Definitive solid-state 185/187Re NMR spectral evidence for and analysis of the origin of high-order quadrupole-induced effects for I=5/2

Automatic fitting of multiple-field solid-state NMR spectra

The NMR lineshapes produced by half-integer quadrupolar nuclei are sensitive to 11 distinct fit parameters per inequivalent site. To date, automatic fitting routines have failed to replace manual parameter insertion and evaluation due to the importance of local minima and the need for fitting multiple-field magic-angle spinning (MAS) and static spectra simultaneously. Herein we introduce a new tool, AMES-Fit (Automatic Multiple Experiment Simulation and Fitting), to automatically find the global best-fit simulation parameters for a series of multiple-field NMR lineshapes. AMES-Fit uses an adaptive step size random search algorithm to dynamically probe parameter space and requires minimal human input. The best fits are obtained in a few minutes of computation time that would otherwise have required several person-hours of work. The program is freely available and open-source.

Non-covalent matere bonds in perrhenates probed via ultrahigh field rhenium-185/187 NMR and zero-field NQR spectroscopy

Matere bonds (MaB) to rhenium in a set of organic perrhenates are probed via185/187Re solid-state NMR in applied magnetic fields of up to 35.2 T, and via185/187Re NQR. 185/187Re quadrupolar couplings distinguish between MaB samples and control samples, and their precise values are governed by shear strain of the ReO4- anions.

Quantifying the quadrupolar interaction by 45Sc-NMR spectroscopy of single crystals

Single crystals of the compound [ [Formula: see text] ]Cl₄ ⋅ 2H₂O were studied by ⁴⁵Sc-NMR, with the effect of the quadrupolar coupling interaction on the spectra of the spin-7/2 nucleus analysed in the hierarchical framework of perturbation theory. Orientation-dependent spectra acquired at B₀ = 17.6 T showed strong second-order effects due to the comparatively large coupling constant of χ = |14.613 ± 0.006| MHz, with an associated asymmetry parameter of η_Q = 0.540 9 ± 0.000 4. By analysing the splittings of the ±3/2 satellites, which in good approximation are subjected to first-order effects only, the full quadrupolar coupling tensor could be determined. The second-order effects caused by this tensor were calculated according to theoretical predictions for all orientations, and subtracted from both the centres of gravity of the satellites, and the central transitions. This allowed extraction of the full chemical shift tensor, with the eigenvalues being δ₁₁ = (5.6 ± 0.9) ppm, δ₂₂ = (12.4 ± 0.9) ppm, and δ₃₃ = (38.5 ± 0.9) ppm. In spectra acquired at a lower magnetic field of B₀ = 9.4 T, third-order effects could be detected, and similarly quantified using analytical expressions.

Solid-state nuclear magnetic resonance of spin-9/2 nuclei 115 In and 209 Bi in functional inorganic complex oxides

Indium and bismuth are technologically important elements, in particular as oxides for optoelectronic applications. ¹¹⁵ In and ²⁰⁹ Bi are both I = 9/2 nuclei with high natural abundances and moderately high frequencies but large nuclear electric quadrupole moments. Leveraging the quadrupolar interaction as a measure of local symmetry and polyhedral distortions for these nuclei could provide powerful insights on a range of applied materials. However, the absence of reported nuclear magnetic resonance (NMR) parameters on these nuclei, particularly in oxides, hinders their use by the broader materials community. In this contribution, solid-state ¹¹⁵ In and ²⁰⁹ Bi NMR of three recently discovered quaternary bismuth or indium oxides are reported, supported by density functional theory calculations, numerical simulations, diffraction and additional multinuclear (²⁷ Al, ^69,71 Ga, and ¹²¹ Sb) solid-state NMR measurements. The compounds LiIn₂ SbO₆ , BiAlTeO₆ , and BiGaTeO₆ are measured without special equipment at 9.4 T, demonstrating that wideline techniques such as the QCPMG pulse sequence and frequency-stepped acquisition can enable straightforward extraction of quadrupolar tensor information in I = 9/2 ¹¹⁵ In and ²⁰⁹ Bi even in sites with large quadrupolar coupling constants. Relationships are described between the NMR observables and local site symmetry. These are amongst the first reports of the NMR parameters of ¹¹⁵ In, ¹²¹ Sb, and ²⁰⁹ Bi in oxides.

Recent advances in solid-state nuclear magnetic resonance spectroscopy of exotic nuclei

We present a review of recent advances in solid-state nuclear magnetic resonance (SSNMR) studies of exotic nuclei. Exotic nuclei may be spin-1/2 or quadrupolar, and typically have low gyromagnetic ratios, low natural abundances, large quadrupole moments (when I > 1/2), or some combination of these properties, generally resulting in low receptivities and/or prohibitively broad line widths. Some nuclides are little studied for other reasons, also rendering them somewhat exotic. We first discuss some of the recent progress in pulse sequences and hardware development which continues to enable researchers to study new kinds of materials as well as previously unfeasible nuclei. This is followed by a survey of applications to a wide range of exotic nuclei (including e.g., ⁹Be, ²⁵Mg, ³³S, ³⁹K, ⁴³Ca, ^47/49Ti, ⁵³Cr, ⁵⁹Co, ⁶¹Ni, ⁶⁷Zn, ⁷³Ge, ⁷⁵As, ⁸⁷Sr, ¹¹⁵In, ¹¹⁹Sn, ^121/123Sb, ^135/137Ba, ^185/187Re, ²⁰⁹Bi), most of them quadrupolar. The scope of the review is the past ten years, i.e., 2007-2017.

Quadrupole interactions: NMR, NQR, and in between from a single viewpoint

Nuclear spins with quantum numbers >1/2 can interact with a static magnetic field, or a local electric field gradient, to produce quantized energy levels. If the magnetic field interaction dominates, we are doing nuclear magnetic resonance (NMR). If the interaction of the nuclear electric quadrupole with electric field gradients is much stronger, this is nuclear quadrupole resonance (NQR). The two are extremes of a continuum, as the ratio of one interaction to the other changes. In this work, we look at this continuum from a single, unified viewpoint based on a Liouville-space approach: the direct method. This method does not require explicit operators and their commutators, unlike Hamiltonian methods. We derive both the quadrupole-perturbed NMR solution and also the Zeeman-perturbed NQR results. Furthermore, we examine the polarization of these signals, because this is different between pure NMR and pure NQR spectroscopy. Spin 3/2 is the focus here, but the approach is perfectly general and can be applied to any spin. Copyright © 2016 John Wiley & Sons, Ltd.

Quantitative structure parameters from the NMR spectroscopy of quadrupolar nuclei

Nuclear magnetic resonance (NMR) spectroscopy is one of the most important characterization tools in chemistry, however, 3/4 of the NMR active nuclei are underutilized due to their quadrupolar nature. This short review centers on the development of methods that use solid-state NMR of quadrupolar nuclei for obtaining quantitative structural information. Namely, techniques using dipolar recoupling as well as the resolution afforded by double-rotation are presented for the measurement of spin–spin coupling between quadrupoles, enabling the measurement of internuclear distances and connectivities. Two-dimensional J-resolved-type experiments are then presented for the measurement of dipolar and J coupling, between spin-1/2 and quadrupolar nuclei as well as in pairs of quadrupolar nuclei. Select examples utilizing these techniques for the extraction of structural information are given. Techniques are then described that enable the fine refinement of crystalline structures using solely the electric field gradient tensor, measured using NMR, as a constraint. These approaches enable the solution of crystal structures, from polycrystalline compounds, that are of comparable quality to those solved using single-crystal diffraction.

Spin-Spin Coupling between Quadrupolar Nuclei in Solids: (11)B-(75)As Spin Pairs in Lewis Acid-Base Adducts

Solid-state (11)B NMR measurements of Lewis acid-base adducts of the form R3AsBR'3 (R = Me, Et, Ph; R' = H, Ph, C6F5) were carried out at several magnetic field strengths (e.g., B0 = 21.14, 11.75, and 7.05 T). The (11)B NMR spectra of these adducts exhibit residual dipolar coupling under MAS conditions, allowing for the determination of effective dipolar coupling constants, Reff((75)As,(11)B), as well as the sign of the (75)As nuclear quadrupolar coupling constants. Values of Reff((75)As,(11)B) range from 500 to 700 Hz. Small isotropic J-couplings are resolved in some cases, and the sign of (1)J((75)As,(11)B) is determined. Values of CQ((75)As) measured at B0 = 21.14 T for these triarylborane Lewis acid-base adducts range from -82 ± 2 MHz for Et3AsB(C6F5)3 to -146 ± 1 MHz for Ph3AsBPh3. For Ph3AsBH3, two crystallographically nonequivalent sites are identified with CQ((75)As) values of -153 and -151 ± 1 MHz. For the uncoordinated Lewis base, Ph3As, four (75)As sites with CQ((75)As) values ranging from 193.5 to 194.4 ± 2 MHz are identified. At these applied magnetic field strengths, the (75)As quadrupolar interaction does not satisfy high-field approximation criteria, and thus, an exact treatment was used to describe this interaction in (11)B and (75)As NMR spectral simulations. NMR parameters calculated using the ADF and CASTEP program packages support the experimentally derived parameters in both magnitude and sign. These experiments add to the limited body of literature on solid-state (75)As NMR spectroscopy and serve as examples of spin-spin-coupled quadrupolar spin pairs, which are also rarely treated in the literature.

Solid-state (185/187)Re NMR and GIPAW DFT study of perrhenates and Re2(CO)10: chemical shift anisotropy, NMR crystallography, and a metal-metal bond

Advances in solid-state nuclear magnetic resonance (SSNMR) methods, such as dynamic nuclear polarization (DNP), intricate pulse sequences, and increased applied magnetic fields, allow for the study of systems which even very recently would be impractical. However, SSNMR methods using certain quadrupolar probe nuclei (i.e., I > 1/2), such as (185/187)Re remain far from fully developed due to the exceedingly strong interaction between the quadrupole moment of these nuclei and local electric field gradients (EFGs). We present a detailed high-field (B0 = 21.1 T) experimental SSNMR study on several perrhenates (KReO4, AgReO4, Ca(ReO4)2·2H2O), as well as ReO3 and Re2(CO)10. We propose solid ReO3 as a new rhenium SSNMR chemical shift standard due to its reproducible and sharp (185/187)Re NMR resonances. We show that for KReO4, previously poorly understood high-order quadrupole-induced effects (HOQIE) on the satellite transitions can be used to measure the EFG tensor asymmetry (i.e., ηQ) to nearly an order-of-magnitude greater precision than competing SSNMR and nuclear quadrupole resonance (NQR) approaches. Samples of AgReO4 and Ca(ReO4)2·2H2O enable us to comment on the effects of counter-ions and hydration upon Re(vii) chemical shifts. Calcium-43 and (185/187)Re NMR tensor parameters allow us to conclude that two proposed crystal structures for Ca(ReO4)2·2H2O, which would be considered as distinct, are in fact the same structure. Study of Re2(CO)10 provides insights into the effects of Re-Re bonding on the rhenium NMR tensor parameters and rhenium oxidation state on the Re chemical shift value. As overtone NQR experiments allowed us to precisely measure the (185/187)Re EFG tensor of Re2(CO)10, we were able to measure rhenium chemical shift anisotropy (CSA) for the first time in a powdered sample. Experimental observations are supported by gauge-including projector augmented-wave (GIPAW) density functional theory (DFT) calculations, with NMR tensor calculations also provided for NH4ReO4, NaReO4 and RbReO4. These calculations are able to reproduce many of the experimental trends in rhenium δiso values and EFG tensor magnitudes. Using KReO4 as a prototypical perrhenate-containing system, we establish a correlation between the tetrahedral shear strain parameter (|ψ|) and the nuclear electric quadrupolar coupling constant (CQ), which enables the refinement of the structure of ND4ReO4. Shortcomings in traditional DFT approaches, even when including relativistic effects via the zeroth-order regular approximation (ZORA), for calculating rhenium NMR tensor parameters are identified for Re2(CO)10.

Solid-State NMR at the University of Ottawa

This article describes some highlights of the research which has been carried out in my laboratory at the University of Ottawa over the period covering 2005 to 2014. My research is in the general areas of solid-state NMR, applications of quantum chemistry, and biomolecular NMR. The format will follow that of my 2014 Canadian Society for Chemistry Keith Laidler Award presentation given in Vancouver in June 2014 at the 97th Canadian Chemistry Conference and Exhibition. Following a brief introduction, I will present some of our most interesting and exciting recent advances according to the following six themes: 1. Fundamental solid-state NMR. 2. Materials characterization and NMR crystallography. 3. Pharmaceuticals and polymorphism. 4. Non-covalent interactions: Halogen bonds. 5. Biomolecular NMR. 6. Software development.

Dynamic nuclear polarization of (1)H, (13)C, and (59)Co in a tris(ethylenediamine)cobalt(III) crystalline lattice doped with Cr(III)

The study of inorganic crystalline materials by solid-state NMR spectroscopy is often complicated by the low sensitivity of heavy nuclei. However, these materials often contain or can be prepared with paramagnetic dopants without significantly affecting the structure of the crystalline host. Dynamic nuclear polarization (DNP) is generally capable of enhancing NMR signals by transferring the magnetization of unpaired electrons to the nuclei. Therefore, the NMR sensitivity in these paramagnetically doped crystals might be increased by DNP. In this paper we demonstrate the possibility of efficient DNP transfer in polycrystalline samples of [Co(en)3Cl3]2·NaCl·6H2O (en = ethylenediamine, C2H8N2) doped with Cr(III) in varying concentrations between 0.1 and 3 mol %. We demonstrate that (1)H, (13)C, and (59)Co can be polarized by irradiation of Cr(III) with 140 GHz microwaves at a magnetic field of 5 T. We further explain our findings on the basis of electron paramagnetic resonance spectroscopy of the Cr(III) site and analysis of its temperature-dependent zero-field splitting, as well as the dependence of the DNP enhancement factor on the external magnetic field and microwave power. This first demonstration of DNP transfer from one paramagnetic metal ion to its diamagnetic host metal ion will pave the way for future applications of DNP in paramagnetically doped materials or metalloproteins.

Singularities in the lineshape of a second-order perturbed quadrupolar nucleus and their use in data fitting

Even for large quadrupolar interactions, the powder spectrum of the central transition for a half-integral spin is relatively narrow, because it is unperturbed to first order. However, the second-order perturbation is still orientation dependent, so it generates a characteristic lineshape. This lineshape has both finite step discontinuities and singularities where the spectrum is infinite, in theory. The relative positions of these features are well-known and they play an important role in fitting experimental data. However, there has been relatively little discussion of how high the steps are, so we present explicit formulae for these heights. This gives a full characterization of the features in this lineshape which can lead to an analysis of the spectrum without the usual laborious powder average. The transition frequency, as a function of the orientation angles, shows critical points: maxima, minima and saddle points. The maxima and minima correspond to the step discontinuities and the saddle points generate the singularities. Near a maximum, the contours are ellipses, whose dimensions are determined by the second derivatives of the frequency with respect to the polar and azimuthal angles. The density of points is smooth as the contour levels move up and down, but then drops to zero when a maximum is passed, giving a step. The height of the step is determined by the Hessian matrix-the matrix of all partial second derivatives. The points near the poles and the saddle points require a more detailed analysis, but this can still be done analytically. The resulting formulae are then compared to numerical simulations of the lineshape. We expand this calculation to include a relatively simple case where there is chemical shielding anisotropy and use this to fit experimental (139)La spectra of La2O3.

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 (95)Mo nuclei in structurally related compounds containing [Mo6Br8](4+) cluster cores. Experimentally determined δiso((93)Nb) values are in the range from 2,400 to 3,000 ppm. 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 (79/81)Br NQR and (35)Cl solid-state NMR measurements.

Direct observation of ¹⁷O-¹⁸⁵/¹⁸⁷Re ¹J-coupling in perrhenates by solid-state ¹⁷O VT MAS NMR: temperature and self-decoupling effects

(17)O MAS NMR spectra recorded at 14.1T and room temperature (RT) for (17)O-enriched samples of the two perrhenates, KReO4 and NH4ReO4, exhibit very similar overall appearances of the manifold of spinning sidebands (ssbs) for the satellite transitions (STs) and the central transition (CT). These overall appearances of the spectra are easily simulated in terms of the usual quadrupole coupling and chemical shift interaction parameters. However, a detailed inspection of the line shapes for the individual ssbs of the STs and, in particular, for the CT in the spectrum of KReO4 reveals line-shape features, which to our knowledge have not before been observed experimentally in 1D MAS NMR spectra for any quadrupolar nucleus, nor emerged from simulations for any combination of second-order quadrupolar interaction and chemical shift anisotropy. In contrast, such line-shape features are not observed for the corresponding ssbs (STs and CT) in the 14.1T RT (17)O MAS NMR spectrum of NH4ReO4. Considering the additional interaction of a combination of residual heteronuclear (17)O-(185/)(187)Re dipolar and scalar J coupling between this spin pair of two quadrupolar nuclei, spectral simulations for KReO4 show that these interactions are able to account for the observed line shapes, although the expected (1)J((17)O-(185/)(187)Re) six-line spin-spin splittings are not resolved. Low-temperature, high-field (21.1T) (17)O VT MAS NMR spectra of both KReO4 and NH4ReO4 show that full resolution into six-line multiplets for the centerbands are achieved at -90°C and -138°C, respectively. This allows determination of (1)J((17)O-(187)Re)=-268Hz and -278Hz for KReO4 and NH4ReO4, respectively, i.e., an isotropic (1)J coupling and its sign between two quadrupolar nuclei, observed for the first time directly from solid-state one-pulse 1D MAS NMR spectra, without resort to additional 1D or 2D experiments. Determination of T1((187)Re) spin-lattice relaxation times, observed indirectly through a 2D (17)O EXSY experiment for NH4ReO4 at several low temperatures, show that the dynamics observed for the ReO4(-) anion in the (17)O VT MAS NMR spectra at low temperatures are caused by self-decoupling of (1)J((17)O-(187)Re). The (1)J((17)O-(187)Re) values determined here for ReO4(-) from solid-state (17)O MAS NMR, along with literature (1)J((17)O-M) values for oxoanions (M being a quadrupolar nucleus) obtained from liquid-state NMR, have allowed correlations to be established between the reduced coupling constant (1)K((17)O-M)=2π(1)J((17)O-M)/(γ17OγMℏ) and the atomic number of M.

QUEST-QUadrupolar Exact SofTware: a fast graphical program for the exact simulation of NMR and NQR spectra for quadrupolar nuclei

We present a new program for the exact simulation of solid-state NMR spectra of quadrupolar nuclei in stationary powdered samples which employs diagonalization of the combined Zeeman-quadrupolar Hamiltonian. The program, which we call QUEST (QUadrupolar Exact SofTware), can simulate NMR spectra over the full regime of Larmor and quadrupolar frequency ratios, which encompasses scenarios ranging from high-field NMR to nuclear quadrupole resonance (NQR, where the Larmor frequency is zero) and does not make use of approximations when treating the quadrupolar interaction. With the use of the fast powder averaging scheme of Alderman, Solum, and Grant, exact NMR spectral simulations are only marginally slower than the second-order perturbation theory counterpart. The program, which uses a graphical user interface, also incorporates chemical shift anisotropy and non-coincident chemical shift and quadrupolar tensor frames. The program is validated against newly-acquired experimental data through several examples including: the low-field (79/81)Br NMR spectra of CaBr(2), the (14)N overtone NMR spectrum of glycine, the (187)Re NQR spectra of Re(2)(CO)(10), and lastly the (127)I overtone NQR spectrum of SrI(2), which, to the best of our knowledge, represents the first direct acquisition of an overtone NQR spectrum for a powdered sample.