature dependence on approaching the phase transition, whereas in the polymer network dispersion it is temperature-independent. The increase of T ₂ ^?1 provides information on the effect of spatial constraints on molecular mobility and on the surface orientational order parameter. Using deuteron relaxometry, one can measure the degree of orientational order in the isotropic phase not only in cylindrical but also in spherical cavities and enclosures of irregular shape, where the standard approach based on quadrupolar splitting of the NMR spectrum fails.     

Quadrupolar glass state in para-hydrogen and ortho-deuterium under pressure

The main features of the possible quadrupolar glass state in ortho-deuterium and para-hydrogen under high pressure are predicted and considered in replica-symmetric approximation in analogy with glassy behavior of diluted ortho-hydrogen at low pressures. The quadrupolar model with J=2 is suggested. The orientational order and glass regime grow continuously on cooling, as is the case with ortho-para hydrogen mixtures at zero pressure.     

High resolution heteronuclear correlation NMR spectroscopy between quadrupolar nuclei and protons in the solid state

A high resolution two-dimensional solid state NMR experiment is presented that correlates half-integer quadrupolar spins with protons. In this experiment the quadrupolar nuclei evolve during t1 under a split-t1, FAM-enhanced MQMAS pulse scheme. After each t1 period ending at the MQMAS echo position, single quantum magnetization is transferred, via a cross polarization process in the mixing time, from the quadrupolar nuclei to the protons. High-resolution proton signals are then detected in the t2 time domain during wPMLG5* homonuclear decoupling. The experiment has been demonstrated on a powder sample of sodium citrate and 23Na-1H 2D correlation spectra have been obtained. From the HETCOR spectra and the regular MQMAS spectrum, the three crystallographically inequivalent Na+ sites in the asymmetric unit were assigned. This MQMAS-wPMLG HETCOR pulse sequence can be used for spectral editing of half-integer quadrupolar nuclei coupled to protons.     

Application of solid-state NMR restraint potentials in membrane protein modeling

We have developed a set of orientational restraint potentials for solid-state NMR observables including (15)N chemical shift and (15)N-(1)H dipolar coupling. Torsion angle molecular dynamics simulations with available experimental (15)N chemical shift and (15)N-(1)H dipolar coupling as target values have been performed to determine orientational information of four membrane proteins and to model the structures of some of these systems in oligomer states. The results suggest that incorporation of the orientational restraint potentials into molecular dynamics provides an efficient means to the determination of structures that optimally satisfy the experimental observables without an extensive geometrical search.     

Measuring oxygen-phosphorus distances and the orientation of electric field gradient tensors using 17O-[31P] REDOR in phosphate glasses

Rotational echo double resonance (REDOR) of spin-12 nuclei is an extremely useful tool for the determination of distances in solids as well as of relative orientations of chemical shift and dipole tensors. We present the corresponding version for measuring the relative orientation of electric quadrupole and dipole tensors and demonstrate its applicability for non-bridging oxygens in phosphate glasses using 17O-[31P] REDOR NMR. The orientational information is found in the changes of the second-order quadrupole patterns as a function of the echo delay. Results and numeric simulations are presented for 17O-[31P] REDOR NMR of 17O-enriched sodium phosphate glasses. For non-bridging oxygens, the symmetric quadrupole tensor is found to be aligned along the phosphorus-oxygen bond. The distance between P and the non-bridging oxygen is calculated for two glasses of different compositions.     

Equilibrium states and quasi-static magnetization switching of a multilayer structure

The equilibrium orientations of magnetic moments that correspond to various values and directions of the biasing field are found in a set of magnetic films with cubic crystalline anisotropy and uniaxial induced anisotropy. The films are coupled by exchange interaction of the antiferromagnetic type. Field intervals are established where noncollinear and bistability states causing orientational phase transitions and hysteresis exist. Ninety degree magnetization switching (per switching cycle) of the magnetic moments of the films, as well as an orientational phase transition of bifurcation character, is discovered. Hysteresis loops for 180° in-plane magnetization switching are constructed.     

Removal of sidebands in double-rotation NMR in real time

Double-rotation (DOR) is the only technique generally capable of yielding high-resolution NMR spectra of half-integer quadrupolar nuclei in one dimension for solids without the need for sophisticated coherence pathway selection. Unfortunately, due to the low outer rotor spinning frequencies currently available, the spectra often contain a large number of spinning sidebands which may overlap with the resonances of interest. We implement a simple, robust, and easy to use family of pulse sequences, which in practice are fully analogous to the 'total suppression of sidebands' (TOSS) sequences, to suppress all sidebands arising from the spinning of the outer rotor in DOR experiments. By removing the rotor phase dependence of the evolution of the sidebands, the sidebands destructively interfere with one another during the course of signal averaging to yield 'solution-like' spectra of half-integer quadrupolar nuclei in solids. Advantages and shortcomings of the method compared to other DOR sideband suppression methods are explored with the aid of simulations.     

Deforming composite grids for solving fluid structure problems

We describe a mixed Eulerian–Lagrangian approach for solving fluid–structure interaction (FSI) problems. The technique, which uses deforming composite grids (DCG), is applied to FSI problems that couple high speed compressible flow with elastic solids. The fluid and solid domains are discretized with composite overlapping grids. Curvilinear grids are aligned with each interface and these grids deform as the interface evolves. The majority of grid points in the fluid domain generally belong to background Cartesian grids which do not move during a simulation. The FSI-DCG approach allows large displacements of the interfaces while retaining high quality grids. Efficiency is obtained through the use of structured grids and Cartesian grids. The governing equations in the fluid and solid domains are evolved in a partitioned approach. We solve the compressible Euler equations in the fluid domains using a high-order Godunov finite-volume scheme. We solve the linear elastodynamic equations in the solid domains using a second-order upwind scheme. We develop interface approximations based on the solution of a fluid–solid Riemann problem that results in a stable scheme even for the difficult case of light solids coupled to heavy fluids. The FSI-DCG approach is verified for three problems with known solutions, an elastic-piston problem, the superseismic shock problem and a deforming diffuser. In addition, a self convergence study is performed for an elastic shock hitting a fluid filled cavity. The overall FSI-DCG scheme is shown to be second-order accurate in the max-norm for smooth solutions, and robust and stable for problems with discontinuous solutions for a wide range of constitutive parameters.     

NMR evidence for higher-order multipole order parameters in NpO2

We report a microscopic investigation of multipolar order parameters in the ordered state of NpO2 conducted via 17O NMR on a single crystal. From the angular dependence of hyperfine fields at 17O nuclei, we have obtained clear evidence for the appearance of field-induced antiferro-octupolar as well as field-induced antiferro-dipolar moments below T0 = 26 K. We have also observed oscillatory spin-echo decay, which is well understood in terms of small electric field gradients created by antiferro-quadrupolar ordering. This reveals that the quadrupolar order parameter is directly observable by means of NMR. The present NMR studies provide definitive support for a proposed longitudinal triple-q type octupolar-quadrupolar ordering model for NpO2.