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

Simulating multipulse NMR spectra of polycrystalline solids in the frequency domain

An approach is presented for simulating multipulse nuclear magnetic resonance (NMR) spectra of polycrystalline solids directly in the frequency domain. The approach integrates the symmetry pathway concept for multipulse NMR with efficient algorithms for calculating spinning sideband amplitudes and performing interpolated finite-element numerical integration over all crystallite orientations in a polycrystalline sample. The numerical efficiency is achieved through a set of assumptions used to approximate the evolution of a sparse density matrix through a pulse sequence as a set of individual transition pathway signals. The utility of this approach for simulating the spectra of complex materials, such as glasses and other structurally disordered materials, is demonstrated.

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.

Experimental Evidence for Non-Fermi-Contact J Coupling Across Chalcogen Bonds in Ionic Salt Cocrystal Polymorphs

A pair of novel polymorphic ionic cocrystals of 3,4-dicyanotelluradiazole and tetraphenylphosphonium bromide are synthesized and are characterized by single-crystal XRD. Strong and directional non-covalent chalcogen bonds (ChB) between Te and Br are analyzed via solid-state NMR to reveal large and anisotropic J(125Te,79/81Br) coupling tensors, providing unequivocal evidence for non-Fermi contact contributions across ChBs. Along with large 79/81Br quadrupolar couplings for the Br- anions, these data provide new tools to characterize chalcogen bonds and to differentiate between ChB polymorphs.

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.

3D to 0D cesium lead bromide: A 79/81Br NMR, NQR and theoretical investigation

Inorganic metal halides offer unprecedented tunability through elemental variation of simple three-element compositions, but can exhibit complicated phase behaviour, degradation, and microscopic phenomena (disorder/dynamics) that play an integral role for the bulk-level chemical and physical properties of these materials. Understanding the halogen chemical environment in such materials is crucial to addressing many of the concerns regarding implementing these materials in commercial applications. In this study, a combined solid-state nuclear magnetic resonance, nuclear quadrupole resonance and quantum chemical computation approach is used to interrogate the Br chemical environment in a series of related inorganic lead bromide materials: CsPbBr₃, CsPb₂Br₅, and Cs₄PbBr₆. The quadrupole coupling constants (C_Q) were determined to range from 61 to 114 MHz for ⁸¹Br, with CsPbBr₃ exhibiting the largest measured C_Q and Cs₄PbBr₆ the smallest. GIPAW DFT was shown to be an excellent pre-screening tool for estimating the EFG of Br materials and can increase experimental efficiency by providing good starting estimates for acquisition. Finally, the combination of theory and experiment to inform the best methods for expanding further to the other quadrupolar halogens is discussed.

Exploring the Potential of Multinuclear Solid-State 1 H, 13 C, and 35 Cl Magnetic Resonance To Characterize Static and Dynamic Disorder in Pharmaceutical Hydrochlorides

Crystallographic disorder, whether static or dynamic, can be detrimental to the physical and chemical stability, ease of crystallization and dissolution rate of an active pharmaceutical ingredient. Disorder can result in a loss of manufacturing control leading to batch-to-batch variability and can lengthen the process of structural characterization. The range of NMR active nuclei makes solid-state NMR a unique technique for gaining nucleus-specific information about crystallographic disorder. Here, we explore the use of high-field ³⁵ Cl solid-state NMR at 23.5 T to characterize both static and dynamic crystallographic disorder: specifically, dynamic disorder occurring in duloxetine hydrochloride (1), static disorder in promethazine hydrochloride (2), and trifluoperazine dihydrochloride (3). In all structures, the presence of crystallographic disorder was confirmed by ¹³ C cross-polarization magic-angle spinning (CPMAS) NMR and supported by GIPAW-DFT calculations, and in the case of 3, ¹ H solid-state NMR provided additional confirmation. Applying ³⁵ Cl solid-state NMR to these compounds, we show that higher magnetic fields are beneficial for resolving the crystallographic disorder in 1 and 3, while broad spectral features were observed in 2 even at higher fields. Combining the data obtained from ¹ H, ¹³ C, and ³⁵ Cl NMR, we show that 3 exhibits a unique case of disorder involving the ⁺ N-H hydrogen positions of the piperazinium ring, driving the chloride anions to occupy three distinct sites.

TensorView for MATLAB: Visualizing tensors with Euler angle decoding

TensorView for MATLAB is a GUI-based visualization tool for depicting second-rank Cartesian tensors as surfaces on three-dimensional molecular models. Both ellipsoid and ovaloid tensor display formats are supported, and the software allows for easy conversion of Euler angles from common rotation schemes (active, passive, ZXZ, and ZYZ conventions) with visual feedback. In addition, the software displays all four orientation-equivalent Euler angle solutions for the placement of a single tensor in the molecular frame and can report relative orientations of two tensors with all 16 orientation-equivalent Euler angle sets that relate them. The salient relations are derived and illustrated through several examples. TensorView for MATLAB expands and complements the earlier implementation of TensorView within the Mathematica programming environment and can be run without a MATLAB license. TensorView for MATLAB is available through github at https://github.com/LeoSvenningsson/TensorViewforMatlab, and can also be accessed directly via the NMRbox resource.

Recent progress in solid-state NMR of spin-½ low-γ nuclei applied to inorganic materials

Significant technological and methodological advances in solid-state NMR techniques in recent years have increased the accessibility of nuclei with small magnetic moments (hereafter termed low-γ) underpinning an increased range of applications of such nuclei. These methodological advances are briefly summarised, including improvements in hardware and pulse sequences, as well as important developments in associated computational methods (e.g. first principles calculations, spectral simulation). Here spin-½ nuclei are the focus, with this Perspective complementing a very recent review that looked at half-integer spin low-γ quadrupolar nuclei. Reference is made to some of the original reports of such spin-½ nuclei, but recent progress in the relevant methodology and applications to inorganic materials (most within the last 10 years) of these nuclei are the focus. An overview of the current state-of-the-art of studying these nuclei is thereby provided for both NMR spectroscopists and materials researchers.

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 Techniques for the Structural Characterization of Geminal Alane-Phosphane Frustrated Lewis Pairs and Secondary Adducts

The first comprehensive solid-state nuclear magnetic resonance (NMR) characterization of geminal alane-phosphane frustrated Lewis pairs (Al/P FLPs) is reported. Their relevant NMR parameters (isotropic chemical shifts, direct and indirect 27 Al-31 P spin-spin coupling constants, and 27 Al nuclear electric quadrupole coupling tensor components) have been determined by numerical analysis of the experimental NMR line shapes and compared with values computed from the known crystal structures by using density functional theory (DFT) methods. Our work demonstrates that the 31 P NMR chemical shifts for the studied Al/P FLPs are very sensitive to slight structural inequivalences. The 27 Al NMR central transition signals are spread out over a broad frequency range (>200 kHz), owing to the presence of strong nuclear electric quadrupolar interactions that can be well-reproduced by the static 27 Al wideband uniform rate smooth truncation (WURST) Carr-Purcell-Meiboom-Gill (WCPMG) NMR experiment. 27 Al chemical shifts and quadrupole tensor components offer a facile and clear distinction between three- and four-coordinate aluminum environments. For measuring internuclear Al⋅⋅⋅P distances a new resonance-echo saturation-pulse double-resonance (RESPDOR) experiment was developed by using efficient saturation via frequency-swept WURST pulses. The successful implementation of this widely applicable technique indicates that internuclear Al⋅⋅⋅P distances in these compounds can be measured within a precision of ±0.1 Å.

Recent progress in solid-state nuclear magnetic resonance of half-integer spin low-γ quadrupolar nuclei applied to inorganic materials

An overview is presented of recent progress in the solid-state nuclear magnetic resonance (NMR) observation of low-γ nuclei, with a focus on applications to inorganic materials. The technological and methodological advances in the last 20 years, which have underpinned the increased accessibility of low-γ nuclei for study by solid-state NMR techniques, are summarised, including improvements in hardware, pulse sequences and associated computational methods (e.g., first principles calculations and spectral simulation). Some of the key initial observations from inorganic materials of these nuclei are highlighted along with some recent (most within the last 10 years) illustrations of their application to such materials. A summary of other recent reviews of the study of low-γ nuclei by solid-state NMR is provided so that a comprehensive understanding of what has been achieved to date is available.

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.

Field-stepped ultra-wideline NMR at up to 36 T: On the inequivalence between field and frequency stepping

Field-stepped NMR spectroscopy at up to 36 T using the series-connected hybrid (SCH) magnet at the U.S. National High Magnetic Field Laboratory is demonstrated for acquiring ultra-wideline powder spectra of nuclei with very large quadrupolar interactions. Historically, NMR evolved from the continuous-wave (cw) field-swept method in the early days to the pulsed Fourier-transform method in the modern era. Spectra acquired using field sweeping are generally considered to be equivalent to those acquired using the pulsed method. Here, it is shown that field-stepped wideline spectra of half-integer spin quadrupolar nuclei acquired using WURST/CPMG methods can be significantly different from those acquired with the frequency-stepped method commonly used with superconducting magnets. The inequivalence arises from magnetic field-dependent NMR interactions such as the anisotropic chemical shift and second-order quadrupolar interactions; the latter is often the main interaction leading to ultra-wideline powder patterns of half-integer spin quadrupolar nuclei. This inequivalence needs be taken into account to accurately and correctly determine the quadrupolar coupling and chemical shift parameters. A simulation protocol is developed for spectral fitting to facilitate analysis of field-stepped ultra-wideline NMR spectra acquired using powered magnets. A MATLAB program which implements this protocol is available on request.

Efficient epoxidation over dinuclear sites in titanium silicalite-1

Titanium silicalite-1 (TS-1) is a zeolitic material with MFI framework structure, in which 1 to 2 per cent of the silicon atoms are substituted for titanium atoms. It is widely used in industry owing to its ability to catalytically epoxidize olefins with hydrogen peroxide (H₂O₂), leaving only water as a byproduct^1,2; around one million tonnes of propylene oxide are produced each year using this process³. The catalytic properties of TS-1 are generally attributed to the presence of isolated Ti(IV) sites within the zeolite framework¹. However, despite almost 40 years of experimental and computational investigation^4-10, the structure of these active Ti(IV) sites is unconfirmed, owing to the challenges of fully characterizing TS-1. Here, using a combination of spectroscopy and microscopy, we characterize in detail a series of highly active and selective TS-1 propylene epoxidation catalysts with well dispersed titanium atoms. We find that, on contact with H₂¹⁷O₂, all samples exhibit a characteristic solid-state ¹⁷O nuclear magnetic resonance signature that is indicative of the formation of bridging peroxo species on dinuclear titanium sites. Further, density functional theory calculations indicate that cooperativity between two titanium atoms enables propylene epoxidation via a low-energy reaction pathway with a key oxygen-transfer transition state similar to that of olefin epoxidation by peracids. We therefore propose that dinuclear titanium sites, rather than isolated titanium atoms in the framework, explain the high efficiency of TS-1 in propylene epoxidation with H₂O₂. This revised view of the active-site structure may enable further optimization of TS-1 and the industrial epoxidation process.

Field-stepwise-swept QCPMG solid-state 115In NMR of indium oxide

Experimental and theoretical investigations of indium-115 electric-field-gradient (EFG) tensors of indium(III) oxide, In₂O₃, have been presented. Field-stepwise-swept QCPMG solid-state ¹¹⁵In NMR experiments are carried out at T ​= ​120 ​K, observed at 52.695 ​MHz, and in the range of external magnetic fields between 4.0 and 6.5 ​T. The spectral simulations yield the quadrupolar coupling constant, C_Q value, of 183(2) MHz and the asymmetry parameter, η_Q, of 0.05(5), for In(1), and that of 126(2) MHz and η_Q of 0.86(5) for In(2). Quantum chemical calculations are carried out to provide ¹¹⁵In EFG tensor orientations with respect to the molecular structure. A relationship between operative frequencies and variable ranges of external magnetic fields is briefly discussed for field-swept solid-state ¹¹⁵In NMR.

Bulk and Nanocrystalline Cesium Lead-Halide Perovskites as Seen by Halide Magnetic Resonance

Lead-halide perovskites increasingly mesmerize researchers because they exhibit a high degree of structural defects and dynamics yet nonetheless offer an outstanding (opto)electronic performance on par with the best examples of structurally stable and defect-free semiconductors. This highly unusual feature necessitates the adoption of an experimental and theoretical mindset and the reexamination of techniques that may be uniquely suited to understand these materials. Surprisingly, the suite of methods for the structural characterization of these materials does not commonly include nuclear magnetic resonance (NMR) spectroscopy. The present study showcases both the utility and versatility of halide NMR and NQR (nuclear quadrupole resonance) for probing the structure and structural dynamics of CsPbX3 (X = Cl, Br, I), in both bulk and nanocrystalline forms. The strong quadrupole couplings, which originate from the interaction between the large quadrupole moments of, e.g., the 35Cl, 79Br, and 127I nuclei, and the local electric-field gradients, are highly sensitive to subtle structural variations, both static and dynamic. The quadrupole interaction can resolve structural changes with accuracies commensurate with synchrotron X-ray diffraction and scattering. It is shown that space-averaged site-disorder is greatly enhanced in the nanocrystals compared to the bulk, while the dynamics of nuclear spin relaxation indicates enhanced structural dynamics in the nanocrystals. The findings from NMR and NQR were corroborated by ab initio molecular dynamics, which point to the role of the surface in causing the radial strain distribution and disorder. These findings showcase a great synergy between solid-state NMR or NQR and molecular dynamics simulations in shedding light on the structure of soft lead-halide semiconductors.

Solid-state Be-9 NMR of beryllium compounds

Despite the favorable NMR-spectroscopic features of the 9Be isotope, the exploration of solid Beryllium compounds by this method has been very limited, owing to safety concerns regarding their preparation and handling. The present review aims to be the first comprehensive one on this topic, summarizing the classical and modern methodologies available for determining the relevant 9Be NMR observables in the solid state. Results on molecular crystals, oxidic materials, and intermetallic systems will be discussed in terms of their informational content in relation to atomic and electronic structure and dynamics, leading to suggestions for future paths of investigation.

Solid-State NMR Techniques for the Structural Characterization of Cyclic Aggregates Based on Borane-Phosphane Frustrated Lewis Pairs

Modern solid-state NMR techniques offer a wide range of opportunities for the structural characterization of frustrated Lewis pairs (FLPs), their aggregates, and the products of cooperative addition reactions at their two Lewis centers. This information is extremely valuable for materials that elude structural characterization by X-ray diffraction because of their nanocrystalline or amorphous character, (pseudo-)polymorphism, or other types of disordering phenomena inherent in the solid state. Aside from simple chemical shift measurements using single-pulse or cross-polarization/magic-angle spinning NMR detection techniques, the availability of advanced multidimensional and double-resonance NMR methods greatly deepened the informational content of these experiments. In particular, methods quantifying the magnetic dipole-dipole interaction strengths and indirect spin-spin interactions prove useful for the measurement of intermolecular association, connectivity, assessment of FLP-ligand distributions, and the stereochemistry of adducts. The present review illustrates several important solid-state NMR methods with some insightful applications to open questions in FLP chemistry, with a particular focus on supramolecular associates.

Rapid Identification of Halogen Bonds in Co-Crystalline Powders via 127 I Nuclear Quadrupole Resonance Spectroscopy

¹²⁷ I nuclear quadrupole resonance (NQR) spectroscopy is established as a rapid and robust method to indicate the formation of iodine-nitrogen halogen bonds in co-crystalline powders. Once the relevant spectral frequency range has been established, diagnostic ¹²⁷ I NQR spectra can be acquired in seconds. The method is demonstrated for a series of co-crystals of 1,4-diiodobenzene. Changes in the ¹²⁷ I quadrupolar coupling constant (C_Q ) by up to 74.4 MHz correlate with the length of the C-I donor covalent bond and inversely with the I⋅⋅⋅N halogen-bond length. The predictive power of this technique is validated on two previously unknown co-crystalline powders prepared mechanochemically. Single-crystal growth via co-sublimation and structure determination by single-crystal X-ray diffraction cross-validates the findings. Natural localized molecular-orbital analyses provide insight into the origins of the quadrupolar coupling constants.

Linear-scaling ab initio simulations of spin diffusion in rotating solids

We investigated the utility of locally restricting the basis sets involved in low-order correlations in Liouville space (LCL) calculations of spin diffusion. Using well-known classical models of spin diffusion, we describe a rationale for selecting the optimal basis set for such calculations. We then show that the use of these locally restricted basis sets provides the same computational accuracy as the full LCL set while reducing the computational time by several orders of magnitude. Speeding up the calculations also enables us to use higher maximum spin orders and increase the computational accuracy. Furthermore, unlike exact and full LCL calculations, locally restricted LCL calculations scale linearly with the system size and should thus enable the ab initio study of spin diffusion in spin systems containing several thousand spins.

TensorView: A software tool for displaying NMR tensors

The representation of nuclear magnetic resonance (NMR) tensors as surfaces on three-dimensional molecular models is an information-rich presentation that highlights the geometric relationship between tensor principal components and the underlying molecular and electronic structure. Here, we describe a new computational tool, TensorView, for depicting NMR tensors on the molecular framework. This package makes use of the graphical interface and built-in molecular display functionality present within the Mathematica programming environment and is robust for displaying tensor properties from a broad range of commercial and user-specific computational chemistry packages. Two mathematical forms for representing tensor interaction surfaces are presented, the popular ellipsoidal construct and the more technically correct "ovaloid" form. Examples are provided for chemical shielding and shift tensors, dipole-dipole and quadrupolar couplings, and atomic anisotropic displacement parameters (thermal ellipsoids) derived from NMR crystallography.

121/123Sb Nuclear Quadrupole Resonance Spectroscopy: Characterization of Non-Covalent Pnictogen Bonds and NQR Crystallography

Pnictogen (or pnicogen) bonding is an attractive interaction between the electrophilic region of group 15 elements (N, P, As, Sb, Bi) and a nucleophile. This interaction for which unique applications in catalysis have recently been uncovered continues to gain popularity. Here, we investigate a series of pnictogen-bonded cocrystals based on SbF₃ and SbCl₃, prepared via mechanochemical ball milling, with ^121/123Sb ( I = ⁵/₂ and ⁷/₂, respectively) nuclear quadrupole resonance (NQR) spectroscopy. Observed NQR frequency shifts upon cocrystallization are on the order of 0.1 to 10 MHz and are clearly diagnostic of the formation of pnictogen bonds to antimony. Further evidence for pnictogen bonding is obtained by complementary ¹³C cross-polarization magic-angle spinning solid-state NMR experiments. DFT calculations of NMR parameters as well as natural localized molecular orbital analyses support the experimental findings and elucidate the electronic origins of the experimental NQR frequency shifts. This work provides insights into the changes in the antimony quadrupolar coupling constant upon pnictogen bonding: strikingly, the decreases noted here parallel those known for hydrogen bonds, but contrast with the increases reported for halogen bonds. The utility of the observed antimony nuclear quadrupolar coupling constants in constraining structural models of cocrystals for which diffraction-based structures are unavailable, i.e., a rudimentary implementation of NQR crystallography, is established. Overall, this work offers a new approach to understand emerging classes of electrophilic interactions and to contextualize them in the broader landscape of established chemical bonding paradigms.

Natural abundance solid-state 33S NMR study of NbS3: applications for battery conversion electrodes

The first known solid-state ³³S NMR spectrum of disulfide (S₂²⁻) anions is reported, in the Li-ion battery conversion material NbS₃.

Quadrupolar 14N NMR Relaxation from Force-Field and Ab Initio Molecular Dynamics in Different Solvents

Quadrupolar NMR spin relaxation rates and corresponding line widths were computed for the quadrupolar nucleus ¹⁴N for neat acetonitrile as well as for 1-methyl-1,3-imidazole and 1-methyl-1,3,4-triazole in different solvents. Molecular dynamics (MD) was performed with forces from the Kohn-Sham (KS) theory (ab initio MD) and force-field molecular mechanics (classical MD), followed by KS electric field gradient (EFG) calculations. For acetonitrile the agreement of the ¹⁴N line width with experiment is very good. Relative line widths for the azole nitrogens are improved over simpler approximations used previously in conjunction with single-point calculations at the multiconfigurational self-consistent field level. Overall, the NMR line widths are computed within a factor of 2 of the experimental values, giving access to reasonable estimates both of the dynamic EFG variance in the solvated systems as well as the associated correlation times that determine the relaxation rates.

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.

79/81Br nuclear quadrupole resonance spectroscopic characterization of halogen bonds in supramolecular assemblies

One- and two-dimensional bromine-79/81 NQR spectroscopy of halogen bond donors in a series of cocrystals shows changes in resonance frequency of up to 20 MHz and differentiates between crystallographically non-equivalent bromine sites.

Despite the applicability of solid-state NMR to study the halogen bond, the direct NMR detection of ^79/81Br covalently bonded to carbon remains impractical due to extremely large spectral widths, even at ultra-high magnetic fields. In contrast, nuclear quadrupole resonance (NQR) offers comparatively sharp resonances. Here, we demonstrate the abilities of ^79/81Br NQR to characterize the electronic changes in the C–Br···N halogen bonding motifs found in supramolecular assemblies constructed from 1,4-dibromotetrafluorobenzene and nitrogen-containing heterocycles. An increase in the bromine quadrupolar coupling constant is observed, which correlates linearly with the halogen bond distance (d_Br···N). Notably, ^79/81Br NQR is able to distinguish between two symmetry-independent halogen bonds in the same crystal structure. This approach offers a rapid and reliable indication for the occurrence of a halogen bond, with experimental times limited only by the observation of ^79/81Br NQR resonances.

Structural Insights from 59 Co Solid-State NMR Experiments on Organocobalt(I) Catalysts

A series of fumarate-based organocobalt(I) [CoCp(CO)(fumarate)] catalysts is synthesized and characterized by X-ray crystallography, multinuclear (¹³ C and ⁵⁹ Co) solid-state NMR spectroscopy, and ⁵⁹ Co NQR spectroscopy. Given the dearth of ⁵⁹ Co solid-state NMR studies on Co^I compounds, the present work constitutes the first systematic characterization of the ⁵⁹ Co electric field gradient and chemical shift tensors for a series of cobalt complexes in this oxidation state. Using X-ray crystallography, the molecular geometry about the Co^I centre is found to be nearly identical in all compounds studied herein. Owing to the ⁵⁹ Co nucleus' large chemical shift range, solid-state NMR experiments are found to be able to detect small structural differences between the individual organocobalt(I) compounds. With the aid of density functional theory calculations on these complexes, it is shown that the ⁵⁹ Co chemical shift anisotropy and the ⁵⁹ Co quadrupolar coupling constant are both extremely sensitive gauges of the Fu-Co-Cp bond angle, providing a link between these ⁵⁹ Co NMR observables and the catalysts' structures.

A Modular Implementation for the Simulation of 1D and 2D Solid-State NMR Spectra of Quadrupolar Nuclei in the Virtual Multifrequency Spectrometer-Draw Graphical Interface

We present the implementation of the solid state (SoS)NMR module for the simulation of several 1D and 2D NMR spectra of all the elements in the periodic table in the virtual multifrequency spectrometer (VMS). This module is fully integrated with the graphical user interface of VMS (VMS-Draw) [Licari et al., J. Comput. Chem. 36, 2015, 321-334], a freeware tool which allows a user-friendly handling of structures and analyses of advanced spectroscopical properties of chemical compounds-from model systems to real-world applications. Besides the numerous modules already available in VMS for the study of electronic, optical, vibrational, vibronic, and EPR properties, here the simulation of NMR spectra is presented with a particular emphasis on those techniques usually employed to investigate solid state systems. The SoSNMR module benefits from its ability to work under both periodic and nonperiodic conditions, such that small molecules/molecular clusters can be treated, as well as extended three-dimensional systems enforcing (or not) translational periodicity. These features allow VMS to simulate spectra resulting from NMR calculations by some popular quantum chemistry codes, namely Gaussian09/16, Castep, and Quantum Espresso. The effectiveness of the SoSNMR module of VMS is examined throughout the manuscript, and applied to simulate 1D static, MAS, and VAS NMR spectra as well as 2D correlation (90°, MAS) and MQMAS spectra of active NMR nuclei embedded in different amorphous and crystalline systems of actual interest in chemistry and material science. Finally, the program is able to simulate the spectra of both the total ensemble of spin-active nuclei present in the system and of subensembles differentiated depending on the chemical environment of the first and second coordination sphere in a very general way applicable to any kind of systems.

Insight into the local environment of magnesium and calcium in low-coordination-number organo-complexes using 25Mg and 43Ca solid-state NMR: a DFT study

With the increasing number of organocalcium and organomagnesium complexes under development, there is a real need to be able to characterize in detail their local environment in order to fully rationalize their reactivity. For crystalline structures, in cases when diffraction techniques are insufficient, additional local spectroscopies like ²⁵Mg and ⁴³Ca solid-state NMR may provide valuable information to help fully establish the local environment of the metal ions. In this current work, a prospective DFT investigation on crystalline magnesium and calcium complexes involving low-coordination numbers and N-bearing organic ligands was carried out, in which the ²⁵Mg and ⁴³Ca NMR parameters [isotropic chemical shift, chemical shift anisotropy (CSA) and quadrupolar parameters] were calculated for each structure. The analysis of the calculated parameters in relation to the local environment of the metal ions revealed that they are highly sensitive to very small changes in geometry/distances, and hence that they could be used to assist in the refinement of crystal structures. Moreover, such calculations provide a guideline as to how the NMR measurements will need to be performed, revealing that these will be very challenging.

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.

Enhanced efficiency of solid-state NMR investigations of energy materials using an external automatic tuning/matching (eATM) robot

We have developed and explored an external automatic tuning/matching (eATM) robot that can be attached to commercial and/or home-built magic angle spinning (MAS) or static nuclear magnetic resonance (NMR) probeheads. Complete synchronization and automation with Bruker and Tecmag spectrometers is ensured via transistor-transistor-logic (TTL) signals. The eATM robot enables an automated "on-the-fly" re-calibration of the radio frequency (rf) carrier frequency, which is beneficial whenever tuning/matching of the resonance circuit is required, e.g. variable temperature (VT) NMR, spin-echo mapping (variable offset cumulative spectroscopy, VOCS) and/or in situ NMR experiments of batteries. This allows a significant increase in efficiency for NMR experiments outside regular working hours (e.g. overnight) and, furthermore, enables measurements of quadrupolar nuclei which would not be possible in reasonable timeframes due to excessively large spectral widths. Additionally, different tuning/matching capacitor (and/or coil) settings for desired frequencies (e.g.⁷Li and ³¹P at 117 and 122MHz, respectively, at 7.05 T) can be saved and made directly accessible before automatic tuning/matching, thus enabling automated measurements of multiple nuclei for one sample with no manual adjustment required by the user. We have applied this new eATM approach in static and MAS spin-echo mapping NMR experiments in different magnetic fields on four energy storage materials, namely: (1) paramagnetic ⁷Li and ³¹P MAS NMR (without manual recalibration) of the Li-ion battery cathode material LiFePO₄; (2) paramagnetic ¹⁷O VT-NMR of the solid oxide fuel cell cathode material La₂NiO_4+δ; (3) broadband ⁹³Nb static NMR of the Li-ion battery material BNb₂O₅; and (4) broadband static ¹²⁷I NMR of a potential Li-air battery product LiIO₃. In each case, insight into local atomic structure and dynamics arises primarily from the highly broadened (1-25MHz) NMR lineshapes that the eATM robot is uniquely suited to collect. These new developments in automation of NMR experiments are likely to advance the application of in and ex situ NMR investigations to an ever-increasing range of energy storage materials and systems.

Determination of nuclear quadrupolar parameters using singularities in field-swept NMR patterns

We propose a simple data-analysis scheme to determine the coupling constant and the asymmetry parameter of nuclear quadrupolar interactions in field-swept nuclear magnetic resonance (NMR) for static powder samples. This approach correlates the quadrupolar parameters to the positions of the singularities, which can readily be found out as sharp peaks in the field-swept pattern. Moreover, the parameters can be determined without quantitative acquisition and elaborate calculation of the overall profile of the pattern. Since both experimental and computational efforts are significantly reduced, the approach presented in this work will enhance the power of the field-swept NMR for yet unexplored quadrupolar nuclei. We demonstrate this approach in ³³S in α-S₈ and ³⁵Cl in chloranil. The accuracy of the obtained quadrupolar parameters is also discussed.

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.

Direct Characterization of Metal-Metal Bonds between Nuclei with Strong Quadrupolar Interactions via NMR Spectroscopy

Metal-metal bonds can be difficult to characterize directly. We demonstrate that J couplings between metal nuclei experiencing strong quadrupolar interactions can be easily measured from well-defined splittings in NMR spectra of powdered samples. Using (69/71)Ga NMR, it is shown that homonuclear J coupling, which is four orders of magnitude smaller than the quadrupolar coupling in a series of compounds featuring gallium-gallium bonds, can be extracted with a 2-D NMR experiment. The dependence of the multiplets on crystal symmetry reveals information on the structures of two Ga-Ga-bonded compounds for which diffraction data are unavailable. Interpretation of the data in a molecular orbital framework provides insight into the nature of the metal-metal bond.

Feasibility of arsenic and antimony NMR spectroscopy in solids: an investigation of some group 15 compounds

The feasibility of obtaining (75)As and (1)(21/123)Sb NMR spectra for solids at high and moderate magnetic field strengths is explored. Arsenic-75 nuclear quadrupolar coupling constants and chemical shifts have been measured for arsenobetaine bromide and tetraphenylarsonium bromide. Similarly, (121/123)Sb NMR parameters have been measured for tetraphenylstibonium bromide and potassium hexahydroxoantimonate. The predicted pseudo-tetrahedral symmetry at arsenic and the known trigonal bipyramidal symmetry at antimony in their respective tetraphenyl-bromide "salts" are reflected in the measured (75)As and (121)Sb nuclear quadrupole coupling constants, CQ((75)As)=7.8MHz and CQ((121)Sb)=159MHz, respectively. Results of density functional theory quantum chemistry calculations for isolated molecules using ADF and first-principles calculations using CASTEP, a gauge-including projector augmented wave method to deal with the periodic nature of solids, are compared with experiment. Although the experiments can be time consuming, measurements of (75)As and (121)Sb NMR spectra (at 154 and 215MHz, respectively, i.e., at B0=21.14T) with linewidths in excess of 1MHz are feasible using uniform broadband excitation shaped pulse techniques (e.g., WURST and WURST-QCPMG).

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.