11B Chemical Shift Anisotropies in Borates from 11B MAS, MQMAS, and Single-Crystal NMR Spectroscopy

High-Precision Determination of NMR Interaction Parameters by Measurement of Single Crystals: A Review of Classical and Advanced Methods

In this review, the process of extracting precise values for NMR interaction tensors from single crystal samples is systematically explored. Starting with a description of the orientation dependence of the considered interactions, i.e., chemical shift, dipolar, and quadrupole interaction, the techniques for acquiring and analysing single-crystal spectra are outlined. This includes the 'classical' approach, which requires the acquisition of three rotation patterns around three rotation axes that are orthogonal to each other, as well as more recent strategies aimed at reducing the number of required NMR spectra. One such strategy is the 'single-rotation method', which exploits the symmetry relations between tensors in the crystal structure to reduce the necessary amount of orientation-dependent data. This concept may be extended to additionally include the orientation of the goniometer axis itself in the data fit, which may be termed the 'minimal-rotation method'. Other, more exotic schemes, such as the use of specialised probe designs or the investigation of single crystals under magic-angle-spinning, are also briefly discussed. Actual values of NMR interaction tensors as determined from the various single-crystal methods have been collected and are provided in tables for spin I=1/2, I=1, and half-integer spins with I>1/2.

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.

Determining Local Magnetic Susceptibility Tensors in Paramagnetic Lanthanide Crystalline Powders from Solid-State NMR Chemical Shift Anisotropies

Exploring magnetic properties at the molecular level is a challenge that has been met by developing many experimental and theoretical solutions, such as polarized neutron diffraction (PND), muon-spin rotation (μ-SR), electron paramagnetic resonance (EPR), SQUID-based magnetometry measurements, and advanced modeling on open-shell systems and relativistic calculations. These methods are powerful tools that shed light on the local magnetic response in specifically designed magnetic materials such as contrast agents, for MRI, molecular magnets, magnetic tags for biological NMR, etc. All of these methods have their advantages and disadvantages. In order to complement the possibilities offered by these methods, we propose a new tool that implements a new approach combining simulation and fitting for high-resolution solid-state NMR spectra of lanthanide-based paramagnetic species. This method relies on a rigorous acquisition thanks to short high-power adiabatic pulses (SHAP) of high-resolution solid-state NMR isotropic and anisotropic data on a powdered magnetic material. It is also based on an efficient modeling of this data thanks to a semiempirical model based on a parametrization of the local magnetism and the crystal structure provided by diffraction methods. The efficiency of the calculation relies on a thorough simplification of the electron-nucleus interactions (point-dipole interaction, no Fermi contact) which is validated by experimental analysis. By taking advantage of the efficient calculation possibilities offered by our method, we can compare a great number of simulated spectra to experimental data and find the best-matching local magnetic susceptibility tensor. This method was applied to a series of isostructural lanthanide oxalates which are used as a benchmark system for many analytical methods. We present the results of thorough solid-state NMR and extensive modeling of the hyperfine interaction (including up to 400 paramagnetic centers) that yield local magnetic susceptibility tensor measurements that are self-consistent as well as consistent with bulk susceptibility measurements.

Na2B11H13 and Na11(B11H14)3(B11H13)4 as potential solid-state electrolytes for Na-ion batteries

Solid-state sodium batteries have attracted great attention owing to their improved safety, high energy density, large abundance and low cost of sodium compared to the current Li-ion batteries. Sodium-boranes have been studied as potential solid-state electrolytes and the search for new materials is necessary for future battery applications. Here, a facile and cost-effective solution-based synthesis of Na₂B₁₁H₁₃ and Na₁₁(B₁₁H₁₄)₃(B₁₁H₁₃)₄ is demonstrated. Na₂B₁₁H₁₃ presents an ionic conductivity in the order of 10^-7 S cm^-1 at 30 °C, but undergoes an order-disorder phase transition and reaches 10^-3 S cm^-1 at 100 °C, close to that of liquids and the solid-state electrolyte Na-β-Al₂O₃. The formation of a mixed-anion solid-solution, Na₁₁(B₁₁H₁₄)₃(B₁₁H₁₃)₄, partially stabilises the high temperature structural polymorph observed for Na₂B₁₁H₁₃ at room temperature and it exhibits Na⁺ conductivity higher than its constituents (4.7 × 10^-5 S cm^-1 at 30 °C). Na₂B₁₁H₁₃ and Na₁₁(B₁₁H₁₄)₃(B₁₁H₁₃)₄ exhibit an oxidative stability limit of 2.1 V vs. Na⁺/Na.

Single-crystal NMR spectroscopy

Single-crystal (SC) NMR spectroscopy is a solid-state NMR method that has been used since the early days of NMR to study the magnitude and orientation of tensorial nuclear spin interactions in solids. This review first presents the field of SC NMR instrumentation, then provides a survey of software for analysis of SC NMR data, and finally it highlights selected applications of SC NMR in various fields of research. The aim of the last part is not to provide a complete review of all SC NMR literature but to provide examples that demonstrate interesting applications of SC NMR.

Dihydrogen Splitting by Intramolecular Borane-Phosphane Frustrated Lewis Pairs: A Comprehensive Characterization Strategy Using Solid State NMR and DFT Calculations

Four hydrogenated intramolecular phosphane-borane frustrated Lewis pair (B/P FLP) compounds bearing unsaturated cyclic or aromatic carbon backbones have been synthesized and structurally characterized using ¹¹ B, ³¹ P, ¹ H and ² H solid-state NMR spectroscopy. A comparison of the spectra with those of the corresponding free B/P FLPs shows that both ¹¹ B isotropic chemical shifts as well as nuclear electric quadrupolar coupling constants decrease significantly upon FLP hydrogenation, revealing the breakage of the partial B-P bond present in the starting materials. Likewise, the ³¹ P isotropic chemical shift, the chemical shift anisotropy, and the asymmetry parameter decrease significantly upon FLP hydrogenation, reflecting the formation of a more symmetric, C_3v -like local environment. ¹¹ B{³¹ P} rotational echo double resonance (REDOR) experiments can be used to measure the B-P internuclear distance (about 3.2 Å) of these compounds. Observation of the hydrogen atoms bound to the Lewis centers is best accomplished via ³¹ P{¹ H} and ¹¹ B{¹ H} cross-polarization-heteronuclear correlation experiments or by direct observation of the ² H MAS NMR signals on especially prepared FLP-D₂ adducts. For accurately measuring the phosphorus-deuterium distance via ³¹ P{² H} rotational echo adiabatic passage double resonance (REAPDOR), it is essential to take the secondary dipolar coupling of ³¹ P with the boron-bonded ² H nuclei explicitly into consideration, by simulating a ² H_P -³¹ P-² H_B three-spin system based on structural input. All of the experimental NMR interaction parameters are found in excellent agreement with values calculated by DFT methods, using the geometries obtained either by energy optimization or from single-crystal structures.

NMR interaction tensors of 51V and 207Pb in vanadinite, Pb5(VO4)3Cl, determined from DFT calculations and single-crystal NMR measurements, using only one general rotation axis

Orientation-dependent NMR spectra of a single crystal of the mineral vanadinite, Pb₅(VO₄)₃Cl, were acquired using only one rotation axis with a general orientation in the hexagonal crystal lattice (space group P6₃/m). The chemical shift (CS) tensors for the ²⁰⁷Pb on Wyckoff positions 6h and 4f, and both CS and quadrupole coupling tensor Q for ⁵¹V at the positions 6h were determined by including the NMR response of symmetry-related atoms in the unit cell (and in case of ²⁰⁷Pb at 4f, also the isotropic shift from MAS NMR spectra). This previously suggested 'single rotation method' greatly reduces the necessary amount of data acquisition and analysis. The precise orientation of the rotation axis could not be found by X-ray diffraction experiments because of the high linear absorption coefficient of vanadinite, which is chiefly due to its high lead content. The axis orientation was therefore included into the multi-parameter data fit routine. This NMR-based approach is widely applicable, and offers an alternative way of orienting single crystals. The NMR parameters derived from the tensor eigenvalues are δ_iso=(-1729±9) ppm, Δδ=(-1071±5) ppm, η_CS=0.362±0.008 for ²⁰⁷Pb at positions 6h, and δ_iso=(-1619±2) ppm, Δδ=(-780±58) ppm, η_CS=0.06±0.08 for positions 4f. For ⁵¹V, δ_iso=(-509±3) ppm, Δδ=(-37±2) ppm, η_CS=0.78±0.09, with the quadrupolar coupling described by χ=(2.52±0.01) MHz and η_Q=0.047±0.003. In contrast to the precisely determined tensor eigenvalues, the orientation of the eigenvectors in the crystal ab -plane of the vanadinite system could only be resolved by resorting to data obtained from density functional theory (DFT) calculations.

Methane adsorption and methanol desorption of copper modified boron silicate

Boron silicate (BS) with a chabazite framework structure was synthesised using a direct route and rigorously characterized before it was ion-exchanged with copper to form Cu-BS. Employing in situ infrared spectroscopy, we show that Cu-BS is capable of oxidising methane to methoxy species and methanol interacts with the boron sites without deprotonation.

Boron silicate (BS) with a chabazite framework structure was synthesized and ion-exchanged with copper to form Cu-BS which was capable of oxidizing methane to methoxy species.

Accurate determination of chemical shift tensor orientations of single-crystals by solid-state magic angle spinning NMR

An improved implementation of single-crystal magic-angle-spinning (MAS) NMR is presented which gives access to chemical shift tensors both in orientation (relative to the crystal axis system) and principal axis values. For mounting arbitrary crystals inside ordinary MAS rotors, a mounting tool is described which allows to relate the crystal orientation determined by diffraction techniques to the rotor coordinate system. The crystal is finally mounted into a MAS rotor equipped with a special insert which allows a defined reorientation of the single-crystal by 90°. The approach is based on the idea that the dispersive spectra, which are obtained when applying read-pulses at specific rotor-phases, not only yield the size of the eigenvalues but also encode the orientation of the different chemical shift (rank-2) tensors. For this purpose two 2D-data sets with orthogonal crystal orientation are fitted simultaneously. The presented analysis for chemical shift tensors is supported by an analytical formula which allows fast calculation of phase and amplitude of individual spinning side-bands and by a protocol which solves the problem of finding the correct reference phase of the spectrum. Different rotor-synchronized pulse-sequences are introduced for the same reason. Experiments are performed on L-alanine and O-phosphorylethanolamine and the observed errors are analyzed in detail. The experimental data are opposed to DFT-computed chemical shift tensors which have been obtained by the extended embedded ion method.

Local Electronic Structure in γ-LiAlO2 Studied by Single-Crystal 27Al NMR and DFT Calculations

From single-crystal ²⁷Al NMR experiments, the full tensors for both the electrical field gradient (EFG) and the chemical shift (CS) for the aluminum atoms in γ-LiAlO₂ have been determined. A simultaneous fit of the quadrupolar splittings observed for the four ²⁷Al in the unit cell gave the EFG tensor in the crystal frame, from which a quadrupolar coupling constant of χ = C_Q = 3.330 ± 0.005 MHz and an asymmetry parameter of η_Q = 0.656 ± 0.002 were derived. The experimentally determined quadrupolar splittings were sufficiently sensitive to quantify small deviations of both rotation axis direction and starting direction by the data fitting routine. For determination of the CS tensor, the evolution of the outer satellite centers over the crystal rotation was tracked, and the contribution of the quadrupolar shift was subtracted according to the previously determined EFG tensor. The resulting CS tensor of ²⁷Al yields an isotropic chemical shift of δ_iso = 81.8 ± 0.25 ppm and an asymmetry parameter of η_CS = 0.532 ± 0.004, in good agreement with the fit of a MAS NMR spectrum acquired at B₀ = 21.1 T. From both experiments and DFT calculations using the Castep code, we find the eigenvectors of the EFG and CS tensors to be practically colinear.

Anion-induced palladium nanoparticle formation during the on-surface growth of molecular assemblies

We demonstrate a process that results in the formation of palladium nanoparticles during the assembly of molecular thin films. These nanoparticles are embedded in the films and are generated by a chemical reaction of the counter anions of the molecular components with the metal salt that is used for cross-linking these components.

Structure–composition relationships of bioactive borophosphosilicate glasses probed by multinuclear 11B, 29Si, and 31P solid state NMR

By combining ¹¹B, ²⁹Si, and ³¹P nuclear magnetic resonance (NMR) experimental results, we present the first comprehensive structural investigation of 15 borophosphosilicate (BPS) glasses of the Na₂O–CaO–B₂O₃–SiO₂–P₂O₅ system.

Nuclear quadrupole coupling parameters and structural nature of the nonlinear optical material Li2B4O7 by NMR

The structural nature underlying the nonlinear optical (NLO) properties of Li2B4O7 is characterized by nuclear magnetic resonance (NMR). The rotation patterns of (11)B NMR were measured. We observed sixteen different spectra which were divided into two groups, corresponding to two types of boron atoms, 4-coordinated B(1) and 3-coordinated B(2), which have different boron-oxygen rings and lie at chemically inequivalent sites. From these results, the quadrupole parameter and the principal axis of the electric field gradient (EFG) tensor were determined for the two borons.

PRESTO polarization transfer to quadrupolar nuclei: implications for dynamic nuclear polarization

We show both experimentally and numerically that in experiments involving transfer of magnetization from ¹H to the quadrupolar nuclei under MAS, the PRESTO technique consistently outperforms the traditionally used CP method, affording more quantitative intensities, improved lineshapes, better sensitivity, and easier optimization.

Spectral assignments and NMR parameter-structure relationships in borates using high-resolution 11B NMR and density functional theory

High-resolution, solid-state (11)B NMR spectra have been obtained at high magnetic fields for a range of polycrystalline borates using double-rotation (DOR), multiple-quantum magic angle spinning and isotopic dilution. DOR linewidths can be less than 0.2 ppm in isotopically diluted samples, allowing highly accurate values for the isotropic chemical shift, δiso, and electric field gradient to be obtained. The experimental values are used as a test of density functional calculations using both projector augmented wave based CASTEP and WIEN2k. The CASTEP calculations of δiso are generally in very good agreement with experiment, having r.m.s. deviation 0.40 ppm. WIEN2k calculations of electric field gradient magnitude, CQ, and asymmetry, η, are also in excellent agreement with experiment, with r.m.s. deviations 0.038 MHz and 0.042 respectively. However, whilst CASTEP gives a similar deviation for η (0.043) it overestimates CQ by ∼15%. After scaling of the calculated electric field gradient by 0.842 the deviation in CQ is practically identical to that of the WIEN2k calculations. The spectral assignments that follow from the experimental and computational results allow identification of correlations between δiso and (a) the average B-O-B bond angle, θ[combining overline], for both three and four coordinated boron, giving δiso(B(III)) = (185.1 -θ[combining overline])/3.42 ppm and δiso(B(IV)) = (130.2 -θ[combining overline])/5.31 ppm; and (b) the ring-site T(3) unit trigonal planar angular deviation, Stri, giving δiso(T(3)(ring)) = (1.642 × 10(-2)-Stri)/(8.339 × 10(-4)) ppm.

Contribution of first-principles calculations to multinuclear NMR analysis of borosilicate glasses

Boron-11 and silicon-29 NMR spectra of xSiO(2)-(1-x)B(2)O(3) glasses (x=0.40, 0.80 and 0.83) have been calculated using a combination of molecular dynamics (MD) simulations with density functional theory (DFT) calculations of NMR parameters. Structure models of 200 atoms have been generated using classical force fields and subsequently relaxed at the PBE-GGAlevel of DFT theory. The gauge including projector augmented wave (GIPAW) method is then employed for computing the shielding and electric field gradient tensors for each silicon and boron atom. Silicon-29 MAS and boron-11 MQMAS NMR spectra of two glasses (x=0.40 and 0.80) have been acquired and theoretical spectra are found to well agree with the experimental data. For boron-11, the NMR parameter distributions have been analysed using a Kernel density estimation (KDE) approach which is shown to highlight its main features. Accordingly, a new analytical model that incorporates the observed correlations between the NMR parameters is introduced. It significantly improves the fit of the (11)B MQMAS spectra and yields, therefore, more reliable NMR parameter distributions. A new analytical model for a quantitative description of the dependence of the silicon-29 and boron-11 isotropic chemical shift upon the bond angles is proposed, which incorporates possibly the effect of SiO(2)-B(2)O(3) intermixing. Combining all the above procedures, we show how distributions of Si-O-T and B-O-T (T=Si, B) bond angles can be estimated from the distribution of isotropic chemical shift of silicon-29 and boron-11, respectively.

Challenges in numerical simulations of solid-state NMR experiments: spin exchange pulse sequences

While simulations are essential for interpretation of solid-state NMR experiments, large spin systems involved in e.g. spin-diffusion experiments and/or dynamic effects like chemical exchange pose great challenges for the numerical simulations, where we typically want to include effects of finite pulses and other external manipulations in the simulation. In this paper, these topics are reviewed and addressed by simple numerical simulations. The numerical simulations comprise a 2-spin simulation of (2)H two-site jumps and a 332-spin simulation of a CHHC experiment for a small protein.

Solid-state NMR characterization of a controlled-pore glass and of the effects of electron irradiation

Controlled-pore glasses (CPGs) are silica-based materials which provide an adequate model system for a better understanding of the radiation chemistry of glasses, especially under nanoscopic confinement. This paper presents a characterization of a nanoporous CPG before and after electron irradiation using multinuclear solid-state magnetic resonance (NMR). 1H MAS NMR has been used for studying the surface proton sites and it is observed that the irradiation leads to a dehydration of the material. Accordingly, concerning the silicon sites near the surface, the observed variation of the Q4, Q3 and Q2 species from 1H-29Si CPMAS spectra shows an increase of the surface polymerization under irradiation, implying in majority a Q2 to Q3/Q4 conversion mechanism. Similarly, 1H-17 O CPMAS measurements exhibit an increase of Si-O-Si groups at the expenses of Si-OH groups. In addition, modifications of the environment of the residual boron atoms are also put in evidence from 11B MAS and MQMAS NMR These data show that MAS NMR methods provide sensitive tools for the characterization of these porous glasses and of the tiny modifications occurring under electron irradiation.

Effects of T2-relaxation in MAS NMR spectra of the satellite transitions for quadrupolar nuclei: a 27Al MAS and single-crystal NMR study of alum KAl(SO4)2.12H2O

Asymmetries in the manifold of spinning sidebands (ssbs) from the satellite transitions have been observed in variable-temperature 27Al MAS NMR spectra of alum (KAl(SO4)2.12H2O), recorded in the temperature range from -76 to 92 degrees C. The asymmetries decrease with increasing temperature and reflect the fact that the ssbs exhibit systematically different linewidths for different spectral regions of the manifold. From spin-echo 27Al NMR experiments on a single-crystal of alum, it is demonstrated that these variations in linewidth originate from differences in transverse (T2) relaxation times for the two inner (m=1/2<-->m=3/2 and m=-1/2<-->m=-3/2) and correspondingly for the two outer (m=3/2<-->m=5/2 and m=-3/2<-->m=-5/2) satellite transitions. T2 relaxation times in the range 0.5-3.5 ms are observed for the individual satellite transitions at -50 degrees C and 7.05 T, whereas the corresponding T1 relaxation times, determined from similar saturation-recovery 27Al NMR experiments, are almost constant (T1=0.07-0.10 s) for the individual satellite transitions. The variation in T2 values for the individual 27Al satellite transitions for alum is justified by a simple theoretical approach which considers the cross-correlation of the local fluctuating fields from the quadrupolar coupling and the heteronuclear (27Al-1H) dipolar interaction on the T2 relaxation times for the individual transitions. This approach and the observed differences in T2 values indicate that a single random motional process modulates both the quadrupolar and heteronuclear dipolar interactions for 27Al in alum at low temperatures.

Refinement of Borate Structures from 11B MAS NMR Spectroscopy and Density Functional Theory Calculations of 11B Electric Field Gradients

The refinement of borate structures using DFT calculations combined with experimental (11)B quadrupole coupling parameters from solid-state NMR spectroscopy is presented. The (11)B electric field gradient (EFG) tensors, calculated using the WIEN2k software for trigonal and tetrahedral boron sites in a series of model compounds, exhibit a convincing linear correlation with the quadrupole coupling tensor elements, determined from (11)B MAS NMR spectra of the central or satellite transitions. The model compounds include Li(2)B(4)O(7), Mg(2)B(2)O(5), Mg(3)B(2)O(6), NH(4)B(C(6)H(5))(4), and colemanite (CaB(3)O(4)(OH)(3).H(2)O). The (11)B quadrupole moment, Q = 0.0409 +/- 0.0002 barn, derived from the linear correlation, is in excellent agreement with the accepted value for Q((11)B). This demonstrates that DFT (WIEN2k) calculations can provide precise (11)B quadrupole coupling parameters on an absolute scale. On the other hand, DFT calculations based on the reported crystal structures for datolite (CaBSiO(4)(OH)) and danburite (CaB(2)Si(2)O(8)) cannot reproduce the experimental (11)B quadrupole coupling parameters to the same high precision. However, optimization of these structures by minimization of the forces between the atoms (obtained by DFT) results in a significant improvement between the calculated and experimental (11)B quadrupole coupling parameters, which indicates that reliable refinements of the borate structures are obtained by this method. Finally, the DFT calculations also provide important structural information about the sign and orientation of the EFG tensor elements in the crystal frame, a kind of information that cannot be achieved from (11)B NMR experiments on powdered samples.

Separated quadrupolar field experiment

We describe an NMR experiment that produces spectra correlating the first-order quadrupolar spectrum and the central transition spectrum of half-integer quadrupolar spins, allowing one to separate the quadrupolar parameters in overlapping spectra under both static and magic-angle-spinning conditions. Promising fields of applications include situations where the sample cannot easily be rotated, or where it cannot be rotated at the magic angle.