Assigning powders to crystal structures by high-resolution (1)H-(1)H double quantum and (1)H-(13)C J-INEPT solid-state NMR spectroscopy and first principles computation. A case study of penicillin G

Spiers Memorial Lecture: NMR crystallography

Chemical function is directly related to the spatial arrangement of atoms. Consequently, the determination of atomic-level three-dimensional structures has transformed molecular and materials science over the past 60 years. In this context, solid-state NMR has emerged to become the method of choice for atomic-level characterization of complex materials in powder form. In the following we present an overview of current methods for chemical shift driven NMR crystallography, illustrated with applications to complex materials.

Enantiospecificity in NMR enabled by chirality-induced spin selectivity

Spin polarization in chiral molecules is a magnetic molecular response associated with electron transport and enantioselective bond polarization that occurs even in the absence of an external magnetic field. An unexpected finding by Santos and co-workers reported enantiospecific NMR responses in solid-state cross-polarization (CP) experiments, suggesting a possible additional contribution to the indirect nuclear spin-spin coupling in chiral molecules induced by bond polarization in the presence of spin-orbit coupling. Herein we provide a theoretical treatment for this phenomenon, presenting an effective spin-Hamiltonian for helical molecules like DNA and density functional theory (DFT) results on amino acids that confirm the dependence of J-couplings on the choice of enantiomer. The connection between nuclear spin dynamics and chirality could offer insights for molecular sensing and quantum information sciences. These results establish NMR as a potential tool for chiral discrimination without external agents.

Internuclear distance measurements between 1H and 14N in multi-component rigid solids at fast MAS

¹H-¹⁴N internuclear distances are readily and accurately measured using the symmetry-based phase-modulated resonance-echo saturation-pulse double-resonance (PM-S-RESPDOR) method in rigid solids. The fraction curve, (S₀ - S')/S₀, is represented by a single variable of a ¹H-¹⁴N heteronuclear dipolar coupling, where S₀ and S' are the PM-S-RESPDOR signal intensity with and without ¹⁴N PM saturation pulse, respectively. Analytical equation of the fraction curve easily provides ¹H-¹⁴N couplings. This treatment is only applicable when NH proton resonance is well separated from the other proton peaks. With the limited ¹H resolution even at fast MAS > 60 kHz, unfortunately, this condition is not necessarily satisfied especially in multi-component systems which often appear in pharmaceutical applications. To overcome this problem, T-HMQC filtering is applied to suppress the ¹H signals other than NH proton prior to the PM-S-RESPDOR experiments. The method is well demonstrated on two components acetaminophen-oxalic acid (APAP-OXA) systems. Further analysis of orientation dependence of T-HMQC and PM-S-RESPDOR shows that the analytical equation can be safely applied in the analysis of T-HMQC filtered PM-S-RESPDOR experiments.

A Machine Learning Model of Chemical Shifts for Chemically and Structurally Diverse Molecular Solids

Nuclear magnetic resonance (NMR) chemical shifts are a direct probe of local atomic environments and can be used to determine the structure of solid materials. However, the substantial computational cost required to predict accurate chemical shifts is a key bottleneck for NMR crystallography. We recently introduced ShiftML, a machine-learning model of chemical shifts in molecular solids, trained on minimum-energy geometries of materials composed of C, H, N, O, and S that provides rapid chemical shift predictions with density functional theory (DFT) accuracy. Here, we extend the capabilities of ShiftML to predict chemical shifts for both finite temperature structures and more chemically diverse compounds, while retaining the same speed and accuracy. For a benchmark set of 13 molecular solids, we find a root-mean-squared error of 0.47 ppm with respect to experiment for ¹H shift predictions (compared to 0.35 ppm for explicit DFT calculations), while reducing the computational cost by over four orders of magnitude.

Complete resonance assignment of a pharmaceutical drug at natural isotopic abundance from DNP-Enhanced solid-state NMR

Solid-state dynamic nuclear polarization enhanced magic angle spinning (DNP-MAS) NMR measurements coupled with density functional theory (DFT) calculations enable the full resonance assignment of a complex pharmaceutical drug molecule without the need for isotopic enrichment. DNP dramatically enhances the NMR signals, thereby making possible previously intractable two-dimensional correlation NMR spectra at natural abundance. Using inputs from DFT calculations, herein we describe a significant improvement to the structure elucidation process for complex organic molecules. Further, we demonstrate that a series of two-dimensional correlation experiments, including ¹⁵N-¹³C TEDOR, ¹³C-¹³C INADEQUATE/SARCOSY, ¹⁹F-¹³C HETCOR, and ¹H-¹³C HETCOR, can be obtained at natural isotopic abundance within reasonable experiment times, thus enabling a complete resonance assignment of sitagliptin, a pharmaceutical used for the treatment of type 2 diabetes.

Bayesian probabilistic assignment of chemical shifts in organic solids

A prerequisite for NMR studies of organic materials is assigning each experimental chemical shift to a set of geometrically equivalent nuclei. Obtaining the assignment experimentally can be challenging and typically requires time-consuming multidimensional correlation experiments. An alternative solution for determining the assignment involves statistical analysis of experimental chemical shift databases, but no such database exists for molecular solids. Here, by combining the Cambridge Structural Database with a machine learning model of chemical shifts, we construct a statistical basis for probabilistic chemical shift assignment of organic crystals by calculating shifts for more than 200,000 compounds, enabling the probabilistic assignment of organic crystals directly from their two-dimensional chemical structure. The approach is demonstrated with the ¹³C and ¹H assignment of 11 molecular solids with experimental shifts and benchmarked on 100 crystals using predicted shifts. The correct assignment was found among the two most probable assignments in more than 80% of cases.

Machine learning-accelerated quantum mechanics-based atomistic simulations for industrial applications

Atomistic simulations have become an invaluable tool for industrial applications ranging from the optimization of protein-ligand interactions for drug discovery to the design of new materials for energy applications. Here we review recent advances in the use of machine learning (ML) methods for accelerated simulations based on a quantum mechanical (QM) description of the system. We show how recent progress in ML methods has dramatically extended the applicability range of conventional QM-based simulations, allowing to calculate industrially relevant properties with enhanced accuracy, at reduced computational cost, and for length and time scales that would have otherwise not been accessible. We illustrate the benefits of ML-accelerated atomistic simulations for industrial R&D processes by showcasing relevant applications from two very different areas, drug discovery (pharmaceuticals) and energy materials. Writing from the perspective of both a molecular and a materials modeling scientist, this review aims to provide a unified picture of the impact of ML-accelerated atomistic simulations on the pharmaceutical, chemical, and materials industries and gives an outlook on the exciting opportunities that could emerge in the future.

NMR crystallography of molecular organics

Developments of NMR methodology to characterise the structures of molecular organic structures are reviewed, concentrating on the previous decade of research in which density functional theory-based calculations of NMR parameters in periodic solids have become widespread. With a focus on demonstrating the new structural insights provided, it is shown how "NMR crystallography" has been used in a spectrum of applications from resolving ambiguities in diffraction-derived structures (such as hydrogen atom positioning) to deriving complete structures in the absence of diffraction data. As well as comprehensively reviewing applications, the different aspects of the experimental and computational techniques used in NMR crystallography are surveyed. NMR crystallography is seen to be a rapidly maturing subject area that is increasingly appreciated by the wider crystallographic community.

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.

Rapid Structure Determination of Molecular Solids Using Chemical Shifts Directed by Unambiguous Prior Constraints

NMR-based crystallography approaches involving the combination of crystal structure prediction methods, ab initio calculated chemical shifts and solid-state NMR experiments are powerful methods for crystal structure determination of microcrystalline powders. However, currently structural information obtained from solid-state NMR is usually included only after a set of candidate crystal structures has already been independently generated, starting from a set of single-molecule conformations. Here, we show with the case of ampicillin that this can lead to failure of structure determination. We propose a crystal structure determination method that includes experimental constraints during conformer selection. In order to overcome the problem that experimental measurements on the crystalline samples are not obviously translatable to restrict the single-molecule conformational space, we propose constraints based on the analysis of absent cross-peaks in solid-state NMR correlation experiments. We show that these absences provide unambiguous structural constraints on both the crystal structure and the gas-phase conformations, and therefore can be used for unambiguous selection. The approach is parametrized on the crystal structure determination of flutamide, flufenamic acid, and cocaine, where we reduce the computational cost by around 50%. Most importantly, the method is then shown to correctly determine the crystal structure of ampicillin, which would have failed using current methods because it adopts a high-energy conformer in its crystal structure. The average positional RMSE on the NMR powder structure is ⟨r_av⟩ = 0.176 Å, which corresponds to an average equivalent displacement parameter U_eq = 0.0103 Ų.

Chemical shifts in molecular solids by machine learning

Due to their strong dependence on local atonic environments, NMR chemical shifts are among the most powerful tools for strucutre elucidation of powdered solids or amorphous materials. Unfortunately, using them for structure determination depends on the ability to calculate them, which  comes at the cost of high accuracy first-principles calculations. Machine learning has recently emerged as a way to overcome the need for quantum chemical calculations, but for chemical shifts in solids it is hindered by the chemical and combinatorial space spanned by molecular solids, the strong dependency of chemical shifts on their environment, and the lack of an experimental database of shifts. We propose a machine learning method based on local environments to accurately predict chemical shifts of molecular solids and their polymorphs to within DFT accuracy. We also demonstrate that the trained model is able to determine, based on the match between experimentally measured and ML-predicted shifts, the structures of cocaine and the drug 4-[4-(2-adamantylcarbamoyl)-5-tert-butylpyrazol-1-yl]benzoic acid.

Solid-state nuclear magnetic resonance combined with quantum chemical shift predictions is limited by high computational cost. Here, the authors use machine learning based on local atomic environments to predict experimental chemical shifts in molecular solids with accuracy similar to density functional theory.

Ab initio random structure searching of organic molecular solids: assessment and validation against experimental data

This paper explores the capability of using the DFT-D ab initio random structure searching (AIRSS) method to generate crystal structures of organic molecular materials, focusing on a system (m-aminobenzoic acid; m-ABA) that is known from experimental studies to exhibit abundant polymorphism. Within the structural constraints selected for the AIRSS calculations (specifically, centrosymmetric structures with Z = 4 for zwitterionic m-ABA molecules), the method is shown to successfully generate the two known polymorphs of m-ABA (form III and form IV) that have these structural features. We highlight various issues that are encountered in comparing crystal structures generated by AIRSS to experimental powder X-ray diffraction (XRD) data and solid-state magic-angle spinning (MAS) NMR data, demonstrating successful fitting for some of the lowest energy structures from the AIRSS calculations against experimental low-temperature powder XRD data for known polymorphs of m-ABA, and showing that comparison of computed and experimental solid-state NMR parameters allows different hydrogen-bonding motifs to be discriminated.

Positional Variance in NMR Crystallography

We propose a method to quantify positional uncertainties in crystal structures determined by chemical-shift-based NMR crystallography. The method combines molecular dynamics simulations and density functional theory calculations with experimental and computational chemical shift uncertainties. In this manner we find the average positional accuracy as well as the isotropic and anisotropic positional accuracy associated with each atom in a crystal structure determined by NMR crystallography. The approach is demonstrated on the crystal structures of cocaine, flutamide, flufenamic acid, the K salt of penicillin G, and form 4 of the drug 4-[4-(2-adamantylcarbamoyl)-5-tert-butylpyrazol-1-yl]benzoic acid (AZD8329). We find that, for the crystal structure of cocaine, the uncertainty corresponds to a positional RMSD of 0.17 Å. This is a factor of 2.5 less than for single-crystal X-ray-diffraction-based structure determination.

Structure elucidation of a complex CO2-based organic framework material by NMR crystallography

A three-dimensional structural model of a complex CO2-based organic framework made from high molecular weight, self-assembled, flexible and multi-functional oligomeric constituents has been determined de novo by solid-state NMR including DNP-enhanced experiments. The complete assignment of the 15N, 13C and 1H resonances was obtained from a series of two-dimensional through space and through bond correlation experiments. MM-QM calculations were used to generate different model structures for the material which were then evaluated by comparing multiple experimental and calculated NMR parameters. Both NMR and powder X-ray diffraction were evaluated as tools to determine the packing by crystal modelling, and at the level of structural modelling used here PXRD was found not to be a useful complement. The structure determined reveals a highly optimised H-bonding network that explains the unusual selectivity of the self-assembly process which generates the material. The NMR crystallography approach used here should be applicable for the structure determination of other complex solid materials.

Polymorphs of Theophylline Characterized by DNP Enhanced Solid-State NMR

We show how dynamic nuclear polarization (DNP) enhanced solid-state NMR spectroscopy can be used to characterize polymorphs and solvates of organic solids. We applied DNP to three polymorphs and one hydrated form of the asthma drug molecule theophylline. For some forms of theophylline, sample grinding and impregnation with the radical-containing solution, which are necessary to prepare the samples for DNP, were found to induce polymorphic transitions or desolvation between some forms. We present protocols for sample preparation for solid-state magic-angle spinning (MAS) DNP experiments that avoid the polymorphic phase transitions in theophylline. These protocols include cryogrinding, grinding under inert atmosphere, and the appropriate choice of the impregnating liquid. By applying these procedures, we subsequently demonstrate that two-dimensional correlation experiments, such as (1)H-(13)C and (1)H-(15)N HETCOR or (13)C-(13)C INADEQUATE, can be obtained at natural isotopic abundance in reasonable times, thus enabling more advanced structural characterization of polymorphs.

The use of a selective saturation pulse to suppress t1 noise in two-dimensional (1)H fast magic angle spinning solid-state NMR spectroscopy

A selective saturation pulse at fast magic angle spinning (MAS) frequencies (60+kHz) suppresses t1 noise in the indirect dimension of two-dimensional (1)H MAS NMR spectra. The method is applied to a synthetic nucleoside with an intense methyl (1)H signal due to triisopropylsilyl (TIPS) protecting groups. Enhanced performance in terms of suppressing the methyl signal while minimising the loss of signal intensity of nearby resonances of interest relies on reducing spin diffusion--this is quantified by comparing two-dimensional (1)H NOESY-like spin diffusion spectra recorded at 30-70 kHz MAS. For a saturation pulse centred at the methyl resonance, the effect of changing the nutation frequency at different MAS frequencies as well as the effect of changing the pulse duration is investigated. By applying a pulse of duration 30 ms and nutation frequency 725 Hz at 70 kHz MAS, a good compromise of significant suppression of the methyl resonance combined with the signal intensity of resonances greater than 5 ppm away from the methyl resonance being largely unaffected is achieved. The effectiveness of using a selective saturation pulse is demonstrated for both homonuclear (1)H-(1)H double quantum (DQ)/single quantum (SQ) MAS and (14)N-(1)H heteronuclear multiple quantum coherence (HMQC) two-dimensional solid-state NMR experiments.

An NMR crystallography study of the hemihydrate of 2', 3'-O-isopropylidineguanosine

An NMR crystallography study of the hemihydrate of 2', 3'-O-isopropylidineguanosine (Gace) is presented, together with powder X-ray diffraction and thermogravimetric analysis. (1)H double-quantum and (14)N-(1)H HMQC spectra recorded at 850MHz and 75kHz MAS (using a JEOL 1mm probe) are presented together with a (1)H-(13)C refocused INEPT spectrum recorded at 500MHz and 12.5kHz MAS using eDUMBO-122(1)H homonuclear decoupling. NMR chemical shieldings are calculated using the GIPAW (gauge-including projector augmented wave) method; good two-dimensional agreement between calculation and experiment is observed for (13)C and (1)H chemical shifts for directly bonded CH and CH3 peaks. There are two Gace molecules in the asymmetric unit cell: differences in specific (1)H chemical shifts are rationalised in terms of the strength of CH-π and intermolecular hydrogen bonding interactions.

35Cl solid-state NMR of HCl salts of active pharmaceutical ingredients: structural prediction, spectral fingerprinting and polymorph recognition

A series of HCl salts of active pharmaceutical ingredients (APIs) have been characterized via³⁵Cl solid-state NMR (SSNMR) spectroscopy and first-principles plane-wave DFT calculations of ³⁵Cl NMR interaction tensors.

De novo determination of the crystal structure of a large drug molecule by crystal structure prediction-based powder NMR crystallography

The crystal structure of form 4 of the drug 4-[4-(2-adamantylcarbamoyl)-5-tert-butyl-pyrazol-1-yl]benzoic acid is determined using a protocol for NMR powder crystallography at natural isotopic abundance combining solid-state (1)H NMR spectroscopy, crystal structure prediction, and density functional theory chemical shift calculations. This is the first example of NMR crystal structure determination for a molecular compound of previously unknown structure, and at 422 g/mol this is the largest compound to which this method has been applied so far.

Exploiting the Synergy of Powder X-ray Diffraction and Solid-State NMR Spectroscopy in Structure Determination of Organic Molecular Solids

We report a strategy for structure determination of organic materials in which complete solid-state nuclear magnetic resonance (NMR) spectral data is utilized within the context of structure determination from powder X-ray diffraction (XRD) data. Following determination of the crystal structure from powder XRD data, first-principles density functional theory-based techniques within the GIPAW approach are exploited to calculate the solid-state NMR data for the structure, followed by careful scrutiny of the agreement with experimental solid-state NMR data. The successful application of this approach is demonstrated by structure determination of the 1:1 cocrystal of indomethacin and nicotinamide. The ¹H and ¹³C chemical shifts calculated for the crystal structure determined from the powder XRD data are in excellent agreement with those measured experimentally, notably including the two-dimensional correlation of ¹H and ¹³C chemical shifts for directly bonded ¹³C-¹H moieties. The key feature of this combined approach is that the quality of the structure determined is assessed both against experimental powder XRD data and against experimental solid-state NMR data, thus providing a very robust validation of the veracity of the structure.

A general protocol for determining the structures of molecularly ordered but noncrystalline silicate frameworks

A general protocol is demonstrated for determining the structures of molecularly ordered but noncrystalline solids, which combines constraints provided by X-ray diffraction (XRD), one- and two-dimensional solid-state nuclear magnetic resonance (NMR) spectroscopy, and first-principles quantum chemical calculations. The approach is used to determine the structure(s) of a surfactant-directed layered silicate with short-range order in two dimensions but without long-range periodicity in three-dimensions (3D). The absence of long-range 3D molecular order and corresponding indexable XRD reflections precludes determination of a space group for this layered silicate. Nevertheless, by combining structural constraints obtained from solid-state (29)Si NMR analyses, including the types and relative populations of distinct (29)Si sites, their respective (29)Si-O-(29)Si connectivities and separation distances, with unit cell parameters (though not space group symmetry) provided by XRD, a comprehensive search of candidate framework structures leads to the identification of a small number of candidate structures that are each compatible with all of the experimental data. Subsequent refinement of the candidate structures using density functional theory calculations allows their evaluation and identification of "best" framework representations, based on their respective lattice energies and quantitative comparisons between experimental and calculated (29)Si isotropic chemical shifts and (2)J((29)Si-O-(29)Si) scalar couplings. The comprehensive analysis identifies three closely related and topologically equivalent framework configurations that are in close agreement with all experimental and theoretical structural constraints. The subtle differences among such similar structural models embody the complexity of the actual framework(s), which likely contain coexisting or subtle distributions of structural order that are intrinsic to the material.

Powder crystallography of pharmaceutical materials by combined crystal structure prediction and solid-state 1H NMR spectroscopy

A protocol for the ab initio crystal structure determination of powdered solids at natural isotopic abundance by combining solid-state NMR spectroscopy, crystal structure prediction, and DFT chemical shift calculations was evaluated to determine the crystal structures of four small drug molecules: cocaine, flutamide, flufenamic acid, and theophylline. For cocaine, flutamide and flufenamic acid, we find that the assigned (1)H isotropic chemical shifts provide sufficient discrimination to determine the correct structures from a set of predicted structures using the root-mean-square deviation (rmsd) between experimentally determined and calculated chemical shifts. In most cases unassigned shifts could not be used to determine the structures. This method requires no prior knowledge of the crystal structure, and was used to determine the correct crystal structure to within an atomic rmsd of less than 0.12 Å with respect to the known reference structure. For theophylline, the NMR spectra are too simple to allow for unambiguous structure selection.

Resolving nitrogen-15 and proton chemical shifts for mobile segments of elastin with two-dimensional NMR spectroscopy

In this study, one- and two-dimensional NMR experiments are applied to uniformly (15)N-enriched synthetic elastin, a recombinant human tropoelastin that has been cross-linked to form an elastic hydrogel. Hydrated elastin is characterized by large segments that undergo "liquid-like" motions that limit the efficiency of cross-polarization. The refocused insensitive nuclei enhanced by polarization transfer experiment is used to target these extensive, mobile regions of this protein. Numerous peaks are detected in the backbone amide region of the protein, and their chemical shifts indicate the completely unstructured, "random coil" model for elastin is unlikely. Instead, more evidence is gathered that supports a characteristic ensemble of conformations in this rubber-like protein.

Applications of high-resolution 1H solid-state NMR

This article reviews the large increase in applications of high-resolution (1)H magic-angle spinning (MAS) solid-state NMR, in particular two-dimensional heteronuclear and homonuclear (double-quantum and spin-diffusion NOESY-like exchange) experiments, in the last five years. These applications benefit from faster MAS frequencies (up to 80 kHz), higher magnetic fields (up to 1 GHz) and pulse sequence developments (e.g., homonuclear decoupling sequences applicable under moderate and fast MAS). (1)H solid-state NMR techniques are shown to provide unique structural insight for a diverse range of systems including pharmaceuticals, self-assembled supramolecular structures and silica-based inorganic-organic materials, such as microporous and mesoporous materials and heterogeneous organometallic catalysts, for which single-crystal diffraction structures cannot be obtained. The power of NMR crystallography approaches that combine experiment with first-principles calculations of NMR parameters (notably using the GIPAW approach) are demonstrated, e.g., to yield quantitative insight into hydrogen-bonding and aromatic CH-π interactions, as well as to generate trial three-dimensional packing arrangements. It is shown how temperature-dependent changes in the (1)H chemical shift, linewidth and DQ-filtered signal intensity can be analysed to determine the thermodynamics and kinetics of molecular level processes, such as the making and breaking of hydrogen bonds, with particular application to proton-conducting materials. Other applications to polymers and biopolymers, inorganic compounds and bioinorganic systems, paramagnetic compounds and proteins are presented. The potential of new technological advances such as DNP methods and new microcoil designs is described.

Identifying guanosine self assembly at natural isotopic abundance by high-resolution 1H and 13C solid-state NMR spectroscopy

By means of the (1)H chemical shifts and the proton-proton proximities as identified in (1)H double-quantum (DQ) combined rotation and multiple-pulse spectroscopy (CRAMPS) solid-state NMR correlation spectra, ribbon-like and quartet-like self-assembly can be identified for guanosine derivatives without isotopic labeling for which it was not possible to obtain single crystals suitable for diffraction. Specifically, characteristic spectral fingerprints are observed for dG(C10)(2) and dG(C3)(2) derivatives, for which quartet-like and ribbon-like self-assembly has been unambiguously identified by (15)N refocused INADEQUATE spectra in a previous study of (15)N-labeled derivatives (Pham, T. N.; et al. J. Am. Chem. Soc.2005, 127, 16018). The NH (1)H chemical shift is observed to be higher (13-15 ppm) for ribbon-like self-assembly as compared to 10-11 ppm for a quartet-like arrangement, corresponding to a change from NH···N to NH···O intermolecular hydrogen bonding. The order of the two NH(2)(1)H chemical shifts is also inverted, with the NH(2) proton closest in space to the NH proton having a higher or lower (1)H chemical shift than that of the other NH(2) proton for ribbon-like as opposed to quartet-like self-assembly. For the dG(C3)(2) derivative for which a single-crystal diffraction structure is available, the distinct resonances and DQ peaks are assigned by means of gauge-including projector-augmented wave (GIPAW) chemical shift calculations. In addition, (14)N-(1)H correlation spectra obtained at 850 MHz under fast (60 kHz) magic-angle spinning (MAS) confirm the assignment of the NH and NH(2) chemical shifts for the dG(C3)(2) derivative and allow longer range through-space N···H proximities to be identified, notably to the N7 nitrogens on the opposite hydrogen-bonding face.

A natural abundance solid-state 25Mg NMR study of layered magnesium phosphates

Natural abundance 25Mg solid-state magic-angle spinning and static NMR spectra of several representative layered magnesium phosphates were acquired at 21.1 and 9.4 T by using quadrupolar echo and double-frequency sweep quadrupolar Carr–Purcell–Meiboom–Gill pulse sequences. The spectra were dominated by the second-order quadrupolar interaction. The electric field gradient tensor parameters were extracted from the spectra via spectral simulations. These parameters, such as the quadrupolar coupling constant (CQ), appear to be sensitive to some parameters describing the distortion of the MgO6 octahedron in the layer. The empirical relationships between CQ and several structural parameters were established and used to obtain partial information on the Mg environment in a layered material (MgHPO4·1.2H2O) with unknown structure. Theoretical calculations suggest that the CQ values of the Mg sites are affected not only by the oxygen atoms in the first coordination sphere, but also by the spatial arrangements of the atoms in the second and third coordination spheres and beyond.

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.

NMR crystallography of campho[2,3-c]pyrazole (Z' = 6): combining high-resolution 1H-13C solid-state MAS NMR spectroscopy and GIPAW chemical-shift calculations

(1)H-(13)C two-dimensional magic-angle spinning (MAS) solid-state NMR correlation spectra, recorded with the MAS-J-HMQC experiment, are presented for campho[2,3-c]pyrazole. For each (13)C moiety, there are six resonances associated with the six distinct molecules in the asymmetric unit cell (Z' = 6). The one-bond C-H correlations observed in the 2D (1)H-(13)C MAS-J-HMQC spectra allow the experimental determination of the (1)H and (13)C chemical shifts associated with the separate CH, CH(2), and CH(3) groups. (1)H and (13)C chemical shifts calculated by using the GIPAW (Gauge Including Projector Augmented Waves) plane-wave pseudopotential approach are presented. Calculations for the whole unit cell (12 × 29 = 348 atoms, with geometry optimization of all atoms) allow the assignment of the experimental (1)H and (13)C chemical shifts to the six distinct molecules. The calculated chemical shifts for the full crystal structure are compared with those for isolated molecules as extracted from the geometry-optimized crystal structure. In this way, the effect of intermolecular interactions on the observed chemical shifts is quantified. In particular, the calculations are sufficiently precise to differentiate the small (<1 ppm) differences between the (1)H chemical shifts of the six resonances associated with each distinct CH or CH(2) moiety.

Complete (1)H resonance assignment of beta-maltose from (1)H-(1)H DQ-SQ CRAMPS and (1)H (DQ-DUMBO)-(13)C SQ refocused INEPT 2D solid-state NMR spectra and first principles GIPAW calculations

A disaccharide is a challenging case for high-resolution (1)H solid-state NMR because of the 24 distinct protons (14 aliphatic and 10 OH) having (1)H chemical shifts that all fall within a narrow range of approximately 3 to 7 ppm. High-resolution (1)H (500 MHz) double-quantum (DQ) combined rotation and multiple pulse sequence (CRAMPS) solid-state NMR spectra of beta-maltose monohydrate are presented. (1)H-(1)H DQ-SQ CRAMPS spectra are presented together with (1)H (DQ)-(13)C correlation spectra obtained with a new pulse sequence that correlates a high-resolution (1)H DQ dimension with a (13)C single quantum (SQ) dimension using the refocused INEPT pulse-sequence element to transfer magnetization via one-bond (13)C-(1)H J couplings. Compared to the observation of only a single broad peak in a (1)H DQ spectrum recorded at 30 kHz magic-angle spinning (MAS), the use of DUMBO (1)H homonuclear decoupling in the (1)H DQ CRAMPS experiment allows the resolution of distinct DQ correlation peaks which, in combination with first-principles chemical shift calculations based on the GIPAW (Gauge Including Projector Augmented Waves) plane-wave pseudopotential approach, enables the assignment of the (1)H resonances to the 24 distinct protons. We believe this to be the first experimental solid-state NMR determination of the hydroxyl OH (1)H chemical shifts for a simple sugar. Variable-temperature (1)H-(1)H DQ CRAMPS spectra reveal small increases in the (1)H chemical shifts of the OH resonances upon decreasing the temperature from 348 K to 248 K.

Determining relative proton-proton proximities from the build-up of two-dimensional correlation peaks in 1H double-quantum MAS NMR: insight from multi-spin density-matrix simulations

The build-up of intensity-as a function of the number, n(rcpl), of POST-C7 elements used for the excitation and reconversion of double-quantum (DQ) coherence (DQC)-is analysed for the fifteen distinct DQ correlation peaks that are observed experimentally for the eight separate (1)H resonances in a (1)H (500 MHz) DQ CRAMPS solid-state (12.5 kHz MAS) NMR spectrum of the dipeptide beta-AspAla (S. P. Brown, A. Lesage, B. Elena, and L. Emsley, J. Am. Chem. Soc., 2004, 126, 13230). The simulation in SPINEVOLUTION (M. Veshtort and R. G. Griffin, J. Magn. Reson., 2006, 178, 248) of t(1) ((1)H DQ evolution) FIDs for clusters of eight dipolar-coupled protons gives separate simulated (1)H DQ build-up curves for the CH(2)(a), CH(2)(b), CH(Asp), CH(Ala), NH and OH (1)H single-quantum (SQ) (1)H resonances. An analysis of both the simulated and experimental (1)H DQ build-up leads to the following general observations: (i) considering the build-up of (1)H DQ peaks at a particular SQ frequency, maximum intensity is observed for the DQC corresponding to the shortest H-H distance; (ii) for the maximum intensity (1)H DQ peak at a particular SQ frequency, the recoupling time for the observed maximum intensity depends on the corresponding H-H distance, e.g., maximum intensity for the CH(2)(a)-CH(2)(b) (H-H distance = 1.55 A) and OH-CH(Asp) (H-H distance = 2.49 A) DQ peaks is observed at n(rcpl) = 2 and 3, respectively; (iii) for DQ peaks involving a CH(2) proton at a non-CH(2) SQ frequency, there is much reduced intensity and a maximum intensity at a short recoupling time; (iv) for the other lower intensity (1)H DQ peaks at a particular SQ frequency, maximum intensity is observed for the same (or close to the same) recoupling time, but the relative intensity of the DQ peaks is a reliable indicator of the relative H-H distance-the ratio of the maximum intensities for the peaks at the CH(Ala) SQ frequency due to the two DQCs with the NH and OH protons are found to be approximately in the ratio of the squares of the corresponding dipolar coupling constants. While the simulated (1)H DQ build-up curves reproduce most of the features of the experimental curves, maximum intensity is often observed at a longer recoupling time in simulations. In this respect, simulations for two to eight spins show a trend towards a faster decay for an increasing number of considered spins. Finally, simulations show that increasing either the Larmor frequency (to 1 GHz) or the MAS frequency (to 125 kHz) does not lead to changes in the marked differences between the (1)H DQ build-up curves at the CH(Asp) SQ frequency for DQCs to the CH(2)(a) and OH protons that correspond to similar H-H distances (2.39 A and 2.49 A, respectively).

Calculation of NMR chemical shifts in organic solids: accounting for motional effects

NMR chemical shifts were calculated from first principles for well defined crystalline organic solids. These density functional theory calculations were carried out within the plane-wave pseudopotential framework, in which truly extended systems are implicitly considered. The influence of motional effects was assessed by averaging over vibrational modes or over snapshots taken from ab initio molecular dynamics simulations. It is observed that the zero-point correction to chemical shifts can be significant, and that thermal effects are particularly noticeable for shielding anisotropies and for a temperature-dependent chemical shift. This study provides insight into the development of highly accurate first principles calculations of chemical shifts in solids, highlighting the role of motional effects on well defined systems.

Powder NMR crystallography of thymol

A protocol for the structure determination of powdered solids at natural abundance by NMR is presented and illustrated for the case of the small drug molecule thymol. The procedure uses proton spin-diffusion data from two-dimensional NMR experiments in combination with periodic DFT refinements incorporating (1)H and (13)C NMR chemical shifts. For thymol, the method yields a crystal structure for the powdered sample, which differs by an atomic root-mean-square-deviation (all atoms except methyl group protons) of only 0.07 A from the single crystal X-ray diffraction structure with DFT-optimized proton positions.