Uniform chi-squared model probabilities in NMR crystallography

A nearly universal component of NMR crystallography is the ranking of candidate structures based on how well their first-principles-predicted NMR parameters align with the results of solid-state NMR experiments. Here, a novel approach for assigning probabilities to candidate models is proposed that quantifies the likelihood that each model is the correct experimental structure. This method employs hierarchical Bayesian inference and leverages explicit prior probabilities derived from a uniform distribution of potential candidate structures with respect to chi-squared values. The resulting uniform chi-squared (UC) model provides a more cautious estimate of candidate probabilities compared to previous approaches, assigning decreased likelihood to the best-fit structure and increased likelihood to alternate candidates. Although developed here within the context of NMR crystallography, the UC model represents a general method for assigning likelihoods based on chi-squared goodness-of-fit assessments.

Repulsive Lateral Interaction of Water Molecules at the Initial Stages of Adsorption in Microporous AlPO4-11 According to 27Al NMR and DFT

Lateral (adsorbate-adsorbate) interactions between adsorbed molecules affect various physical and chemical properties of microporous adsorbents and catalysts, influencing their functional properties. In this work, we studied the hydration of microporous AlPO4-11 aluminophosphate, which has an unusually ordered structure upon adsorption of water vapor, and according to 27Al NMR data, only tetrahedrally or octahedrally coordinated Al sites are present in the AlPO4-11. These 27Al NMR data are consistent with the results of density functional theory (DFT) calculations of hydrated AlPO4-11, which revealed the presence of a strong repulsive lateral interaction at the initial stage of adsorption, suppressing the adsorption of water on neighboring (separated by one -O-P-O- bridge) Al crystallographic sites. As a result, of all the different aluminum sites, only half of the Al1 sites adsorb two water molecules and acquire octahedral coordination.

Practical considerations on the use of low RF-fields and cosine modulation in high-resolution NMR of I = 3/2 spin quadrupolar nuclei in solids

Despite its ease in experimental set up, the low sensitivity of MQMAS experiments is often a limiting factor in many practical applications. This is mainly due to the large radiofrequency (RF) field requirement of the two short hard-pulses often used for the optimum MQ excitation and conversion steps. Very recently, two novel MQMAS experiments have been proposed for I = 3/2 nuclei, namely lp-MQMAS and coslp-MQMAS, enabling an efficient MQ excitation/conversion with a reduced RF requirement, by utilizing two long pulses lasting one rotor period each, with or without cosine modulation. In this study, we focus on the practical considerations of these new methods and discuss their pros and cons to elucidate their appropriate use under both moderate and fast spinning conditions. Using four I = 3/2 (⁸⁷Rb, ⁷¹Ga, ³⁵Cl and ²³Na) nuclei at a moderate magnetic field (B₀ = 14.1 T), we show the superior use of these experiments, especially for samples with large C_Q values and/or low-gamma nuclei. Compared to all other existing sequences, the coslp-MQMAS method with initial WURST signal enhancement is the most robust, efficient and resolved high-resolution 2D method for spin 3/2 nuclei. Furthermore, using {²³Na}-¹H spin systems, we demonstrate the sensitivity advantage of the WURST coslp-MQ-HETCOR acquisition upon ¹H detection and fast MAS conditions.

Lattice Dynamics in the NASICON NaZr2(PO4)3 Solid Electrolyte from Temperature-Dependent Neutron Diffraction, NMR, and Ab Initio Computational Studies

Natrium super ionic conductor (NASICON) compounds form a rich and highly chemically tunable family of crystalline materials that are of widespread interest because they include exemplars with high ionic conductivity, low thermal expansion, and redox tunability. This makes them suitable candidates for applications ranging from solid-state batteries to nuclear waste storage materials. The key to an understanding of these properties, including the origins of effective cation transport and low, anisotropic (and sometimes negative) thermal expansion, lies in the lattice dynamics associated with specific details of the crystal structure. Here we closely examine the prototypical NASICON compound, NaZr₂(PO₄)₃, and obtain detailed insights into such behavior via variable-temperature neutron diffraction and ²³Na and ³¹P solid-state NMR studies, coupled with comprehensive density functional theory-based calculations of NMR parameters. Temperature-dependent NMR studies yield some surprising trends in the chemical shifts and the quadrupolar coupling constants that are not captured by computation unless the underlying vibrational modes of the crystal are explicitly taken into account. Furthermore, the trajectories of the sodium, zirconium, and oxygen atoms in our dynamical simulations show good qualitative agreement with the anisotropic thermal parameters obtained at higher temperatures by neutron diffraction. The work presented here widens the utility of NMR crystallography to include thermal effects as a unique probe of interesting lattice dynamics in functional materials.

Small pore SAPO-14-based zeolites with improved propylene selectivity in methanol to olefins

Methanol to olefins (MTO) is an important non petroleum route to prepare light olefins, however, it still remains a challenge to improve the one-pass propylene selectivity towards the industrial SAPO-34...

Accelerating the acquisition of high-resolution quadrupolar MQ/ST-HETCOR 2D spectra under fast MAS via 1H detection and through-space population transfers

Recently, we established an experimental setup protocol to perform the population transfer from half-integer quadrupolar spin to ¹H nuclei under fast MAS in the context of MQ-HETCOR experiments. In this article, we further develop the high-resolution 2D HETCOR methods by ST-based approaches, making use of the sensitivity advantage of STMAS over its MQMAS counterpart. In a similar manner to the previous work, which utilized CP and RINEPT for the population transfer, we also demonstrate the experimental setup protocol for PRESTO. Using {²³Na}-¹H and {²⁷Al}-¹H spin systems of powder samples, we compare a series of MQ/ST-HETCOR 2D spectra to discuss the pros and cons of the distinct MQ/ST-based approaches for spin 3/2 and 5/2 nuclei, respectively. We also incorporate two experimental tricks to reduce the experimental time of such long 2D experiments, the Optimized Rotor-Synchronization (ORS) and the Non-Uniform Sampling (NUS), in the context of high-resolution spectra of half-integer quadrupolar spin nuclei.

Solid-state nuclear magnetic resonance study of polymorphism in tris(8-hydroxyquinolinate)aluminium

Tris(8-hydroxyquinolinate)aluminium (Alq₃ ) is a metal-organic coordination complex, which is a widely used electroluminescent material in organic light-emitting diode technology. Crystalline Alq₃ is known to occur in five polymorphic forms (denoted α, β, γ, δ, and ε), although the structures of some of these polymorphs have been the subject of considerable debate. In particular, the structure of α-Alq₃ , which is a model for the local structure in amorphous films used in devices, is highly complex and has never been conclusively solved. In this work, we use solid-state nuclear magnetic resonance (NMR) and density functional theory (DFT) calculations to investigate the local structure of four Alq₃ samples. We find that the first structure proposed for α-Alq₃ is inconsistent with all of the samples studied, and DFT calculations further suggest that this structure is energetically unfavourable. Instead, samples containing the meridional (mer) isomeric form are found to contain local structures consistent with ε-Alq₃ , and a sample containing the facial (fac) isomeric form is consistent with a mixture of γ-Alq₃ and δ-Alq₃ . We also investigate the influence of different strategies for dispersion correction in DFT geometry optimisations. We find that a recently proposed modified semiempirical dispersion correction scheme gives good agreement with experiment. Furthermore, the DFT calculations also show that distinction between mer and fac isomers on the basis of η_Q that has been assumed in previous work is not always justified.

A comparison of through-space population transfers from half-integer spin quadrupolar nuclei to 1H using MQ-HETCOR and MQ-SPAM-HETCOR under fast MAS

In this article, we compare the various schemes of magnetization transfer from half-integer quadrupolar spins to ¹H nuclei and we establish an efficient protocol to perform these transfers under MQMAS high-resolution with the MQ-HETCOR and MQ-SPAM-HETCOR experiments under fast MAS. The MQMAS efficiencies are analyzed with SIMPSON simulations, and the CPMAS and RINEPT magnetization transfers are compared at 62.5 kHz MAS using {²³Na}-¹H and {²⁷Al}-¹H MQ-HETCOR and MQ-SPAM-HETCOR experiments performed on NaH₂PO4, Na₂HPO₄, Na citrate dihydrate and ipa-AlPO-14 powder samples. We discuss the pros and cons of these approaches, aiming to record 2D spectra of the best possible quality under fast MAS. We also incorporate some experimental approaches to reduce the total experiment time of such long 2D experiments.

Improved NMR transfer of magnetization from protons to half-integer spin quadrupolar nuclei at moderate and high magic-angle spinning frequencies

Half-integer spin quadrupolar nuclei are the only magnetic isotopes for the majority of the chemical elements. Therefore, the transfer of polarization from protons to these isotopes under magic-angle spinning (MAS) can provide precious insights into the interatomic proximities in hydrogen-containing solids, including organic, hybrid, nanostructured and biological solids. This transfer has recently been combined with dynamic nuclear polarization (DNP) in order to enhance the NMR signal of half-integer quadrupolar isotopes. However, the cross-polarization transfer lacks robustness in the case of quadrupolar nuclei, and we have recently introduced as an alternative technique a D -RINEPT (through-space refocused insensitive nuclei enhancement by polarization transfer) scheme combining a heteronuclear dipolar recoupling built from adiabatic pulses and a continuous-wave decoupling. This technique has been demonstrated at 9.4 T with moderate MAS frequencies, ν R ≈ 10 -15 kHz, in order to transfer the DNP-enhanced 1 H polarization to quadrupolar nuclei. Nevertheless, polarization transfers from protons to quadrupolar nuclei are also required at higher MAS frequencies in order to improve the 1 H resolution. We investigate here how this transfer can be achieved at ν R ≈ 20 and 60 kHz. We demonstrate that the D -RINEPT sequence using adiabatic pulses still produces efficient and robust transfers but requires large radio-frequency (rf) fields, which may not be compatible with the specifications of most MAS probes. As an alternative, we introduce robust and efficient variants of the D -RINEPT and PRESTO (phase-shifted recoupling effects a smooth transfer of order) sequences using symmetry-based recoupling schemes built from single and composite π pulses. Their performances are compared using the average Hamiltonian theory and experiments at B 0 = 18.8  T on γ -alumina and isopropylamine-templated microporous aluminophosphate (AlPO4 -14), featuring low and significant 1 H-1 H dipolar interactions, respectively. These experiments demonstrate that the 1 H magnetization can be efficiently transferred to 27 Al nuclei using D -RINEPT with SR 4 1 2 (2700 90180 ) recoupling and using PRESTO with R 22 2 7 (1800 ) or R 16 7 6 (2700 90180 ) schemes at ν R = 20 or 62.5 kHz, respectively. The D -RINEPT and PRESTO recoupling schemes complement each other since the latter is affected by dipolar truncation, whereas the former is not. We also analyze the losses during these recoupling schemes, and we show how these magnetization transfers can be used at ν R = 62.5  kHz to acquire in 72 min 2D HETCOR (heteronuclear correlation) spectra between 1 H and quadrupolar nuclei, with a non-uniform sampling (NUS).

Refining crystal structures using 13C NMR chemical shift tensors as a target function

A two-step process is described for refining crystal structures from any source.

The accuracy challenge of the DFT-based molecular assignment of 13C MAS NMR characterization of surface intermediates in zeolite catalysis

The influence of the model and method choice on the DFT predicted ¹³C NMR chemical shifts of zeolite surface methoxide species has been systematically analyzed. Twelve ¹³C NMR chemical shift calculation protocols on full periodic and hybrid periodic-cluster DFT calculations with varied structural relaxation procedures are examined. The primary assessment of the accuracy of the computational protocols has been carried out for the Si-O(CH₃)-Al surface methoxide species in ZSM-5 zeolite with well-defined experimental NMR parameters (chemical shift, δ(¹³C) value) as a reference. Different configurations of these surface intermediates and their location inside the ZSM-5 pores are considered explicitly. The predicted δ value deviates by up to ±0.8 ppm from the experimental value of 59 ppm due to the varied confinement of the methoxide species at different zeolite sites (model accuracy). The choice of the exchange-correlation functional (method accuracy) introduces ±1.5 ppm uncertainty in the computed chemical shifts. The accuracy of the predicted ¹³C NMR chemical shifts for the computational assignment of spectral characteristics of zeolite intermediates has been further analyzed by considering the potential intermediate species formed upon methane activation by Cu/ZSM-5 zeolite. The presence of Cu species in the vicinity of surface methoxide increases the prediction uncertainty to ±2.5 ppm. The full geometry relaxation of the local environment of an active site at an appropriate level of theory is critical to ensure a good agreement between the experimental and computed NMR data. Chemical shifts (δ) calculated via full geometry relaxation of a cluster model of a relevant portion of the zeolite lattice site are in the best agreement with the experimental values. Our analysis indicates that the full geometry optimization of a cluster model at the PBE0-D3/6-311G(d,p) level of theory followed by GIAO/PBE0-D3/aug-cc-pVDZ calculations is the most suitable approach for the calculation of ¹³C chemical shifts of zeolite surface intermediates.

Recent advances in computational 31 P NMR: Part 1. Chemical shifts

This is the first part of two closely related reviews dealing with the computation of phosphorus-31 nuclear magnetic resonance chemical shifts in a wide series of organophosphorus compounds including complexes, clusters, and bioorganic phosphorus compounds. In particular, the analysis of the accuracy factors, such as substitution effects, solvent effects, vibrational corrections, and relativistic effects, is presented. This review is dedicated to the Full Member of the Russian Academy of Sciences Professor Boris A. Trofimov in view of his invaluable contribution to the field of synthesis, nuclear magnetic resonance, and computation studies of organophosphorus compounds.

Investigation of 205 Tl NMR shielding, structural, and electronical properties in thallium halides by applying PBE-GGA, YS-PBE0 and mBJ functionals

We report the structural, electronical, and heavy nuclear ²⁰⁵ Tl Nuclear Magnetic Resonance (NMR) shielding properties of thallium halides TlX (X = F, Cl, Br, and I) by the first principles calculation. The Perdew-Burke-Ernzerhof Generalized Gradient Approximation, Yukawa Screened-PBE0 hybrid functional, and modified Becke-Johnson (mBJ) functionals including the relativistic and spin-orbit coupling effects are applied for calculation of the exchange-correlation potentials. Calculated PDOS spectra display that the valence band is composed of the X-s, Tl-5d, X-p, and Tl-6s states, and these states play an important role in ²⁰⁵ Tl NMR shielding. Our findings indicate that the nuclear magnetic shielding parameters depend on the electronic properties. Obtained results by mBJ show that there is a close agreement between the experimental and the calculated NMR parameters.

A Bayesian approach to NMR crystal structure determination

Nuclear Magnetic Resonance (NMR) spectroscopy is particularly well suited to determine the structure of molecules and materials in powdered form. Structure determination usually proceeds by finding the best match between experimentally observed NMR chemical shifts and those of candidate structures. Chemical shifts for the candidate configurations have traditionally been computed by electronic-structure methods, and more recently predicted by machine learning. However, the reliability of the determination depends on the errors in the predicted shifts. Here we propose a Bayesian framework for determining the confidence in the identification of the experimental crystal structure, based on knowledge of the typical errors in the electronic structure methods. We demonstrate the approach on the determination of the structures of six organic molecular crystals. We critically assess the reliability of the structure determinations, facilitated by the introduction of a visualization of the similarity between candidate configurations in terms of their chemical shifts and their structures. We also show that the commonly used values for the errors in calculated ¹³C shifts are underestimated, and that more accurate, self-consistently determined uncertainties make it possible to use ¹³C shifts to improve the accuracy of structure determinations. Finally, we extend the recently-developed ShiftML model to render it more efficient, accurate, and, most importantly, to evaluate the uncertainties in its predictions. By quantifying the confidence in structure determinations based on ShiftML predictions we further substantiate that it provides a valid replacement for first-principles calculations in NMR crystallography.

Is the 31 P chemical shift anisotropy of aluminophosphates a useful parameter for NMR crystallography?

The ³¹ P chemical shift anisotropy (CSA) offers a potential source of new information to help determine the structures of aluminophosphate (AlPO) framework materials. We investigate how to measure the CSAs, which are small (span of ~20-30 ppm) for AlPOs, demonstrating the need for CSA-amplification experiments (often in conjunction with ²⁷ Al and/or ¹ H decoupling) at high magnetic field (20.0 T) to obtain accurate values. We show that the most shielded component of the chemical shift tensor, δ₃₃ , is related to the length of the shortest P─O bond, whereas the more deshielded components, δ₁₁ and δ₂₂ can be related more readily to the mean P─O bond lengths and P─O─Al angles. Using the case of Mg-doped STA-2 as an example, the CSA is shown to be much larger for P(OAl)_4-n (OMg)_n environments, primarily owing to a much shorter P─O(Mg) bond affecting δ₃₃ , however, because the mean P─O bond lengths and P─O─T (T = Al, Mg) bond angles do not change significantly between P(OAl)₄ and P(OAl)_4-n (OMg)_n sites, the isotropic chemical shifts for these species are similar, leading to overlapped spectral lines. When the CSA information is included, spectral assignment becomes unambiguous, therefore, although the specialist conditions required might preclude the routine measurement of ³¹ P CSAs in AlPOs, in some cases (particularly doped materials), the experiments can still provide valuable additional information for spectral assignment.

Alumina: discriminative analysis using 3D correlation of solid-state NMR parameters

Synthetic transition aluminas (χ, κ, θ, γ, δ, η, ρ) exhibit unique adsorptive and catalytic properties leading to numerous practical applications. Generated by thermal transformation of aluminium (oxy)hydroxides, structural differences between them arise from the variability of aluminium coordination numbers and degree of dehydroxylation. Unequivocal identification of these phases using X-ray diffraction has proven to be very difficult. Quadrupolar interactions of 27Al nuclei, highly sensitive to each site symmetry, render advanced 27Al solid-state NMR a unique spectroscopic tool to fingerprint and identify the different phases. In this paper, 27Al NMR spectroscopic data on alumina reported in literature are collected in a comprehensive library. Based on this dataset, a new 3D correlative method of NMR parameters is presented, enabling fingerprinting and identification of such phases. Providing a gold standard from crystalline samples, this approach demonstrates that any sort of crystalline, ill crystallized or amorphous, mixed periodic or aperiodically ordered transition alumina can now be assessed beyond the current limitations of characterisation. Adopting the presented approach as a standard characterisation of alumina samples will readily reveal NMR parameter-structure-property relations suitable to develop new or improved applications of alumina. Methodological guidance is provided to assist consistent implementation of this characterisation throughout the fields involved.

Perspective: Current advances in solid-state NMR spectroscopy

In contrast to the rapid and revolutionary impact of solution-state Nuclear Magnetic Resonance (NMR) on modern chemistry, the field of solid-state NMR has matured more slowly. This reflects the major technical challenges of much reduced spectral resolution and sensitivity in solid-state as compared to solution-state spectra, as well as the relative complexity of the solid state. In this perspective, we outline the technique developments that have pushed resolution to intrinsic limits and the approaches, including ongoing major developments in the field of Dynamic Nuclear Polarisation, that have enhanced spectral sensitivity. The information on local structure and dynamics that can be obtained using these gains in sensitivity and resolution is illustrated with a diverse range of examples from large biomolecules to energy materials and pharmaceuticals and from both ordered and highly disordered materials. We discuss how parallel developments in quantum chemical calculation, particularly density functional theory, have enabled experimental data to be translated directly into information on local structure and dynamics, giving rise to the developing field of "NMR crystallography."

Recent Advances in Solid-State Nuclear Magnetic Resonance Spectroscopy

The sensitivity of nuclear magnetic resonance (NMR) spectroscopy to the local atomic-scale environment offers great potential for the characterization of a diverse range of solid materials. Despite offering more information than its solution-state counterpart, solid-state NMR has not yet achieved a similar level of recognition, owing to the anisotropic interactions that broaden the spectral lines and hinder the extraction of structural information. Here, we describe the methods available to improve the resolution of solid-state NMR spectra and the continuing research in this area. We also highlight areas of exciting new and future development, including recent interest in combining experiment with theoretical calculations, the rise of a range of polarization transfer techniques that provide significant sensitivity enhancements, and the progress of in situ measurements. We demonstrate the detailed information available when studying dynamic and disordered solids and discuss the future applications of solid-state NMR spectroscopy across the chemical sciences.

Heteronuclear correlation experiments of 23Na-27Al in rotating solids

We demonstrated that the heteronuclear correlation experiments between two quadrupolar nuclei, ²³Na and ²⁷Al, with close Larmor frequencies can be achieved via D-HMQC and D-RINEPT approaches by using a diplexer connected to a conventional probe in magic-angle-spinning solid-state NMR. Low-power heteronuclear dipolar recoupling schemes can be applied on ²³Na or ²⁷Al to establish polarization transfers between the central transitions of ²³Na and ²⁷Al for a model compound, NaAlO₂. Further, we showed a practical implementation of the two dimensional ²³Na-²⁷Al dipolar-based heteronuclear correlation experiment on a heterogeneous catalyst, Na₂CO₃/γ-Al₂O₃. This allows to determine spatial proximities between different ²³Na and ²⁷Al sites, thus the surface Na species adjacent to octahedral-coordination Al can be clearly discriminated.

Recent advances in application of (27)Al NMR spectroscopy to materials science

Valuable information about the local environment of the aluminum nucleus can be obtained through (27)Al Nuclear Magnetic Resonance (NMR) parameters like the isotropic chemical shift, scalar and quadrupolar coupling constants, and relaxation rate. With nearly 250 scientific articles per year dealing with (27)Al NMR spectroscopy, this analytical tool has become popular because of the recent progress that has made the acquisition and interpretation of the NMR data much easier. The application of (27)Al NMR techniques to various classes of compounds, either in solution or solid-state, has been shown to be extremely informative concerning local structure and chemistry of aluminum in its various environments. The development of experimental methodologies combined with theoretical approaches and modeling has contributed to major advances in spectroscopic characterization especially in materials sciences where long-range periodicity and classical local NMR probes are lacking. In this review we will present an overview of results obtained by (27)Al NMR as well as the most relevant methodological developments over the last 25years, concerning particularly on progress in the application of liquid- and solid-state (27)Al NMR to the study of aluminum-based materials such as aluminum polyoxoanions, zeolites, aluminophosphates, and metal-organic-frameworks.

Combining solid-state NMR spectroscopy with first-principles calculations - a guide to NMR crystallography

Recent advances in the application of first-principles calculations of NMR parameters to periodic systems have resulted in widespread interest in their use to support experimental measurement. Such calculations often play an important role in the emerging field of "NMR crystallography", where NMR spectroscopy is combined with techniques such as diffraction, to aid structure determination. Here, we discuss the current state-of-the-art for combining experiment and calculation in NMR spectroscopy, considering the basic theory behind the computational approaches and their practical application. We consider the issues associated with geometry optimisation and how the effects of temperature may be included in the calculation. The automated prediction of structural candidates and the treatment of disordered and dynamic solids are discussed. Finally, we consider the areas where further development is needed in this field and its potential future impact.

Solid-state NMR and DFT predictions of differences in COOH hydrogen bonding in odd and even numbered n-alkyl fatty acids

n-Alkyl fatty acids with an even or odd number of carbons are predicted to differ in COOH hydrogen bonding in the solid state.

Recent developments in solid-state NMR spectroscopy of crystalline microporous materials

Microporous materials, having pores and channels on the same size scale as small to medium molecules, have found many important applications in current technologies, including catalysis, gas separation and drug storage and delivery. Many of their properties and functions are related to their detailed local structure, such as the type and distribution of active sites within the pores, and the specific structures of these active sites. Solid-state NMR spectroscopy has a strong track record of providing the requisite detailed atomic-level insight into the structures of microporous materials, in addition to being able to probe dynamic processes occurring on timescales spanning many orders of magnitude (i.e., from s to ps). In this Perspective, we provide a brief review of some of the basic experimental approaches used in solid-state NMR spectroscopy of microporous materials, and then discuss some more recent advances in this field, particularly those applied to the study of crystalline materials such as zeolites and metal-organic frameworks. These advances include improved software for aiding spectral interpretation, the development of the NMR-crystallography approach to structure determination, new routes for the synthesis of isotopically-labelled materials, methods for the characterisation of host-guest interactions, and methodologies suitable for observing NMR spectra of paramagnetic microporous materials. Finally, we discuss possible future directions, which we believe will have the greatest impact on the field over the coming years.

An NMR crystallographic approach to monitoring cation substitution in the aluminophosphate STA-2

The substitution of the divalent cations Mg(2+) and Zn(2+) into the aluminophosphate (AlPO) framework of STA-2 has been studied using an "NMR crystallographic" approach, combining multinuclear solid-state NMR spectroscopy, X-ray diffraction and first-principles calculations. Although the AlPO framework itself is inherently neutral, the positive charge of the organocation template in an as-made material is usually balanced either by the coordination to the framework of anions from the synthesis solution, such as OH(-) or F(-), and/or by the substitution of aliovalent cations. However, the exact position and distribution of the substituted cations can be difficult to determine, but can have a significant impact upon the catalytic properties a material exhibits once calcined. For as-made Mg substituted STA-2, the positive charge of the organocation template is balanced by the substitution of Mg(2+) for Al(3+) and, where required, by hydroxide anions coordinated to the framework [27] Al MAS NMR spectra show that Al is present in both tetrahedral and five-fold coordination, with the latter dependent on the amount of substituted cations, and confirms the bridging nature of the hydroxyl groups, while high-resolution MQMAS spectra are able to show that Mg appears to preferentially substitute on the Al1 site. This conclusion is also supported by first-principles calculations. The calculations also show that (31)P chemical shifts depend not only on the topologically-distinct site in the SAT framework, but also on the number of next-nearest-neighbour Mg species, and the exact nature of the coordinated hydroxyls (whether the P atom forms part of a six-membered ring, P(OAl)2OH, where OH bridges between two Al atoms). The calculations demonstrate a strong correlation between the (31)P isotropic chemical shift and the average 〈P-O-M〉 bond angle. In contrast, for Zn substituted STA-2, both X-ray diffraction and NMR spectroscopy show less preference for substitution onto Al1 or Al2, with both appearing to be present, although that into Al1 appears slightly more favoured.

A simulated annealing approach for solving zeolite crystal structures from two-dimensional NMR correlation spectra

An improved NMR crystallography strategy is presented for determining the structures of network materials such as zeolites from just a single two-dimensional (2D) NMR correlation spectrum that probes nearest-neighbor interactions, combined with the unit cell parameters and space group information measured in a diffraction experiment. The correlation information contained within a 2D spectrum is converted into a "connectivity matrix" which is incorporated into a cost function whose minimum is searched for using a simulated annealing algorithm. The algorithm was extensively tested on over 150 zeolite frameworks from the International Zeolite Association database of zeolite structures and shown to be very robust and efficient in reconstructing the structures from connectivity information. The structure determination of the pure silica zeolites ITQ-4, Ferrierite, and Sigma-2 from experimental 2D (29)Si double-quantum NMR spectra and powder X-ray diffraction data using this improved approach is also presented.

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.

NMR crystallography: Applications to inorganic materials

Current developments of NMR crystallography as well as some recent applications to diamagnetic inorganic solids are presented. First, we illustrate how solid-state NMR data can be used in combination with diffraction data for the determination of the periodic part of the crystal structures, from the space group selection, to the structure determination over the refinement and validation processes. As ss-NMR, contrary to diffraction (powder and single-crystal), is not restricted to periodic boundary conditions, ss-NMR data can be used to further complete the structural description of materials, including studies of local order/disorder, etc. This illustrated through examples, which are shown and discussed in the second part of this review.

Exploiting periodic first-principles calculations in NMR spectroscopy of disordered solids

Much of the information contained within solid-state nuclear magnetic resonance (NMR) spectra remains unexploited because of the challenges in obtaining high-resolution spectra and the difficulty in assigning those spectra. Recent advances that enable researchers to accurately and efficiently determine NMR parameters in periodic systems have revolutionized the application of density functional theory (DFT) calculations in solid-state NMR spectroscopy. These advances are particularly useful for experimentalists. The use of first-principles calculations aids in both the interpretation and assignment of the complex spectral line shapes observed for solids. Furthermore, calculations provide a method for evaluating potential structural models against experimental data for materials with poorly characterized structures. Determining the structure of well-ordered, periodic crystalline solids can be straightforward using methods that exploit Bragg diffraction. However, the deviations from periodicity, such as compositional, positional, or temporal disorder, often produce the physical properties (such as ferroelectricity or ionic conductivity) that may be of commercial interest. With its sensitivity to the atomic-scale environment, NMR provides a potentially useful tool for studying disordered materials, and the combination of experiment with first-principles calculations offers a particularly attractive approach. In this Account, we discuss some of the issues associated with the practical implementation of first-principles calculations of NMR parameters in solids. We then use two key examples to illustrate the structural insights that researchers can obtain when applying such calculations to disordered inorganic materials. First, we describe an investigation of cation disorder in Y2Ti(2-x)Sn(x)O7 pyrochlore ceramics using (89)Y and (119)Sn NMR. Researchers have proposed that these materials could serve as host phases for the encapsulation of lanthanide- and actinide-bearing radioactive waste. In a second example, we discuss how (17)O NMR can be used to probe the dynamic disorder of H in hydroxyl-humite minerals (nMg2SiO4·Mg(OH)2), and how (19)F NMR can be used to understand F substitution in these systems. The combination of first-principles calculations and multinuclear NMR spectroscopy facilitates the investigation of local structure, disorder, and dynamics in solids. We expect that applications will undoubtedly become more widespread with further advances in computational and experimental methods. Insight into the atomic-scale environment is a crucial first step in understanding the structure-property relationships in solids, and it enables the efficient design of future materials for a range of end uses.

A multinuclear solid-state magnetic resonance and GIPAW DFT study of anhydrous calcium chloride and its hydrates

The group 2 metal halides and corresponding metal halide hydrates serve as useful model systems for understanding the relationship between the electric field gradient (EFG) and chemical shift (CS) tensors at the halogen nuclei and the local molecular and electronic structure. Here, we present a 35/37Cl and 43Ca solid-state nuclear magnetic resonance (SSNMR) study of CaCl2. The 35Cl nuclear quadrupole coupling constant, 8.82(8) MHz, and the isotropic chlorine CS, 105(8) ppm (with respect to dilute NaCl(aq)), are different from the values reported previously for this compound, as well as those reported for CaCl2·2H2O. Chlorine-35 SSNMR spectra are also presented for CaCl2·6H2O, and when taken in concert, the SSNMR observations for CaCl2, CaCl2·2H2O, and CaCl2·6H2O clearly demonstrate the sensitivity of the chlorine EFG and CS tensors to the local symmetry and to changes in the hydration state. For example, the value of δiso decreases with increasing hydration. Gauge-including projector-augmented wave (GIPAW) density functional theory (DFT) calculations are used to substantiate the experimental SSNMR findings, to rule out the presence of other hydrates in our samples, to refine the hydrogen positions in CaCl2·2H2O, and to explore the isostructural relationship between CaCl2 and CaBr2. Finally, the 43Ca CS tensor span is measured to be 31(5) ppm for anhydrous CaCl2, which represents only the fifth CS tensor span measurement for calcium.

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.

Comparing quantum-chemical calculation methods for structural investigation of zeolite crystal structures by solid-state NMR spectroscopy

Combining quantum-chemical calculations and ultrahigh-field NMR measurements of (29)Si chemical shielding (CS) tensors has provided a powerful approach for probing the fine details of zeolite crystal structures. In previous work, the quantum-chemical calculations have been performed on 'molecular fragments' extracted from the zeolite crystal structure using Hartree-Fock methods (as implemented in Gaussian). Using recently acquired ultrahigh-field (29) Si NMR data for the pure silica zeolite ITQ-4, we report the results of calculations using recently developed quantum-chemical calculation methods for periodic crystalline solids (as implemented in CAmbridge Serial Total Energy Package (CASTEP) and compare these calculations to those calculated with Gaussian. Furthermore, in the context of NMR crystallography of zeolites, we report the completion of the NMR crystallography of the zeolite ITQ-4, which was previously solved from NMR data. We compare three options for the 'refinement' of zeolite crystal structures from 'NMR-solved' structures: (i) a simple target-distance based geometry optimization, (ii) refinement of atomic coordinates in which the differences between experimental and calculated (29)Si CS tensors are minimized, and (iii) refinement of atomic coordinates to minimize the total energy of the lattice using CASTEP quantum-chemical calculations. All three refinement approaches give structures that are in remarkably good agreement with the single-crystal X-ray diffraction structure of ITQ-4.