Measuring dipolar and J coupling between quadrupolar nuclei using double-rotation NMR

Predicting 35-Cl electric field gradient tensors in crystalline solids using cluster and fragment-corrected planewave density functional theory

Planewave-corrected methods have proven effective for accurately modeling nuclear magnetic resonance (NMR) parameters in crystalline systems. Recent work extended the application of planewave-corrected calculations beyond the second row, predicting EFG tensor parameters for 35Cl using a simple molecular correction to projector augmented-wave (PAW) density functional theory (DFT). Here we extend this work using fragment and cluster-based calculations coupled with polarizable continuum (PCM) methods to improve further the accuracy of planewave-corrected 35Cl EFG tensor calculations. Benchmark data from a test set comprised of 105 individual 35Cl EFG tensor principal components for chlorine-containing molecular crystals and crystalline chloride salts shows fragment-corrected planewave calculations using the PBE0 hybrid density functional improve the accuracy of predicted EFG tensor components by 30 % relative to traditional planewave calculations. We compare the influence of different geometry optimization methods and density functionals on the accuracy of predicted 35Cl EFG tensor parameters. Four cases of spectral assignment are presented to demonstrate the utility of improving the accuracy of predicted 35Cl EFG tensor parameters.

Double-rotation (DOR) NMR spectroscopy: Progress and perspectives

Double-rotation (DOR) solid-state NMR spectroscopy is a high-resolution technique developed in the late 1980s. Although multiple-quantum magic-angle spinning (MQMAS) became the most widely used high-resolution method for half-integer spin quadrupoles after 1995, development and application of DOR NMR to a variety of chemical and materials science problems has endured. This Trend article recapitulates the development of DOR NMR, discusses various applications, and describes possible future directions. The main technical limitations specific to DOR NMR are simply related to the size of the double rotor system. The relatively large outer rotor (and thus coil) used for most applications over the past 35 years translates into relatively low rotor spinning frequencies, a low filling factor, and weak radiofrequency powers available for excitation and for proton decoupling. Ongoing developments in NMR instrumentation, including ever-shrinking MAS rotors and spherical NMR rotors, could solve many of these problems and may augur a renaissance for DOR NMR.

Can simple 'molecular' corrections outperform projector augmented-wave density functional theory in the prediction of 35 Cl electric field gradient tensor parameters for chlorine-containing crystalline systems?

Many-body expansion (MBE) fragment approaches have been applied to accurately compute nuclear magnetic resonance (NMR) parameters in crystalline systems. Recent examples demonstrate that electric field gradient (EFG) tensor parameters can be accurately calculated for 14 N and 17 O. A key additional development is the simple molecular correction (SMC) approach, which uses two one-body fragment (i.e., isolated molecule) calculations to adjust NMR parameter values established using 'benchmark' projector augmented-wave (PAW) density functional theory (DFT) values. Here, we apply a SMC using the hybrid PBE0 exchange-correlation (XC) functional to see if this can improve the accuracy of calculated 35 Cl EFG tensor parameters. We selected eight organic and two inorganic crystal structures and considered 15 chlorine sites. We find that this SMC improves the accuracy of computed values for both the 35 Cl quadrupolar coupling constant (CQ ) and the asymmetry parameter ( η Q ) by approximately 30% compared with benchmark PAW DFT values. We also assessed a SMC that offers local improvements not only in terms of the quality of the XC functional but simultaneously in the quality of the description of relativistic effects via the inclusion of spin-orbit effects. As the inorganic systems considered contain heavy atoms bonded to the chlorine atoms, we find further improvements in the accuracy of calculated 35 Cl EFG tensor parameters when both a hybrid functional and spin-orbit effects are included in the SMC. On the contrary, for chlorine-containing organics, the inclusion of spin-orbit relativistic effects using a SMC does not improve the accuracy of computed 35 Cl EFG tensor parameters.

The Structure of Boron Monoxide

Boron monoxide (BO), prepared by the thermal condensation of tetrahydroxydiboron, was first reported in 1955; however, its structure could not be determined. With the recent attention on boron-based two-dimensional materials, such as borophene and hexagonal boron nitride, there is renewed interest in BO. A large number of stable BO structures have been computationally identified, but none are supported by experiments. The consensus is that the material likely forms a boroxine-based two-dimensional material. Herein, we apply advanced 11B NMR experiments to determine the relative orientations of B(B)O2 centers in BO. We find that the material is composed of D2h-symmetric O2B-BO2 units that organize to form larger B4O2 rings. Further, powder diffraction experiments additionally reveal that these units organize to form two-dimensional layers with a random stacking pattern. This observation is in agreement with earlier density functional theory (DFT) studies that showed B4O2-based structures to be the most stable.

First-principles calculation of 11B solid-state NMR parameters of boron-rich compounds II: the orthorhombic phases MgB7 and MgB12C2 and the boron modification γ-B28

Based on the work on referencing 11B nuclear magnetic resonance (NMR) spectra for molecular icosahedral boranes and the subsequent transfer to the rhombohedral boron-rich borides of the α-rB12 type, we show that the magic angle spinning (MAS) NMR spectra of boron-rich borides with four or five symmetry-independent boron atoms can also be calculated. The calculations are performed on the level of density functional theory (DFT) using the gauge-including projector-augmented wave (GIPAW) approach. As model compounds o-MgB12C2 and MgB7 are used, for which the experimental spectra could be calculated in excellent agreement with a deviation of 1 to 2 ppm. Based on the calculations, the different B atoms can be assigned to the respective signals, taking into account the quadrupolar coupling constants Cq from computation of the electric field gradient (EFG) with its main axis Vzz. It is shown that due to the specific geometric conditions of icosahedra, the magnitudes of Vzz for the boron atoms involved in exohedral B-B bonds to neighbouring icosahedra depend only on the valence electron density of the bond critical point and the distance. This also applies to the bonds to the interstitial B2 unit in MgB7, but not to bonds to the heteroatom of the C2 dumbbell in o-MgB12C2. Both results are in line with our previous observations for the rhombohedral species (α-rB12; B12X2 with X = P, As, O). Finally, the spectrum of γ-B28 was calculated, whose structure also contains B12 icosahedra and interstitial B2 dumbbells. Here, a very similar bonding situation is found for the icosahedron, but the calculations show that the situation for the B2 unit is clearly different. In general, the only parameter that needs to be varied to fit calculated and measured spectra is the linewidth, as this cannot be calculated. For the cases of o-MgB12C2 and MgB7 signal areas are related to corresponding site multiplicities. A prerequisite for the successful application of the chosen method seems to be the presence of a semiconductor with a sufficiently large band gap, which is the case for the compounds investigated.

First-principles calculation of 11B solid-state NMR parameters of boron-rich compounds I: the rhombohedral boron modifications and B12X2 (X = P, As, O)

In the present study, solid-state nuclear magnetic resonance (NMR) spectra under magic angle spinning conditions of the rhombohedral structures α-B and B12P2 are reported together with the corresponding parameter sets from first principles calculations on α-B B12X2 (X = P, As, O). With the combination of density functional theory (DFT) and the gauge-including projector-augmented wave (GIPAW) approach as the theoretical tools at hand the computed 11B parameters lead to unambiguous explanation of the measurements. Thereby, we overcome common obstacles of processing recorded NMR spectra of solid-state compounds with several crystallographic positions, in particular non-trivial signal assignments and parameter determination due to peak overlap or even unexpected intensity/area ratios. In fact, we find very good agreement between the theoretical results and measured spectra without applying fitting procedures. Using the Perdew-Burke-Ernzerhof (PBE) functional, the results of the common construction types for pseudopotentials and referencing methods for the chemical shift determination are compared. Suggestions and conclusions from experimental 11B NMR studies on parameters according to the icosahedral positions are critically discussed, for instance the early suspected correlation to chemical shifts is not confirmed. Regarding the electric field gradient (EFG) a detailed explanation for obtaining small deviations amongst all investigated structures of the icosahedral polar sites compared to the equatorial sites is given. Our results show an important link between the exohedral bonding situation of compounds with icosahedral structure elements and the main axis of the EFG and therefore, also measurable quadrupole coupling constants if certain geometrical conditions are fulfilled. Finally, this work also contributes to establishing the number of unique sites measured by solid-state NMR methods within the modification of β-B.

GIAO versus GIPAW: Comparison of Methods To Calculate 11B NMR Shifts of Icosahedral Closo-Heteroboranes toward Boron-Rich Borides

In this work, we perform first-principle density functional theory calculations with the Perdew-Burke-Ernzerhof (PBE) exchange correlation functional to compare the results of the gauge-including atomic orbital (GIAO) method with the gauge-including projector-augmented wave (GIPAW) approach for isotropic ¹¹B nuclear magnetic resonance shifts. GIPAW had been used successfully for the theoretical calculation of nuclear magnetic parameters of ¹¹B species in strong ionic solid-phase compounds such as borates but had been applied very rarely to structures where boron is mainly involved in complex covalent bonding situations, for example, in icosahedra of boron-rich borides. Thus, we investigate the accuracy of both well-known methods and reliability of the effective treatment of core electrons on a test set containing 16 experimentally known closo-(hetero)dodecaboranes. In general, we find very good agreement between GIAO and GIPAW when compared to experimental observations. However, accidental degeneracies of the shift values are better predicted by GIPAW. The optimized molecular geometries on the PBE level agree well with gaseous electron diffraction data and lead to theoretical isotropic chemical ¹¹B shifts with root-mean-square errors of 2.1 and 1.0 ppm depending on the used model of converting absolute shieldings to chemical shifts. The comparison with results from hybrid functionals (B3LYP, B3LYP-D2, and PBE0) shows a minor improvement in accuracy, which is in agreement with ¹³C shifts of sp³-hybridized species. In order to prove the reliability of the conversion parameters obtained by PBE, we report the calculated ¹¹B shifts of 1,2-, 1,7-, and 1,12-PCB₁₀H₁₁ with GIAO and GIPAW to our knowledge for the first time. Additionally, Bader's analysis is carried out on the converged electron density for all boron species within the molecular test set, yielding no simple direct relation between charge and isotropic shifts.

Improved Magnetization Transfers among Quadrupolar Nuclei in Two-Dimensional Homonuclear Correlation NMR Experiments Applied to Inorganic Network Structures

We demonstrate that supercycles of previously introduced two-fold symmetry dipolar recoupling schemes may be utilized successfully in homonuclear correlation nuclear magnetic resonance (NMR) spectroscopy for probing proximities among half-integer spin quadrupolar nuclei in network materials undergoing magic-angle-spinning (MAS). These (SR221)M, (SR241)M, and (SR281)M recoupling sequences with M=3 and M=4 offer comparably efficient magnetization transfers in single-quantum–single-quantum (1Q–1Q) correlation NMR experiments under moderately fast MAS conditions, as demonstrated at 14.1 T and 24 kHz MAS in the contexts of 11B NMR on a Na2O–CaO–B2O3–SiO2 glass and 27Al NMR on the open framework aluminophosphate AlPO-CJ19 [(NH4)2Al4(PO4)4HPO4·H2O]. Numerically simulated magnetization transfers in spin–3/2 pairs revealed a progressively enhanced tolerance to resonance offsets and rf-amplitude errors of the recoupling pulses along the series (SR221)M< (SR241)M< (SR281)M for increasing differences in chemical shifts between the two nuclei. Nonetheless, for scenarios of a relatively minor chemical-shift dispersions (≲3 kHz), the (SR221)M supercycles perform best both experimentally and in simulations.

SCFit: Software for single-crystal NMR analysis. Free vs constrained fitting

The design and implementation of a software package for the analysis of single-crystal NMR data is presented. The SCFit software can treat spectra arising from various interactions: (i) chemical shift tensor only; (ii) chemical shift tensor and quadrupolar coupling tensor; (iii) dipolar and indirect nuclear spin-spin coupling tensors; (iv) all four interactions. The software is demonstrated on recently reported ¹⁷O and ³¹P single-crystal NMR data for triphenylphosphine oxide and for two of its halogen-bonded cocrystals. The ¹⁷O single-crystal NMR data represent a case where all four above-mentioned interactions simultaneously affect the spectra. SCFit can fit the chemical shift and quadrupolar coupling in two ways: (i) through an unconstrained fitting process where all tensor parameters are freely optimized or (ii) through a constrained fitting process where the principal components of the tensors may be fixed to values known previously with high precision via the analysis of powder samples. The second strategy is explored in an effort to reduce the number of unknowns in the fitting process; an improvement in the precision of the resulting tensor orientations is noted in some cases.

Dynamic Disorder and Electronic Structures of Electron-Precise Dianionic Diboranes: Insights from Solid-State Multinuclear Magnetic Resonance Spectroscopy

The J(¹¹B,¹¹B) coupling constants of various salts of the electron-precise hexacyanodiborane(6) dianion, [B₂(CN)₆]^2-, were obtained using ¹¹B double-quantum-filtered (DQF) J-resolved solid-state nuclear magnetic resonance (SSNMR) spectroscopy. Our results show that the magnitude of the DQF J splitting is influenced by both the crystallographic symmetry of the system and the presence of dynamics. The splittings are amplified by a factor of 3 as compared to the corresponding theoretical J coupling constants for cases where (1) there is an absence of dynamics but the boron pairs are crystallographically equivalent or (2) the boron pairs are crystallographically inequivalent but are rendered magnetically equivalent on the time scale of the experiment due to dynamic disorder, which was identified by ¹¹B and ¹³C SSNMR experiments. Consequently, molecular motions need to be taken into consideration when interpreting the results of DQF J-resolved experiments, and conversely, these experiments may be used to identify dynamic disorder. Variable-temperature NMR data support the notion of three different motional processes with correlation times ranging from 10² to 10⁶ s^-1 over the temperature range of 248-306 K. When molecular motion and crystallographic symmetry are both accounted for, the J(¹¹B,¹¹B) coupling constants for various [B₂(CN)₆]^2- salts were measured to range from 29.4 to 35.8 Hz, and their electronic origins were determined using natural localized molecular orbital and natural bond orbital analyses. The coupling constants were found to strongly correlate to the hybridization states of the boron orbitals that form the B-B bonds and to the strength of the B-B bonds. This study provides a novel tool to study dynamics in ordered and disordered solids and provides new perspectives on electron-precise dianionic diboranes featuring two-center-two-electron bonds in the context of related compounds featuring multiply and singly bonded boron spin pairs.

An efficient 2D 11B–11B solid-state NMR spectroscopy strategy for monitoring covalent self-assembly of boronic acid-derived compounds: the transformation and unique architecture of bortezomib molecules in the solid state

An efficient 2D ¹¹B–¹¹B ssNMR strategy for exploring the covalent assembly of boronic acid derivatives in the solid state is demonstrated.

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.

Spatial reorientation experiments for NMR of solids and partially oriented liquids

Motional reorientation experiments are extensions of Magic Angle Spinning (MAS) where the rotor axis is changed in order to average out, reintroduce, or scale anisotropic interactions (e.g. dipolar couplings, quadrupolar interactions or chemical shift anisotropies). This review focuses on Variable Angle Spinning (VAS), Switched Angle Spinning (SAS), and Dynamic Angle Spinning (DAS), all of which involve spinning at two or more different angles sequentially, either in successive experiments or during a multidimensional experiment. In all of these experiments, anisotropic terms in the Hamiltonian are scaled by changing the orientation of the spinning sample relative to the static magnetic field. These experiments vary in experimental complexity and instrumentation requirements. In VAS, many one-dimensional spectra are collected as a function of spinning angle. In SAS, dipolar couplings and/or chemical shift anisotropies are reintroduced by switching the sample between two different angles, often 0° or 90° and the magic angle, yielding a two-dimensional isotropic-anisotropic correlation spectrum. Dynamic Angle Spinning (DAS) is a related experiment that is used to simultaneously average out the first- and second-order quadrupolar interactions, which cannot be accomplished by spinning at any unique rotor angle in physical space. Although motional reorientation experiments generally require specialized instrumentation and data analysis schemes, some are accessible with only minor modification of standard MAS probes. In this review, the mechanics of each type of experiment are described, with representative examples. Current and historical probe and coil designs are discussed from the standpoint of how each one accomplishes the particular objectives of the experiment(s) it was designed to perform. Finally, applications to inorganic materials and liquid crystals, which present very different experimental challenges, are discussed. The review concludes with perspectives on how motional reorientation experiments can be applied to current problems in chemistry, molecular biology, and materials science, given the many advances in high-field NMR magnets, fast spinning, and sample preparation realized in recent years.

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 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.

New methods and applications in solid-state NMR spectroscopy of quadrupolar nuclei

Solid-state nuclear magnetic resonance (NMR) spectroscopy has long been established as offering unique atomic-scale and element-specific insight into the structure, disorder, and dynamics of materials. NMR spectra of quadrupolar nuclei (I > (1)/2) are often perceived as being challenging to acquire and to interpret because of the presence of anisotropic broadening arising from the interaction of the electric field gradient and the nuclear electric quadrupole moment, which broadens the spectral lines, often over several megahertz. Despite the vast amount of information contained in the spectral line shapes, the problems with sensitivity and resolution have, until very recently, limited the application of NMR spectroscopy of quadrupolar nuclei in the solid state. In this Perspective, we provide a brief overview of the quadrupolar interaction, describe some of the basic experimental approaches used for acquiring high-resolution NMR spectra, and discuss the information that these spectra can provide. We then describe some interesting recent examples to showcase some of the more exciting and challenging new applications of NMR spectra of quadrupolar nuclei in the fields of energy materials, microporous materials, Earth sciences, and biomaterials. Finally, we consider the possible directions that this highly informative technique may take in the future.

Theoretical study of homonuclear J coupling between quadrupolar spins: single-crystal, DOR, and J-resolved NMR

The theory describing homonuclear indirect nuclear spin-spin coupling (J) interactions between pairs of quadrupolar nuclei is outlined and supported by numerical calculations. The expected first-order multiplets for pairs of magnetically equivalent (A2), chemically equivalent (AA'), and non-equivalent (AX) quadrupolar nuclei are given. The various spectral changeovers from one first-order multiplet to another are investigated with numerical simulations using the SIMPSON program and the various thresholds defining each situation are given. The effects of chemical equivalence, as well as quadrupolar coupling, chemical shift differences, and dipolar coupling on double-rotation (DOR) and J-resolved NMR experiments for measuring homonuclear J coupling constants are investigated. The simulated J coupling multiplets under DOR conditions largely resemble the ideal multiplets predicted for single crystals, and a characteristic multiplet is expected for each of the A2, AA', and AX cases. The simulations demonstrate that it should be straightforward to distinguish between magnetic inequivalence and equivalence using J-resolved NMR, as was speculated previously. Additionally, it is shown that the second-order quadrupolar-dipolar cross-term does not affect the splittings in J-resolved experiments. Overall, the homonuclear J-resolved experiment for half-integer quadrupolar nuclei is demonstrated to be robust with respect to the effects of first- and second-order quadrupolar coupling, dipolar coupling, and chemical shift differences.

Boron–boron J coupling constants are unique probes of electronic structure: a solid-state NMR and molecular orbital study

J couplings measured between ¹¹B spin pairs in solid diboron compounds provide insight into electronic structure and crystallographic symmetry.

Central-transition double-quantum sideband NMR spectroscopy of half-integer quadrupolar nuclei: estimating internuclear distances and probing clusters within multi-spin networks

Clusters within quadrupolar spin networks are probed and internuclear distances between quadrupolar nuclei are estimated by central-transition double-quantum sideband NMR spectroscopy.

Symmetry-amplified J splittings for quadrupolar spin pairs: a solid-state NMR probe of homoatomic covalent bonds

Chemically informative J couplings between pairs of quadrupolar nuclei in dimetallic and dimetalloid coordination motifs are measured using J-resolved solid-state NMR experiments. It is shown that the application of a double-quantum filter is necessary to observe the J splittings and that, under these conditions, only a simple doublet is expected. Interestingly, the splitting is amplified if the spins are magnetically equivalent, making it possible to measure highly precise J couplings and unambiguously probe the symmetry of the molecule. This is demonstrated experimentally by chemically breaking the symmetry about a pair of boron spins by reaction with an N-heterocyclic carbene to form a β-borylation reagent. The results show that the J coupling is a sensitive probe of bonding in diboron compounds and that the J values quantify the weakening of the B-B bond which occurs when forming an sp(2)-sp(3) diboron compound, which is relevant to their reactivity. Due to the prevalence of quadrupolar nuclei among transition metals, this work also provides a new approach to probe metal-metal bonding; results for Mn2(CO)10 are provided as an example.