Single- and multiple-quantum cross-polarization in NMR of quadrupolar nuclei in static samples

Cross-polarization from a spin I=1/2 nucleus (e.g., ¹H) to a spin S = 3/2 nucleus (e.g., ²³Na) or a spin S = 5/2 nucleus (e.g., ²⁷A1 or ⁿO) in static powder samples is investigated. The results of conventional (single-quantum), three-quantum, and five-quantum cross-polarization experiments are presented and discussed. Based on a generalization of an existing theory of cross-polarization to quadrupolar nuclei, computer simulations are used to model the intensity and lineshape variations observed in cross-polarized NMR spectra as a function of the radio-frequency field strengths of the two simultaneous spin-locking pulses. These intensity and lineshape variations can also be understood in terms of the spin S = 3/2 or 5/2 nutation rates determined from experimental quadrupolar nutation spectra. The results of this study are intended as a preliminary step towards understanding single- and multiple-quantum cross-polarization to quadrupolar nuclei under MAS conditions and the application of these techniques to the MQMAS NMR experiment.     

Application of27Al NMR techniques to structure determination in solids

There have been great improvements in the quality of²⁷Al NMR spectra from solids over the last decade. The impact of this technique on structure determination for a wide range of solids is briefly reviewed. Emphasis is placed on the effects arising from the presence of the quadrupolar interaction and strategies that allow unambiguous spectral interpretation. It is demonstrated that in addition to the chemical shift, the quadrupolar interaction itself can be a rich source of local information about solids. The insight obtained from²⁷Al NMR into atomic level structure often contains surprises, such that previous models of structure and properties have to be reassessed.     

Indirect covariance NMR spectroscopy of through-bond homo-nuclear correlations for quadrupolar nuclei in solids under high-resolution

Indirect covariance NMR spectroscopy is demonstrated in solids, and we show that it can be used to obtain through-bond 2D homo-nuclear correlation spectra for quadrupolar nuclei under high-resolution. These spectra, generated with indirect covariance from a hetero-nuclear correlation spectrum, are equivalent to those recorded with the through-bond homo-nuclear hetero-nuclear single-quantum correlation (H-HSQC) method very recently proposed. However, the indirect covariance method can save a lot of experiment time, compared to the H-HSQC experiments, which allows introducing a high-resolution quadrupolar filter, thus providing a much better resolution, even on medium-field spectrometers. The covariance concept can be used to generate many different "indirectly-detected" high-resolution homo-nuclear correlation spectra with through-space or through-bond correlations for spin 1/2 or quadrupolar nuclei. We also propose a simple method that decreases the noise in all (direct or indirect) covariance methods.     

EASY-GOING deconvolution: combining accurate simulation and evolutionary algorithms for fast deconvolution of solid-state quadrupolar NMR spectra

A fast and accurate fit program is presented for deconvolution of one-dimensional solid-state quadrupolar NMR spectra of powdered materials. Computational costs of the synthesis of theoretical spectra are reduced by the use of libraries containing simulated time/frequency domain data. These libraries are calculated once and with the use of second-party simulation software readily available in the NMR community, to ensure a maximum flexibility and accuracy with respect to experimental conditions. EASY-GOING deconvolution (EGdeconv) is equipped with evolutionary algorithms that provide robust many-parameter fitting and offers efficient parallellised computing. The program supports quantification of relative chemical site abundances and (dis)order in the solid-state by incorporation of (extended) Czjzek and order parameter models. To illustrate EGdeconv's current capabilities, we provide three case studies. Given the program's simple concept it allows a straightforward extension to include other NMR interactions. The program is available as is for 64-bit Linux operating systems.     

Double rotation27Al NMR in molecular sieves

Although high-resolution NMR spectra can be obtained in solids, the use of²⁷Al NMR to investigate the structure of aluminosilicate and aluminophosphate molecular sieves has been severely limited because anisotropic second-order quadrupolar interactions, responsible for spectral broadening, cannot be eliminated by conventional magic angle spinning (MAS) or multiple pulse techniques. Here we give the principles of the double rotation (DOR) NMR technique which can remove not only the first-order broadenings but also the second-order broadenings in the NMR spectra of quadrupolar nuclei in solids. High-resolution²⁷Al NMR using DOR is capable of resolving discrete framework aluminum sites in aluminophosphate molecular sieves, permitting quantitative investigation of site-specific adsorbate-host interactions, and of discriminating different aluminum species in zeolites.     

Calculation of solid-state NMR lineshapes using contour analysis

Two new methods for calculating lineshapes in solid-state NMR spectra are described. The first method, which we refer to as semi-analytical, allows the rapid calculation of quadrupolar central-transition lineshapes in both static and magic-angle spinning cases. The second method, which is fully numerical, allows the calculation of lineshapes resulting from any combination of interactions, including quadrupolar, dipolar and chemical shift anisotropy, and is not restricted to cases in which the principal axis systems for the different interactions are aligned. Both methods are derived from consideration of the contour lines on a plot of the resonance frequency against the Euler angles, allowing the intensity of the lineshape to be calculated at each frequency. Consequently, highly accurate lineshapes can be calculated more rapidly than previously possible, since only orientations contributing to each specific frequency are considered. For our semi-analytical method, the intensity of each point in the lineshape can be directly calculated in tens of milliseconds on a standard PC. In contrast, established methods can take several hours to calculate the same lineshape.     

Two dimensional NQR separation of inhomogeneous and homogeneous lineshapes in disordered solids

A two-dimensional (2D) zero field NQR separation of inhomogeneous and homogeneous lineshapes technique is described. The nuclear spin Hamiltonian for spinsI>1/2 in zero magnetic field consists to a good approximation only of the electric quadrupole term. The 2D separation technique enables a separate spectroscopic observation of a static and a randomly time-fluctuating dynamic part of the quadrupole interaction. The separation is based on the fact that nuclear spin precession under a static quadrupolar Hamiltonian can be time-reversed whereas this can not be achieved under the action of a randomly time-fluctuaing Hamiltonian. The 2D spectrum displays in theω ₂-domain the inhomogeneously broadened lineshape, which is a convolution of the inhomogeneous static frequency distribution function and the homogeneous (adiabatic) lineshape. Theω ₁-domain shows the pure homogeneous lineshape. A deconvolution of the inhomogeneous lineshape with the homogeneous one yields a pure static inhomogeneous frequency distribution function which is characteristic and theoretically known for many different models of disordered solids like glasses and incommensurate systems. This technique is important in studies where both lineshapes have comparable widths. The 2D NQR separation technique has been applied to⁷⁵As in a proton glass Rb_0.98(NH₄)_0.02H₂AsO₄.     

魔角旋转情形下固体的非均匀相互作用

各向异性非均匀相互作用的慢旋转MAS-NMR谱是一系列的旋转边带,这些边带的强度包含了该相互作用张量的全部信息,只要计算和分析少数几条边带就可以得到这些有用的结构信息,本文用不可约球谐张量算符表示非均匀相互作用,采用Bessel函数展开法分析计算非均匀相互作用产生的旋转边带,这种分析计算方法适用于各种非均匀相互作用。以化学位移和四极相互作用为例的实验与理论符合很好。 关键词：     

Probing amide bond nitrogens in solids using 14N NMR spectroscopy

A novel two-dimensional nuclear magnetic resonance (NMR) experiment is proposed for indirect observation of 14N nuclei in various types of nitrogen-containing solids. In a method somewhat similar to the heteronuclear single-quantum correlation (HSQC) experiment widely used for protein structure determination in solutions, this technique correlates spin S=1/2 nuclei, e.g., 1H, 13C, with the 14N spin I=1 nucleus in solids. The present experiment, however, transfers coherence from neighboring 1H or 13C nuclei to 14N via a combination of J-couplings and residual dipolar splittings (RDS). Projections of the two-dimensional NMR spectra onto the 14N dimension yield powder patterns that reflect the 14N quadrupolar interaction, which can be used to study molecular structure and dynamics. Indirect detection of amide nitrogen-14 via 1H and 13C is shown experimentally on a model compound of N-acetyl-glycine.     

Biaxial Q-shearing of 27Al 3QMAS NMR spectra: Insight into the structural disorder of framework aluminosilicates

In this contribution, we present the application potentiality of biaxial Q-shearing of ²⁷Al 3QMAS NMR spectra in the analysis of structural defects of aluminium units in aluminosilicates. This study demonstrates that the combination of various shearing transformations of the recorded ²⁷Al 3QMAS NMR spectra enables an understanding of the broadening processes of the correlation signals of disordered framework aluminosilicates, for which a wide distribution of ²⁷Al MAS NMR chemical shifts and quadrupolar parameters (i.e., second-order quadrupolar splitting and quadrupole-induced chemical shifts) can be expected. By combining the suitably selected shearing transformation procedures, the mechanisms of the formation of local defects in aluminosilicate frameworks, including Al/Si substitution effects in the next-nearest neighbouring T-sites, variations in bond angles, and/or variations in the physicochemical nature of charge-balancing counter-ions, can be identified. The proposed procedure has been extensively tested on a range of model aluminosilicate materials (kyanite, γ-alumina, metakaolin, analcime, chabazite, natrolite, phillipsite, mordenite, zeolite A, and zeolite Y).     

Refocussing of chemical and paramagnetic shift anisotropies in 2H NMR using the quadrupolar-echo experiment

A simple two-pulse spin-echo experiment is shown to refocus inhomogeneous broadening arising from both chemical and/or paramagnetic shift anisotropy and a first-order I=1 quadrupolar interaction. The method is shown to yield ²H NMR spectra of a paramagnetic solid (CuCl₂ · 2D₂O) and of a non-paramagnetic solid (D₂C₂O₄ · 2D₂O) that are significantly less distorted than those provided by the conventional quadrupolar-echo method. The technique will thus prove useful in studies of motion and dynamics where detailed analysis of the ²H lineshape is performed.     

Generalization of the lineshape useful in magnetic resonance spectroscopy

A new lineshape function is derived from the Tsallis distribution to describe electron paramagnetic resonance (EPR) spectra, and possibly nuclear magnetic resonance (NMR) spectra as well. This lineshape generalizes the Gaussian and Lorentzian lineshapes that are widely used in simulations. The main features of this lineshape function are presented: the normalization, moments, and first derivative. A number of experimental EPR spectra are compared with the results of simulations employing the new lineshape function. The results show that the new lineshape often provides a better approximation of the experimental spectrum. It is also shown that the new parameter of the lineshape function can be used to quantify the intermolecular spin-spin interactions.     

From crystalline to glassy gallium fluoride materials: an NMR study of 69Ga and 71Ga quadrupolar nuclei

Owing to the implementation of acquisition techniques specific for nuclei with very large quadrupolar interaction (full shifted echo and variable offset cumulative spectra (VOCS)), NMR spectra of 69Ga and 71Ga are obtained in crystallised (PbGaF5, Pb3Ga2F12, Pb9Ga2F24 and CsZnGaF6) and glassy (PbF2-ZnF2-GaF3) gallium fluorides. Simulations of both static (full echo or VOCS) and 15 kHz MAS spectra allow to obtain consistent determinations of isotropic chemical shifts and very large quadrupolar parameters (nuQ up to 14 MHz). In the crystalline compounds whose structures are unknown, the number and the local symmetry of the different gallium sites are tentatively worked out. For the glassy systems, a continuous Czjzek's distribution of the NMR quadrupolar parameters accounts for the particular shape of the NMR spectrum.     

Ensemble of single quadrupolar nuclei in rotating solids: sidebands in NMR spectrum

A novel way is proposed to describe the evolution of nuclear magnetic polarization and the induced NMR spectrum. In this method, the effect of a high-intensity external static magnetic field and the effects of proper Hamiltonian left over interaction components, which commute with the first, are taken into account simultaneously and equivalently. The method suits any concrete NMR problem. This brings forth the really existing details in the registered spectra, evoked by Hamiltonian secular terms, which may be otherwise smoothed due to approximate treatment of the effects of the secular terms. Complete analytical expressions are obtained describing the NMR spectra including the rotational sideband sets of single quadrupolar nuclei in rotating solids.     

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.     

Molecular dynamics of half-integer quadrupolar nuclei studied by QCPMG solid-state NMR experiments on static and rotating samples. Theory and simulations

Simulations of QCPMG NMR type experiments have been used to explore dynamic processes of half-integer quadrupolar nuclei in solids. By setting up a theoretical approach that is well suited for efficient numerical simulations the QCPMG type experiments have been analyzed regarding the effect of the magnitude of the EFG- and CSA-tensors, the spin-quantum number, different dynamical processes and MAS. Compared to the QE experiment the QCPMG experiment offers not only intensity gain by an order of magnitude and changes in overall lineshape as a function of the kinetic rate constant but the lineshape of the individual spin-echo sidebands is also very sensitive towards dynamics. Hereby a visual identification of the dynamics is obtained. In common for all the simulations the spin-echo sidebands are narrow in the slow (k< or =10(2) Hz) and the fast (k> or =10(7) Hz) dynamic regime whereas they are broadened in the intermediate regime 10(3)< or =k< or =10(7) Hz. The maximum intensity of the spin-echo sidebands for two-site jumps is highly dependent on the type of anisotropic interactions involved and the type of QCPMG experiment. Hence, in the fast limit the maximum intensity was 140% of the initial intensity when significant CSA was present or under the QCPMG-MAS experiment compared to 89 or 71% for the static experiment influenced by the quadrupolar interaction only. For 3-, 4-, and 6-site jumps the maximum intensity in the fast limit reached up to 339% of the intensity in the static limit.     

A new method for suppressing the central transition in I=3/2 NMR spectra with a demonstration for 23Na in bovine articular cartilage

The splitting and the lineshape of the satellite transitions of 23Na are measures of the residual quadrupolar interaction and its distribution, which are related to the degrees of order and binding of sodium in biological tissues. However, these transitions are often masked by the stronger signals of the central transition and the isotropic sodium ions. A way to suppress the central signals, while preserving the lineshape and the intensity of the satellites, is suggested and tested on a liquid crystal and on bovine articular cartilage.     

From crystalline to glassy gallium fluoride materials: an NMR study of Ga and Ga quadrupolar nuclei

Owing to the implementation of acquisition techniques specific for nuclei with very large quadrupolar interaction (full shifted echo and variable offset cumulative spectra (VOCS)), NMR spectra of ⁶⁹Ga and ⁷¹Ga are obtained in crystallised (PbGaF₅, Pb₃Ga₂F₁₂, Pb₉Ga₂F₂₄ and CsZnGaF₆) and glassy (PbF₂–ZnF₂–GaF₃) gallium fluorides. Simulations of both static (full echo or VOCS) and 15 kHz MAS spectra allow to obtain consistent determinations of isotropic chemical shifts and very large quadrupolar parameters (ν_Q up to 14 MHz). In the crystalline compounds whose structures are unknown, the number and the local symmetry of the different gallium sites are tentatively worked out. For the glassy systems, a continuous Czjzek's distribution of the NMR quadrupolar parameters accounts for the particular shape of the NMR spectrum.     

Dynamical properties of ions confined within dense dispersions of charged anisotropic colloids : A <Superscript>23</Superscript>Na quadrupolar NMR study

We used ²³Na quadrupolar NMR spectroscopy and relaxation measurements to determine the mobility of the sodium counterions confined within dense aqueous dispersions of synthetic Laponite clays as a model of charged anisotropic nano-composite colloids. The lineshape analysis of the ²³Na spectra and the measurements of the Hahn echo attenuation are used to determine the critical clay concentration corresponding to the nematic organisation of the dispersion. As validated by numerical simulations of the ion diffusion within partially oriented nematic dispersion of the anisotropic colloids, the angular variation of the apparent relaxation rates is interpreted as an indice of degree of ordering of the dispersion.     

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.