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

Fragment-Based Deep Learning for Simultaneous Prediction of Polarizabilities and NMR Shieldings of Macromolecules and Their Aggregates

Simultaneous prediction of the molecular response properties, such as polarizability and the NMR shielding constant, at a low computational cost is an unresolved issue. We propose to combine a linear-scaling generalized energy-based fragmentation (GEBF) method and deep learning (DL) with both molecular and atomic information-theoretic approach (ITA) quantities as effective descriptors. In GEBF, the total molecular polarizability can be assembled as a linear combination of the corresponding quantities calculated from a set of small embedded subsystems in GEBF. In the new GEBF-DL(ITA) protocol, one can predict subsystem polarizabilities based on the corresponding molecular wave function (thus electron density and ITA quantities) and DL model rather than calculate them from the computationally intensive coupled-perturbed Hartree-Fock or Kohn-Sham equations and finally obtain the total molecular polarizability via a linear combination equation. As a proof-of-concept application, we predict the molecular polarizabilities of large proteins and protein aggregates. GEBF-DL(ITA) is shown to be as accurate enough as GEBF, with mean absolute percentage error <1%. For the largest protein aggregate (>4000 atoms), GEBF-DL(ITA) gains a speedup ratio of 3 compared with GEBF. It is anticipated that when more advanced electronic structure methods are used, this advantage will be more appealing. Moreover, one can also predict the NMR chemical shieldings of proteins with reasonably good accuracy. Overall, the cost-efficient GEBF-DL(ITA) protocol should be a robust theoretical tool for simultaneously predicting polarizabilities and NMR shieldings of large systems.

Polymorph Identification for Flexible Molecules: Linear Regression Analysis of Experimental and Calculated Solution- and Solid-State NMR Data

The Δδ regression approach of Blade et al. [ J. Phys. Chem. A 2020, 124(43), 8959-8977] for accurately discriminating between solid forms using a combination of experimental solution- and solid-state NMR data with density functional theory (DFT) calculation is here extended to molecules with multiple conformational degrees of freedom, using furosemide polymorphs as an exemplar. As before, the differences in measured 1H and 13C chemical shifts between solution-state NMR and solid-state magic-angle spinning (MAS) NMR (Δδexperimental) are compared to those determined by gauge-including projector augmented wave (GIPAW) calculations (Δδcalculated) by regression analysis and a t-test, allowing the correct furosemide polymorph to be precisely identified. Monte Carlo random sampling is used to calculate solution-state NMR chemical shifts, reducing computation times by avoiding the need to systematically sample the multidimensional conformational landscape that furosemide occupies in solution. The solvent conditions should be chosen to match the molecule's charge state between the solution and solid states. The Δδ regression approach indicates whether or not correlations between Δδexperimental and Δδcalculated are statistically significant; the approach is differently sensitive to the popular root mean squared error (RMSE) method, being shown to exhibit a much greater dynamic range. An alternative method for estimating solution-state NMR chemical shifts by approximating the measured solution-state dynamic 3D behavior with an ensemble of 54 furosemide crystal structures (polymorphs and cocrystals) from the Cambridge Structural Database (CSD) was also successful in this case, suggesting new avenues for this method that may overcome its current dependency on the prior determination of solution dynamic 3D structures.

Frontiers of molecular crystal structure prediction for pharmaceuticals and functional organic materials

The reliability of organic molecular crystal structure prediction has improved tremendously in recent years. Crystal structure predictions for small, mostly rigid molecules are quickly becoming routine. Structure predictions for larger, highly flexible molecules are more challenging, but their crystal structures can also now be predicted with increasing rates of success. These advances are ushering in a new era where crystal structure prediction drives the experimental discovery of new solid forms. After briefly discussing the computational methods that enable successful crystal structure prediction, this perspective presents case studies from the literature that demonstrate how state-of-the-art crystal structure prediction can transform how scientists approach problems involving the organic solid state. Applications to pharmaceuticals, porous organic materials, photomechanical crystals, organic semi-conductors, and nuclear magnetic resonance crystallography are included. Finally, efforts to improve our understanding of which predicted crystal structures can actually be produced experimentally and other outstanding challenges are discussed.

High-field and fast-spinning 1H MAS NMR spectroscopy for the characterization of two-dimensional covalent organic frameworks

Two-dimensional (2D) materials, like 2D covalent organic frameworks (COFs), have been attracting increasing research interest. They are usually obtained as polycrystalline powders. Solid-state NMR spectroscopy is capable of delivering structural information about such materials. Previous studies have applied, for example, 13C cross-polarization magic angle spinning (CP MAS) NMR experiments to characterize 2D COFs. Herein, we demonstrate the usefulness of high-field and fast-spinning 1H MAS NMR spectroscopy to resolve and quantify the signals of different 1H species within 2D COFs, including the edge sites and/or defects. Moreover, 1H-13C heteronuclear correlation (HETCOR) spectroscopy has also been applied and can provide improved resolution to obtain further information about stacking effects as well as edge sites/defects.

Atomic-level structure determination of amorphous molecular solids by NMR

Structure determination of amorphous materials remains challenging, owing to the disorder inherent to these materials. Nuclear magnetic resonance (NMR) powder crystallography is a powerful method to determine the structure of molecular solids, but disorder leads to a high degree of overlap between measured signals, and prevents the unambiguous identification of a single modeled periodic structure as representative of the whole material. Here, we determine the atomic-level ensemble structure of the amorphous form of the drug AZD4625 by combining solid-state NMR experiments with molecular dynamics (MD) simulations and machine-learned chemical shifts. By considering the combined shifts of all 1H and 13C atomic sites in the molecule, we determine the structure of the amorphous form by identifying an ensemble of local molecular environments that are in agreement with experiment. We then extract and analyze preferred conformations and intermolecular interactions in the amorphous sample in terms of the stabilization of the amorphous form of the drug.

Discovering the Solid-State Secrets of Lorlatinib by NMR Crystallography: To Hydrogen Bond or not to Hydrogen Bond

Lorlatinib is an active pharmaceutical ingredient (API) used in the treatment of lung cancer. Here, an NMR crystallography analysis is presented whereby the single-crystal X-ray diffraction structure (CSD: 2205098) determination is complemented by multinuclear (1H, 13C, 14/15N, 19F) magic-angle spinning (MAS) solid-state NMR and gauge-including projector augmented wave (GIPAW) calculation of NMR chemical shifts. Lorlatinib crystallises in the P21 space group, with two distinct molecules in the asymmetric unit cell, Z' = 2. Three of the four NH2 hydrogen atoms form intermolecular hydrogen bonds, N30-H…N15 between the two distinct molecules and N30-H…O2 between two equivalent molecules. This is reflected in one of the NH21H chemical shifts being significantly lower, 4.0 ppm compared to 7.0 ppm. Two-dimensional 1H-13C, 14N-1H and 1H (double-quantum, DQ)-1H (single-quantum, SQ) MAS NMR spectra are presented. The 1H resonances are assigned and specific HH proximities corresponding to the observed DQ peaks are identified. The resolution enhancement at a 1H Larmor frequency of 1 GHz as compared to 500 or 600 MHz is demonstrated.

Zwitterionic or Not? Fast and Reliable Structure Determination by Combining Crystal Structure Prediction and Solid-State NMR

When it comes to crystal structure determination, computational approaches such as Crystal Structure Prediction (CSP) have gained more and more attention since they offer some insight on how atoms and molecules are packed in the solid state, starting from only very basic information without diffraction data. Furthermore, it is well known that the coupling of CSP with solid-state NMR (SSNMR) greatly enhances the performance and the accuracy of the predictive method, leading to the so-called CSP-NMR crystallography (CSP-NMRX). In this paper, we present the successful application of CSP-NMRX to determine the crystal structure of three structural isomers of pyridine dicarboxylic acid, namely quinolinic, dipicolinic and dinicotinic acids, which can be in a zwitterionic form, or not, in the solid state. In a first step, mono- and bidimensional SSNMR spectra, i.e., ¹H Magic-Angle Spinning (MAS), ¹³C and ¹⁵N Cross Polarisation Magic-Angle Spinning (CPMAS), ¹H Double Quantum (DQ) MAS, ¹H-¹³C HETeronuclear CORrelation (HETCOR), were used to determine the correct molecular structure (i.e., zwitterionic or not) and the local molecular arrangement; at the end, the RMSEs between experimental and computed ¹H and ¹³C chemical shifts allowed the selection of the correct predicted structure for each system. Interestingly, while quinolinic and dipicolinic acids are zwitterionic and non-zwitterionic, respectively, in the solid state, dinicotinic acid exhibits in its crystal structure a "zwitterionic-non-zwitterionic continuum state" in which the proton is shared between the carboxylic moiety and the pyridinic nitrogen. Very refined SSNMR experiments were carried out, i.e., ¹⁴N-¹H Phase-Modulated (PM) pulse and Rotational-Echo Saturation-Pulse Double-Resonance (RESPDOR), to provide an accurate N-H distance value confirming the hybrid nature of the molecule. The CSP-NMRX method showed a remarkable match between the selected structures and the experimental ones. The correct molecular input provided by SSNMR reduced the number of CSP calculations to be performed, leading to different predicted structures, while RMSEs provided an independent parameter with respect to the computed energy for the selection of the best candidate.

Pure Isotropic Proton NMR Spectra in Solids using Deep Learning

The resolution of proton solid-state NMR spectra is usually limited by broadening arising from dipolar interactions between spins. Magic-angle spinning alleviates this broadening by inducing coherent averaging. However, even the highest spinning rates experimentally accessible today are not able to completely remove dipolar interactions. Here, we introduce a deep learning approach to determine pure isotropic proton spectra from a two-dimensional set of magic-angle spinning spectra acquired at different spinning rates. Applying the model to 8 organic solids yields high-resolution ¹ H solid-state NMR spectra with isotropic linewidths in the 50-400 Hz range.

Fast magic angle spinning for the characterization of milligram quantities of organic and biological solids at natural isotopic abundance by 13C-13C correlation DNP-enhanced NMR

We show that multidimensional solid-state NMR ¹³C-¹³C correlation spectra of biomolecular assemblies and microcrystalline organic molecules can be acquired at natural isotopic abundance with only milligram quantities of sample. These experiments combine fast Magic Angle Spinning of the sample, low-power dipolar recoupling, and dynamic nuclear polarization performed with AsymPol biradicals, a recently introduced family of polarizing agents. Such experiments are essential for structural characterization as they provide short- and long-range distance information. This approach is demonstrated on diverse sample types, including polyglutamine fibrils implicated in Huntington's disease and microcrystalline ampicillin, a small antibiotic molecule.

Exploring the Potential of Multinuclear Solid-State 1 H, 13 C, and 35 Cl Magnetic Resonance To Characterize Static and Dynamic Disorder in Pharmaceutical Hydrochlorides

Crystallographic disorder, whether static or dynamic, can be detrimental to the physical and chemical stability, ease of crystallization and dissolution rate of an active pharmaceutical ingredient. Disorder can result in a loss of manufacturing control leading to batch-to-batch variability and can lengthen the process of structural characterization. The range of NMR active nuclei makes solid-state NMR a unique technique for gaining nucleus-specific information about crystallographic disorder. Here, we explore the use of high-field ³⁵ Cl solid-state NMR at 23.5 T to characterize both static and dynamic crystallographic disorder: specifically, dynamic disorder occurring in duloxetine hydrochloride (1), static disorder in promethazine hydrochloride (2), and trifluoperazine dihydrochloride (3). In all structures, the presence of crystallographic disorder was confirmed by ¹³ C cross-polarization magic-angle spinning (CPMAS) NMR and supported by GIPAW-DFT calculations, and in the case of 3, ¹ H solid-state NMR provided additional confirmation. Applying ³⁵ Cl solid-state NMR to these compounds, we show that higher magnetic fields are beneficial for resolving the crystallographic disorder in 1 and 3, while broad spectral features were observed in 2 even at higher fields. Combining the data obtained from ¹ H, ¹³ C, and ³⁵ Cl NMR, we show that 3 exhibits a unique case of disorder involving the ⁺ N-H hydrogen positions of the piperazinium ring, driving the chloride anions to occupy three distinct sites.

Narrowing down the conformational space with solid-state NMR in crystal structure prediction of linezolid cocrystals

Many solids crystallize as microcrystalline powders, thus precluding the application of single crystal X-Ray diffraction in structural elucidation. In such cases, a joint use of high-resolution solid-state NMR and crystal structure prediction (CSP) calculations can be successful. However, for molecules showing significant conformational freedom, the CSP-NMR protocol can meet serious obstacles, including ambiguities in NMR signal assignment and too wide conformational search space to be covered by computational methods in reasonable time. Here, we demonstrate a possible way of avoiding these obstacles and making as much use of the two methods as possible in difficult circumstances. In a simple case, our experiments led to crystal structure elucidation of a cocrystal of linezolid (LIN), a wide-range antibiotic, with 2,3-dihydroxybenzoic acid, while a significantly more challenging case of a cocrystal of LIN with 2,4-dihydroxybenzoic acid led to the identification of the most probable conformations of LIN inside the crystal. Having four rotatable bonds, some of which can assume many discreet values, LIN molecule poses a challenge in establishing its conformation in a solid phase. In our work, a set of 27 conformations were used in CSP calculations to yield model crystal structures to be examined against experimental solid-state NMR data, leading to a reliable identification of the most probable molecular arrangements.

Combining X-ray and NMR Crystallography to Explore the Crystallographic Disorder in Salbutamol Oxalate

Salbutamol is an active pharmaceutical ingredient commonly used to treat respiratory distress and is listed by the World Health Organization as an essential medicine. Here, we establish the crystal structure of its oxalate form, salbutamol oxalate, and explore the nature of its crystallographic disorder by combined X-ray crystallography and ¹³C cross-polarization (CP) magic-angle spinning (MAS) solid-state NMR. The *C-OH chiral center of salbutamol (note that the crystal structures are a racemic mixture of the two enantiomers of salbutamol) is disordered over two positions, and the tert-butyl group is rotating rapidly, as revealed by ¹³C solid-state NMR. The impact of crystallization conditions on the disorder was investigated, finding variations in the occupancy ratio of the *C-OH chiral center between single crystals and a consistency across samples in the bulk powder. Overall, this work highlights the contrast between investigating crystallographic disorder by X-ray diffraction and solid-state NMR experiment, and gauge-including projector-augmented-wave (GIPAW) density functional theory (DFT) calculations, with their combined use, yielding an improved understanding of the nature of the crystallographic disorder between the local (i.e., as viewed by NMR) and longer-range periodic (i.e., as viewed by diffraction) scale.

Selective Nuclear Magnetic Resonance Method for Enhancing Long-Range Heteronuclear Correlations in Solids

The long-range heteronuclear correlation remains a significant challenge in solid-state nuclear magnetic resonance (NMR), which is critical in the structural elucidation of biomolecular, material, and pharmaceutical solids. We propose a selective NMR method, heteronuclear selective phase-optimized recoupling (hetSPR), to selectively enhance long-range correlations of interest by utilizing characteristic chemical shifts. Compared to conventional methods, hetSPR can selectively enhance desired heteronuclear correlations (e.g., ¹H-¹³C and ¹H-¹⁹F) by factors up to 5 and largely suppress the unwanted ones. The method proves useful by enhancing the long-range correlation from an intermolecular ¹H-¹⁹F distance of 4.8 Å by a factor of 2.4 in a fluorinated pharmaceutical drug, bicalutamide, under fast magic-angle spinning. It does not use selective pulses and is thus user-friendly even for nonexperts. The new method is expected to boost solid-state NMR to elucidate the structures of various solids.

From Powders to Single Crystals: A Crystallographer's Toolbox for Small-Molecule Structure Determination

Although the crystal structures of small-molecule compounds are often determined from single-crystal X-ray diffraction (scXRD), recent advances in three-dimensional electron diffraction (3DED) and crystal structure prediction (CSP) methods promise to expand the structure elucidation toolbox available to the crystallographer. Herein, a comparative assessment of scXRD, 3DED, and CSP in combination with powder X-ray diffraction is carried out on two former drug candidate compounds and a multicomponent crystal of a key building block in the synthesis of gefapixant citrate.

De Novo Crystal Structure Determination from Machine Learned Chemical Shifts

Determination of the three-dimensional atomic-level structure of powdered solids is one of the key goals in current chemistry. Solid-state NMR chemical shifts can be used to solve this problem, but they are limited by the high computational cost associated with crystal structure prediction methods and density functional theory chemical shift calculations. Here, we successfully determine the crystal structures of ampicillin, piroxicam, cocaine, and two polymorphs of the drug molecule AZD8329 using on-the-fly generated machine-learned isotropic chemical shifts to directly guide a Monte Carlo-based structure determination process starting from a random gas-phase conformation.

Along the road to Crystal Structure Prediction (CSP) of pharmaceutical-like molecules

Computational methods used for predicting crystal structures of organic compounds are mature enough to be routinely used with many rigid and semi-rigid organic molecules. The usefulness of Crystal Structure Prediction...

Solid-State NMR-Driven Crystal Structure Prediction of Molecular Crystals: The Case of Mebendazole

Among all possible NMR crystallography approaches for crystal-structure determination, crystal structure prediction - NMR crystallography (CSP-NMRX) has recently turned out to be a powerful method. In the latter, the original procedure exploited solid-state NMR (SSNMR) information during the final steps of the prediction. In particular, it used the comparison of computed and experimental chemical shifts for the selection of the correct crystal packing. Still, the prediction procedure, generally carried out with DFT methods, may require important computational resources and be quite time-consuming, especially if there are no available constraints to use at the initial stage. Herein, the successful application of this combined prediction method, which exploits NMR information also in the input step to reduce the search space of the predictive algorithm, is presented. Herein, this method was applied on mebendazole, which is characterized by desmotropism. The use of SSNMR data as constraints for the selection of the right tautomer and the determination of the number of independent molecules in the unit cell led to a considerably faster process, reducing the number of calculations to be performed. In this way, the crystal packing was successfully predicted for the three known phases of mebendazole. To evaluate the quality of the predicted structures, these were compared to the experimental ones. The crystal structure of phase B of mebendazole, in particular, was determined de novo by powder diffraction and is presented for the first time in this paper.

NMR-Based Configurational Assignments of Natural Products: Gibbs Sampling and Bayesian Inference Using Floating Chirality Distance Geometry Calculations

Floating chirality restrained distance geometry (fc-rDG) calculations are used to directly evolve structures from NMR data such as NOE-derived intramolecular distances or anisotropic residual dipolar couplings (RDCs). In contrast to evaluating pre-calculated structures against NMR restraints, multiple configurations (diastereomers) and conformations are generated automatically within the experimental limits. In this report, we show that the "unphysical" rDG pseudo energies defined from NMR violations bear statistical significance, which allows assigning probabilities to configurational assignments made that are fully compatible with the method of Bayesian inference. These "diastereomeric differentiabilities" then even become almost independent of the actual values of the force constants used to model the restraints originating from NOE or RDC data.

A toolbox for improving the workflow of NMR crystallography

NMR crystallography is a powerful tool with applications in structural characterization and crystal structure verification, to name two. However, applying this tool presents several challenges, especially for industrial users, in terms of consistency, workflow, time consumption, and the requirement for a high level of understanding of experimental solid-state NMR and GIPAW-DFT calculations. Here, we have developed a series of fully parameterized scripts for use in Materials Studio and TopSpin, based on the .magres file format, with a focus on organic molecules (e.g. pharmaceuticals), improving efficiency, robustness, and workflow. We separate these tools into three major categories: performing the DFT calculations, extracting & visualizing the results, and crystallographic modelling. These scripts will rapidly submit fully parameterized CASTEP jobs, extract data from the calculations, assist in visualizing the results, and expedite the process of structural modelling. Accompanied with these tools is a description on their functionality, documentation on how to get started and use the scripts, and links to video tutorials for guiding new users. Through the use of these tools, we hope to facilitate NMR crystallography and to harmonize the process across users.

Gaussian Process Regression for Materials and Molecules

We provide an introduction to Gaussian process regression (GPR) machine-learning methods in computational materials science and chemistry. The focus of the present review is on the regression of atomistic properties: in particular, on the construction of interatomic potentials, or force fields, in the Gaussian Approximation Potential (GAP) framework; beyond this, we also discuss the fitting of arbitrary scalar, vectorial, and tensorial quantities. Methodological aspects of reference data generation, representation, and regression, as well as the question of how a data-driven model may be validated, are reviewed and critically discussed. A survey of applications to a variety of research questions in chemistry and materials science illustrates the rapid growth in the field. A vision is outlined for the development of the methodology in the years to come.

Pure Isotropic Proton Solid State NMR

Resolution in proton solid state magic angle sample spinning (MAS) NMR is limited by the intrinsically imperfect nature of coherent averaging induced by either MAS or multiple pulse sequence methods. Here, we suggest that instead of optimizing and perfecting a coherent averaging scheme, we could approach the problem by parametrically mapping the error terms due to imperfect averaging in a k-space representation, in such a way that they can be removed in a multidimensional correlation leaving only the desired pure isotropic signal. We illustrate the approach here by determining pure isotropic ¹H spectra from a series of MAS spectra acquired at different spinning rates. For six different organic solids, the approach is shown to produce pure isotropic ¹H spectra that are significantly narrower than the MAS spectrum acquired at the fastest possible rate, with linewidths down to as little as 48 Hz. On average, we observe a 7-fold increase in resolution, and up to a factor of 20, as compared with spectra acquired at 100 kHz MAS. The approach is directly applicable to a range of solids, and we anticipate that the same underlying principle for removing errors introduced here can be applied to other problems in NMR spectroscopy.

Synergy of Solid-State NMR, Single-Crystal X-ray Diffraction, and Crystal Structure Prediction Methods: A Case Study of Teriflunomide (TFM)

In this work, for the first time, we present the X-ray diffraction crystal structure and spectral properties of a new, room-temperature polymorph of teriflunomide (TFM), CSD code 1969989. As revealed by DSC, the low-temperature TFM polymorph recently reported by Gunnam et al. undergoes a reversible thermal transition at -40 °C. This reversible process is related to a change in Z' value, from 2 to 1, as observed by variable-temperature ¹H-¹³C cross-polarization (CP) magic-angle spinning (MAS) solid-state NMR, while the crystallographic system is preserved (triclinic). Two-dimensional ¹³C-¹H and ¹H-¹H double-quantum MAS NMR spectra are consistent with the new room-temperature structure, including comparison with GIPAW (gauge-including projector augmented waves) calculated NMR chemical shifts. A crystal structure prediction procedure found both experimental teriflunomide polymorphs in the energetic global minimum region. Differences between the polymorphs are seen for the torsional angle describing the orientation of the phenyl ring relative to the planarity of the TFM molecule. In the low-temperature structure, there are two torsion angles of 4.5 and 31.9° for the two Z' = 2 molecules, while in the room-temperature structure, there is disorder that is modeled with ∼50% occupancy between torsion angles of -7.8 and 28.6°. These observations are consistent with a broad energy minimum as revealed by DFT calculations. PISEMA solid-state NMR experiments show a reduction in the C-H dipolar coupling in comparison to the static limit for the aromatic CH moieties of 75% and 51% at 20 and 40 °C, respectively, that is indicative of ring flips at the higher temperature. Our study shows the power of combining experiments, namely DSC, X-ray diffraction, and MAS NMR, with DFT calculations and CSP to probe and understand the solid-state landscape, and in particular the role of dynamics, for pharmaceutical molecules.

Spectroscopic Evidence for a Covalent Sigma Au-C Bond on Au Surfaces Using 13C Isotope Labeling

The Au-C linkage has been demonstrated as a robust interface for coupling thin organic films on Au surfaces. However, the nature of the Au-C interaction remains elusive up to now. Surface-enhanced Raman spectroscopy was previously used to assign a band at 412 cm^-1 as a covalent sigma Au-C bond for films generated by spontaneous reduction of the 4-nitrobenzenediazonium salt on Au nanoparticles. However, this assignment is disputed based on our isotopic shift study. We now provide direct evidence for covalent Au-C bonds on the surface of Au nanoparticles using ¹³C cross-polarization/magic angle spinning solid-state NMR spectroscopy combined with isotope substitution. A ¹³C NMR shift at 165 ppm was identified as an aromatic carbon linked to the gold surface, while the shift at 148 ppm was attributed to C-C junctions in the arylated organic film. This demonstration of the covalent sigma Au-C bond fills the gap in metal-C bonds for organic films on surfaces, and it has great practical and theoretical significance in understanding and designing a molecular junction based on the Au-C bond.

Configurational Analysis by Residual Dipolar Couplings: Critical Assessment of "Structural Noise" from Thermal Vibrations

The certainty of configurational assignments of natural products based on anisotropic NMR parameters, such as residual dipolar couplings (RDCs), must be amended by estimates on structural noise emerging from thermal vibrations. We show that vibrational analysis significantly affects the error margins with which RDCs can be back-calculated from molecular models, and the implications of thermal motions on the differentiability of diastereomers are derived.

Solid-state NMR spectroscopy

Solid-state nuclear magnetic resonance (NMR) spectroscopy is an atomic-level method used to determine the chemical structure, three-dimensional structure, and dynamics of solids and semi-solids. This Primer summarizes the basic principles of NMR as applied to the wide range of solid systems. The fundamental nuclear spin interactions and the effects of magnetic fields and radiofrequency pulses on nuclear spins are the same as in liquid-state NMR. However, because of the anisotropy of the interactions in the solid state, the majority of high-resolution solid-state NMR spectra is measured under magic-angle spinning (MAS), which has profound effects on the types of radiofrequency pulse sequences required to extract structural and dynamical information. We describe the most common MAS NMR experiments and data analysis approaches for investigating biological macromolecules, organic materials, and inorganic solids. Continuing development of sensitivity-enhancement approaches, including 1H-detected fast MAS experiments, dynamic nuclear polarization, and experiments tailored to ultrahigh magnetic fields, is described. We highlight recent applications of solid-state NMR to biological and materials chemistry. The Primer ends with a discussion of current limitations of NMR to study solids, and points to future avenues of development to further enhance the capabilities of this sophisticated spectroscopy for new applications.

High Sensitivity Detection of a Solubility Limiting Surface Transformation of Drug Particles by DNP SENS

We investigate the presence of a surface species for the active pharmaceutical ingredient (API) AZD9496 with dynamic nuclear polarization surface enhanced nuclear spectroscopy (DNP SENS). We show that using DNP we can elucidate the presence of an amorphous form of the API at the surface of crystalline particles of the salt form. The amorphous form of the API has distinguishable ¹³C chemical shifts when compared to the salt form under various acidic conditions. The predominant form in frozen particles of AZD9496 is the salt, and we provide evidence to suggest that the amorphous layer at the surface is mainly made up of the dissociated free form.

NMR Chemical Shift and Methylation of 4-Nitroimidazole: Experiment and Theory

Nitroimidazoles and derivatives are a class of active pharmaceutical ingredients (APIs) first introduced sixty years ago. As anti-infection agents, the structure–activity relationships of nitroimidazole compounds have been particularly difficult to study due to their low reduction potentials and unique electronic structures. In this study, we combine dynamic nuclear polarization (DNP)-enhanced solid-state (100K), solid-state (298K), and 1H-13C heteronuclear single quantum coherence (HSQC) solution-state NMR techniques (303K) with density functional theory (DFT) to study the 1H, 13C, and 15N chemical shifts of 4-nitroimidazole (4-NI) and 1-methyl-4-nitroimidazole (CH3-4NI). The 4-NI chemical shifts were observed at 119.4, 136.4, and 144.7ppm for 13C, and at 181.5, 237.4, and 363.0ppm for 15N. The measurements revealed that methylation (deprotonation) of the amino nitrogen N(1) of 4-NI had less effect (Δδ=−4.8ppm) on the N(1) chemical shift but was compensated by shielding of the N(3) (Δδ=11.6ppm) in CH3-4NI. The calculated chemical shifts using DFT for 4-NI and CH3-4NI agreed well with the experimental values (within 2%) for the imidazole carbons. However, larger discrepancies (up to 13%) were observed between the calculated and measured 15N NMR chemical shifts for the imidazole nitrogen atoms of both molecules, which indicate that effects such as imidazole ring resonant structures and molecular dynamics may also contribute to the nitrogen chemical environment.

Revealing the Structure and Oxygen Transport at Interfaces in Complex Oxide Heterostructures via 17O NMR Spectroscopy

Vertically aligned nanocomposite (VAN) films, comprising nanopillars of one phase embedded in a matrix of another, have shown great promise for a range of applications due to their high interfacial areas oriented perpendicular to the substrate. In particular, oxide VANs show enhanced oxide-ion conductivity in directions that are orthogonal to those found in more conventional thin-film heterostructures; however, the structure of the interfaces and its influence on conductivity remain unclear. In this work, ¹⁷O NMR spectroscopy is used to study CeO₂-SrTiO₃ VAN thin films: selective isotopic enrichment is combined with a lift-off technique to remove the substrate, facilitating detection of the ¹⁷O NMR signal from single atomic layer interfaces. By performing the isotopic enrichment at variable temperatures, the superior oxide-ion conductivity of the VAN films compared to the bulk materials is shown to arise from enhanced oxygen mobility at this interface; oxygen motion at the interface is further identified from ¹⁷O relaxometry experiments. The structure of this interface is solved by calculating the NMR parameters using density functional theory combined with random structure searching, allowing the chemistry underpinning the enhanced oxide-ion transport to be proposed. Finally, a comparison is made with 1% Gd-doped CeO₂-SrTiO₃ VAN films, for which greater NMR signal can be obtained due to paramagnetic relaxation enhancement, while the relative oxide-ion conductivities of the phases remain similar. These results highlight the information that can be obtained on interfacial structure and dynamics with solid-state NMR spectroscopy, in this and other nanostructured systems, our methodology being generally applicable to overcome sensitivity limitations in thin-film studies.

Towards Accurate Predictions of Proton NMR Spectroscopic Parameters in Molecular Solids

The factors contributing to the accuracy of quantum-chemical calculations for the prediction of proton NMR chemical shifts in molecular solids are systematically investigated. Proton chemical shifts of six solid amino acids with hydrogen atoms in various bonding environments (CH, CH₂ , CH₃ , OH, SH and NH₃ ) were determined experimentally using ultra-fast magic-angle spinning and proton-detected 2D NMR experiments. The standard DFT method commonly used for the calculations of NMR parameters of solids is shown to provide chemical shifts that deviate from experiment by up to 1.5 ppm. The effects of the computational level (hybrid DFT functional, coupled-cluster calculation, inclusion of relativistic spin-orbit coupling) are thoroughly discussed. The effect of molecular dynamics and nuclear quantum effects are investigated using path-integral molecular dynamics (PIMD) simulations. It is demonstrated that the accuracy of the calculated proton chemical shifts is significantly better when these effects are included in the calculations.

Application of NMR Crystallography to Highly Disordered Templated Materials: Extensive Local Structural Disorder in the Gallophosphate GaPO-34A

We present an NMR crystallographic investigation of two as-made forms of the recently characterized gallophosphate GaPO-34A, which has an unusual framework composition with a Ga:P ratio of 7:6 and contains both hydroxide and fluoride anions and either 1-methylimidazolium or pyridinium as the structure-directing agent. We combine previously reported X-ray crystallographic data with solid-state NMR spectroscopy and periodic density functional theory (DFT) calculations to show that the structure contains at least three distinct types of disorder (occupational, compositional, and dynamic). The occupational disorder arises from the presence of six anion sites per unit cell, but a total occupancy of five of these, leading to full occupancy of four sites and partial occupancy of the fifth and sixth (which are related by symmetry). The mixture of OH and F present leads to compositional disorder on the occupied anion sites, although the occupancy of some sites by F is calculated to be energetically unfavorable and signals relating to F on these sites are not observed by NMR spectroscopy, confirming that the compositional disorder is not random. Finally, a combination of high-field ⁷¹Ga NMR spectroscopy and variable-temperature ¹³C and ³¹P NMR experiments shows that the structure directing agents are dynamic on the microsecond time scale, which can be supported by averaging the ³¹P chemical shifts calculated with the SDA in different orientations. This demonstrates the value of an NMR crystallographic approach, particularly in the case of highly disordered crystalline materials, where the growth of large single crystals for conventional structure determination may not be possible owing to the extent of disorder present.

Crystal structures of two furazidin polymorphs revealed by a joint effort of crystal structure prediction and NMR crystallography

This work presents the crystal structure determination of two elusive polymorphs of furazidin, an antibacterial agent, employing a combination of crystal structure prediction (CSP) calculations and an NMR crystallography approach. Two previously uncharacterized neat crystal forms, one of which has two symmetry-independent molecules (form I), whereas the other one is a Z' = 1 polymorph (form II), crystallize in P2₁/c and P1 space groups, respectively, and both are built by different conformers, displaying different intermolecular interactions. It is demonstrated that the usage of either CSP or NMR crystallography alone is insufficient to successfully elucidate the above-mentioned crystal structures, especially in the case of the Z' = 2 polymorph. In addition, cases of serendipitous agreement in terms of ¹H or ¹³C NMR data obtained for the CSP-generated crystal structures different from the ones observed in the laboratory (false-positive matches) are analyzed and described. While for the majority of analyzed crystal structures the obtained agreement with the NMR experiment is indicative of some structural features in common with the experimental structure, the mentioned serendipity observed in exceptional cases points to the necessity of caution when using an NMR crystallography approach in crystal structure determination.

Monitoring the Site-Specific Solid-State NMR Data in Oligopeptides

Reliable values of the solid-state NMR (SSNMR) parameters together with precise structural data specific for a given amino acid site in an oligopeptide are needed for the proper interpretation of measurements aiming at an understanding of oligopeptides' function. The periodic density functional theory (DFT)-based computations of geometries and SSNMR chemical shielding tensors (CSTs) of solids are shown to be accurate enough to support the SSNMR investigations of suitably chosen models of oriented samples of oligopeptides. This finding is based on a thorough comparison between the DFT and experimental data for a set of tripeptides with both ¹³C_α and ¹⁵N_amid CSTs available from the single-crystal SSNMR measurements and covering the three most common secondary structural elements of polypeptides. Thus, the ground is laid for a quantitative description of local spectral parameters of crystalline oligopeptides, as demonstrated for the backbone ¹⁵N_amid nuclei of samarosporin I, which is a pentadecapeptide (composed of five classical and ten nonproteinogenic amino acids) featuring a strong antimicrobial activity.

Crystal structure determination of an elusive methanol solvate – hydrate of catechin using crystal structure prediction and NMR crystallography

A useful short-cut was developed to limit the number of molecular conformations that need to be regarded in crystal structure prediction calculations, which led to the crystal structure determination of new methanol solvate – hydrate of catechin.

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.