DFT-based 11B solid-state NMR calculations for guiding fine local structure identification and phase-property modulation in ZnxY1-xBO3-0.5x borate oxide ion conductors

Solid-state nuclear magnetic resonance (NMR) spectroscopy serves as a powerful technique for probing local structures. However, the interpretation of NMR signals mainly based on empirical knowledge could lead to imprecise local structural determinations. To address this, density functional theory (DFT)-based theoretical NMR calculations, aided by experimental three-dimensional continuous rotation electronic diffraction (3D cRED) technique, were performed for ZnxY1-xBO3-0.5x borate oxide ion conductors. The calculations provided fine local structure identification for the experimental 11B NMR spectra of ZnxY1-xBO3-0.5x, providing rich information on multiple experimental 11B NMR signals towards the complex boron oxide anions associated with bridging oxygen vacancies and the coexistence of the monoclinic (C2/c), hexagonal (P63/m), and trigonal (R32) phases in ZnxY1-xBO3-0.5x. Owing to the advantages of solid-state NMR in identifying closely related phases compared to X-ray/neutron diffraction technique, along with the advanced 3D cRED technique that allows for rapid phase identification and structure determination, we provide a fine local structure identification and a more inclusive insight into the coexistence of multiple phases in borate with the same composition. More importantly, this work provides guidance for phase and property modulation. Phase modulation in ZnxY1-xBO3-0.5x was carried out with thermodynamic and kinetic modulation and eventually realized the tuning of the local structures and the resultant oxide ion conductivity of ZnxY1-xBO3-0.5x. This work provides a theoretical and experimental platform to access the flexible structural assignment of boron oxide anions and therefore offers new guidance and insights into the defect structures and the phase-property modulation of inorganic solid functional materials beyond borate oxide ion conductors.

Comparison of through-space homonuclear correlations between quadrupolar nuclei in solids

Various two-dimensional (2D) homonuclear correlation experiments have been proposed to observe proximities between identical half-integer spin quadrupolar nuclei in solids. These experiments select either the single- or double-quantum coherences during the indirect evolution period, t₁. We compare here the efficiency and the robustness of the 2D double-quantum to single-quantum (DQ-SQ) and SQ-SQ homonuclear correlations for two half-integer spin quadrupolar isotopes subject to small chemical shift anisotropy (CSA): ¹¹B with a nuclear spin I = 3/2 and ²⁷Al with I = 5/2. Such a comparison is performed using experiments on two model samples: Li₂B₄O₇ for ¹¹B and AlPO₄-14 for ²⁷Al. For both isotopes, the DQ-SQ homonuclear correlations are recommended since they allow probing the proximities between nuclei with close or identical frequencies. In the case of small or moderate isotropic chemical shift differences (e.g. ¹¹B) the [SR2₂¹] or [BR2₂¹] bracketed DQ-SQ recoupling schemes are recommended; whereas it is the BR2₂¹ un-bracketed one otherwise (e.g. ²⁷Al).

Solid-State Photo-NMR Study on Light-Induced Nitrosyl Linkage Isomers Uncovers Their Structural, Electronic, and Diamagnetic Nature

A light-induced linkage NO isomer (MS1) in trans-[Ru(¹⁵NO)(py)₄¹⁹F](ClO₄)₂ is detected and measured for the first time by solid-state MAS NMR. Chemical shift tensors of ¹⁵N and ¹⁹F, along with ⁿJ(¹⁵N-¹⁹F) spin-spin couplings and T₁ relaxation times of MS1, are compared with the ground state (GS) at temperatures T < 250 K. Isotropic chemical shifts (¹⁵N and ¹⁹F) are well resolved for two crystallographically independent cations (A and B) [Ru(¹⁵NO)(py)₄¹⁹F]²⁺, allowing to define separately both populations of MS1 isomers and thermal decay rates for two structural sites. The relaxation times T₁ of ¹⁹F in the case of GS (30/38.6 s for sites A/B) and MS1 (11.6/11.8 s for sites A/B) indicate that both isomers are diamagnetic, which is the first experimental evidence of diamagnetic properties of MS1 in ruthenium nitrosyl. After light irradiation (λ = 420 nm), the NO ligand rotates by nearly 180° from F-Ru-N-O to F-Ru-O-N, whereby the isotropic chemical shifts of δ_iso(¹⁵N) increase and those of δ_iso(¹⁹F) decrease. The ⁿJ(¹⁵N-¹⁹F) couplings increase from ²J(¹⁵N-Ru-¹⁹F)_GS = 71 Hz to ³J(¹⁵N-O-Ru-¹⁹F)_MS1 = 105 Hz. These results are interpreted on the basis of DFT-CASTEP calculations including Bader-, Mulliken-, and Hirshfeld-charge density distributions of both states.

Weak Intermolecular CH···N Hydrogen Bonding: Determination of 13CH-15N Hydrogen-Bond Mediated J Couplings by Solid-State NMR Spectroscopy and First-Principles Calculations

Weak hydrogen bonds are increasingly hypothesized to play key roles in a wide range of chemistry from catalysis to gelation to polymer structure. Here, ¹⁵N/¹³C spin-echo magic-angle spinning (MAS) solid-state nuclear magnetic resonance (NMR) experiments are applied to "view" intermolecular CH···N hydrogen bonding in two selectively labeled organic compounds, 4-[¹⁵N] cyano-4'-[¹³C₂] ethynylbiphenyl (1) and [¹⁵N₃,¹³C₆]-2,4,6-triethynyl-1,3,5-triazine (2). The synthesis of 2-¹⁵N₃,¹³C₆ is reported here for the first time via a multistep procedure, where the key element is the reaction of [¹⁵N₃]-2,4,6-trichloro-1,3,5-triazine (5) with [¹³C₂]-[(trimethylsilyl)ethynyl]zinc chloride (8) to afford its immediate precursor [¹⁵N₃,¹³C₆]-2,4,6-tris[(trimethylsilyl)ethynyl]-1,3,5-triazine (9). Experimentally determined hydrogen-bond-mediated ^2hJ_CN couplings (4.7 ± 0.4 Hz (1) and 4.1 ± 0.3 Hz (2)) are compared with density functional theory (DFT) gauge-including projector augmented wave (GIPAW) calculations, whereby species-independent coupling values ^2hK_CN (29.0 × 10¹⁹ kg m^-2 s^-2 A^-2 (1) and 27.9 × 10¹⁹ kg m^-2 s^-2 A^-2 (2)) quantitatively demonstrate the J couplings for these "weak" CH···N hydrogen bonds to be of a similar magnitude to those for conventionally observed NH···O hydrogen-bonding interactions in uracil (^2hK_NO: 28.1 and 36.8 × 10¹⁹ kg m^-2 s^-2 A^-2). Moreover, the GIPAW calculations show a clear correlation between increasing ^2hJ_CN (and ^3hJ_CN) coupling and reducing C(H)···N and H···N hydrogen-bonding distances, with the Fermi contact term accounting for at least 98% of the isotropic ^2hJ_CN coupling.

A molecular cross-linking approach for hybrid metal oxides

There is significant interest in the development of methods to create hybrid materials that transform capabilities, in particular for Earth-abundant metal oxides, such as TiO₂, to give improved or new properties relevant to a broad spectrum of applications. Here we introduce an approach we refer to as 'molecular cross-linking', whereby a hybrid molecular boron oxide material is formed from polyhedral boron-cluster precursors of the type [B₁₂(OH)₁₂]^2-. This new approach is enabled by the inherent robustness of the boron-cluster molecular building block, which is compatible with the harsh thermal and oxidizing conditions that are necessary for the synthesis of many metal oxides. In this work, using a battery of experimental techniques and materials simulation, we show how this material can be interfaced successfully with TiO₂ and other metal oxides to give boron-rich hybrid materials with intriguing photophysical and electrochemical properties.

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.

Simulating spin dynamics in organic solids under heteronuclear decoupling

Although considerable progress has been made in simulating the dynamics of multiple coupled nuclear spins, predicting the evolution of nuclear magnetisation in the presence of radio-frequency decoupling remains challenging. We use exact numerical simulations of the spin dynamics under simultaneous magic-angle spinning and RF decoupling to determine the extent to which numerical simulations can be used to predict the experimental performance of heteronuclear decoupling for the CW, TPPM and XiX sequences, using the methylene group of glycine as a model system. The signal decay times are shown to be strongly dependent on the largest spin order simulated. Unexpectedly large differences are observed between the dynamics with and without spin echoes. Qualitative trends are well reproduced by modestly sized spin system simulations, and the effects of finite spin-system size can, in favourable cases, be mitigated by extrapolation. Quantitative prediction of the behaviour in complex parameter spaces is found, however, to be very challenging, suggesting that there are significant limits to the role of numerical simulations in RF decoupling problems, even when specialist techniques, such as state-space restriction, are used.

Joint Experimental and Computational 17O and 1H Solid State NMR Study of Ba2In2O4(OH)2 Structure and Dynamics

A structural characterization of the hydrated form of the brownmillerite-type phase Ba₂In₂O₅, Ba₂In₂O₄(OH)₂, is reported using experimental multinuclear NMR spectroscopy and density functional theory (DFT) energy and GIPAW NMR calculations. When the oxygen ions from H₂O fill the inherent O vacancies of the brownmillerite structure, one of the water protons remains in the same layer (O3) while the second proton is located in the neighboring layer (O2) in sites with partial occupancies, as previously demonstrated by Jayaraman et al. (Solid State Ionics2004, 170, 25-32) using X-ray and neutron studies. Calculations of possible proton arrangements within the partially occupied layer of Ba₂In₂O₄(OH)₂ yield a set of low energy structures; GIPAW NMR calculations on these configurations yield ¹H and ¹⁷O chemical shifts and peak intensity ratios, which are then used to help assign the experimental MAS NMR spectra. Three distinct ¹H resonances in a 2:1:1 ratio are obtained experimentally, the most intense resonance being assigned to the proton in the O3 layer. The two weaker signals are due to O2 layer protons, one set hydrogen bonding to the O3 layer and the other hydrogen bonding alternately toward the O3 and O1 layers. ¹H magnetization exchange experiments reveal that all three resonances originate from protons in the same crystallographic phase, the protons exchanging with each other above approximately 150 °C. Three distinct types of oxygen atoms are evident from the DFT GIPAW calculations bare oxygens (O), oxygens directly bonded to a proton (H-donor O), and oxygen ions that are hydrogen bonded to a proton (H-acceptor O). The ¹⁷O calculated shifts and quadrupolar parameters are used to assign the experimental spectra, the assignments being confirmed by ¹H-¹⁷O double resonance experiments.

Solid-state Hadamard NMR spectroscopy: simultaneous measurements of multiple selective homonuclear scalar couplings

Unambiguous measurement of homonuclear scalar couplings (J) in multi-spin scalar network systems is not straightforward. Further, the direct measurement of J-couplings is obscured in solid-state samples due to the dipolar and chemical shift anisotropy (CSA)-dominated line broadening, even under the magic angle spinning (MAS). We present a new multiple frequency selective spin-echo method based on Hadamard matrix encoding, for simultaneous measurement of multiple homonuclear scalar couplings (J) in the solid-state. In contrast to the Hadamard encoded selective excitation schemes known for the solution-state, herein the selectivity is achieved during refocusing period. The Hadamard encoded refocusing scheme concurrently allows to create the spin-spin commutation property between number of spin-pairs of choice in uniformly labelled molecules, which, therefore avoids (1) the repetition of the double selective refocusing experiments for each spin-pair and (2) the synthesis of expensive selective labelled molecules. The experimental scheme is exemplified for determining (1)JCC and (3)JCC values in (13)C6l-Histidine.HCl molecule, which are found to be in excellent agreement with those measured in conventional double frequency selective refocusing mode as well as in the solution-state. This method can be simply extended to 2D/3D pulse schemes and be applied to small bio-molecular solids.

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.

Selective measurements of long-range homonuclear J-couplings in solid-state NMR

We demonstrate here that the principle of frequency-selective spin-echoes can be extended to the measurements of long-range homonuclear scalar J-couplings in the solid-state. Singly or doubly frequency-selective pulses were used to generate either a J-modulated experiment (S) or a reference experiment (S0). The combination of these two distinct experiments provides experimental data that, in favorable cases, are insensitive to incoherent relaxation effects, and which can be used to estimate long-range homonuclear J-couplings in multiple spin-systems. The concept is illustrated in the case of a uniformly (13)C and (15)N labeled sample of L-histidine, where the absolute value of homonuclear J-couplings between two spins separated by one, two or three covalent bonds are measured. Moreover, we show that a (2)J((15)N-C-(15)N) coupling as small as 0.9 Hz can be precisely measured with the method presented here.

The combined effect of quadrupolar and dipolar interactions on the excitation and evolution of triple quantum coherences in ⁷Li solid state magic angle spinning NMR

Magic-angle spinning triple-quantum NMR spectra of lithium-7 provide enhanced spectral dispersion for the inherent low chemical shift range of this nucleus, while maintaining linewidths, which are free of any quadrupolar broadening to first order. Since the quadrupolar interaction of (7)Li is very small, in the order of the radio frequency nutation frequencies and only moderately larger than the spinning rates, such spectra are also only marginally affected by the second order quadrupolar interaction under large magnetic fields. In the current study we demonstrate that the existence of two and more proximate (7)Li spins, as encountered in many materials, affects both excitation and evolution of triple-quantum coherences due to the combined effect of quadrupolar and homonuclear dipolar interactions. We show that the generation of (7)Li triple-quantum coherences using two π/2 pulses separated by one-half rotor period is superior in such cases to a single pulse excitation since the excitation time is shorter; thus the maximum signal is only marginally affected by the homonuclear dipolar couplings. When the quadrupolar-dipolar cross terms dominate the spectra, single- and triple-quantum lineshapes are very similar and therefore a true gain in dispersion is maintained in the latter spectrum. The effects of quadrupolar-dipolar cross terms are experimentally demonstrated by comparing a natural abundance and a (6)Li-diluted samples of lithium acetate, resulting in the possibility of efficient excitation of triple quantum coherences over longer periods of time, and in longer life times of triple-quantum coherences.

Solid-state 11B and 13C NMR, IR, and X-ray crystallographic characterization of selected arylboronic acids and their catechol cyclic esters

Nine arylboronic acids, seven arylboronic catechol cyclic esters, and two trimeric arylboronic anhydrides (boroxines) are investigated using (11)B solid-state NMR spectroscopy at three different magnetic field strengths (9.4, 11.7, and 21.1 T). Through the analysis of spectra of static and magic-angle spinning samples, the (11)B electric field gradient and chemical shift tensors are determined. The effects of relaxation anisotropy and nutation field strength on the (11)B NMR line shapes are investigated. Infrared spectroscopy was also used to help identify peaks in the NMR spectra as being due to the anhydride form in some of the arylboronic acid samples. Seven new X-ray crystallographic structures are reported. Calculations of the (11)B NMR parameters are performed using cluster model and periodic gauge-including projector-augmented wave (GIPAW) density functional theory (DFT) approaches, and the results are compared with the experimental values. Carbon-13 solid-state NMR experiments and spectral simulations are applied to determine the chemical shifts of the ipso carbons of the samples. One bond indirect (13)C-(11)B spin-spin (J) coupling constants are also measured experimentally and compared with calculated values. The (11)B/(10)B isotope effect on the (13)C chemical shift of the ipso carbons of arylboronic acids and their catechol esters, as well as residual dipolar coupling, is discussed. Overall, this combined X-ray, NMR, IR, and computational study provides valuable new insights into the relationship between NMR parameters and the structure of boronic acids and esters.

The PAW/GIPAW approach for computing NMR parameters: a new dimension added to NMR study of solids

In 2001, Mauri and Pickard introduced the gauge including projected augmented wave (GIPAW) method that enabled for the first time the calculation of all-electron NMR parameters in solids, i.e. accounting for periodic boundary conditions. The GIPAW method roots in the plane wave pseudopotential formalism of the density functional theory (DFT), and avoids the use of the cluster approximation. This method has undoubtedly revitalized the interest in quantum chemical calculations in the solid-state NMR community. It has quickly evolved and improved so that the calculation of the key components of NMR interactions, namely the shielding and electric field gradient tensors, has now become a routine for most of the common nuclei studied in NMR. Availability of reliable implementations in several software packages (CASTEP, Quantum Espresso, PARATEC) make its usage more and more increasingly popular, maybe indispensable in near future for all material NMR studies. The majority of nuclei of the periodic table have already been investigated by GIPAW, and because of its high accuracy it is quickly becoming an essential tool for interpreting and understanding experimental NMR spectra, providing reliable assignments of the observed resonances to crystallographic sites or enabling a priori prediction of NMR data. The continuous increase of computing power makes ever larger (and thus more realistic) systems amenable to first-principles analysis. In the near future perspectives, as the incorporation of dynamical effects and/or disorder are still at their early developments, these areas will certainly be the prime target.