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

An NMR crystallographic characterisation of solid (+)-usnic acid

We use a combination of one- and two-dimensional solid-state nuclear magnetic resonance (NMR) spectroscopy and density functional theory (DFT) calculations to obtain a full assignment of the 1H and 13C signals for solid (+)-usnic acid, which contains two molecules in the asymmetric unit. By combining through-space 1H-1H correlation data with computation it is possible to assign signals not just to the same molecules (relative assignment) but to assign the signals to specific crystallographic molecules (absolute assignment). Variable-temperature measurements reveal that there is some variation in many of the 13C chemical shifts with temperature, likely arising from varying populations of different tautomeric forms of the molecule. The NMR spectrum of crystalline (+)-usnic acid is then compared with that of ground Usnea dasopoga lichen (the source material of the usnic acid). The abundance of usnic acid is so great in the lichen that this natural product can be observed directly in the NMR spectrum without further purification. This natural sample of usnic acid appears to have the same crystalline form as that in the pure commercial sample.

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.

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.

The effects of conformation and intermolecular hydrogen bonding on the structure and IR spectra of flutamide; a study based on the matrix isolation technique, ab initio and DFT calculations

In this study, stable conformers of flutamide referred to as an anticancer drug were searched through a relaxed potential energy surface scan carried out at the B3LYP/6-31G(d) level of theory. This was followed by geometry optimization and thermochemistry calculations performed with the HF-SCF, MP2, B3LYP methods and the 6-31G(d), 6-311++G(d,p), aug-cc-pvTZ basis sets for each of the determined minimum energy conformers. The results revealed that flutamide has at least five stable conformers and two of them provide the major contribution to the observed matrix isolation infrared (IR) spectra of the molecule. The effects of conformational variety and intermolecular hydrogen bonding interactions on the observed IR spectra of flutamide were interpreted in the light of the vibrational spectral data obtained for the most stable monomer and dimer forms of the molecule at the same levels of theory. Pulay's "Scaled Quantum Mechanical-Force Field (SQM-FF)" method was used in the refinement of the calculated harmonic wavenumbers, IR intensities and potential energy distributions. This scaling method which proved its superiority to both anharmonic frequency calculations and other scaling methods helped us to correctly interpret the remarkable differences between the matrix IR spectra of flutamide in argon and the condensed phase IR spectra of the molecule in solvents such as KBr, H₂O, D₂O, ethanol and methanol.

Ultrafast Magic Angle Spinning Solid-State NMR Spectroscopy: Advances in Methodology and Applications

Solid-state NMR spectroscopy is one of the most commonly used techniques to study the atomic-resolution structure and dynamics of various chemical, biological, material, and pharmaceutical systems spanning multiple forms, including crystalline, liquid crystalline, fibrous, and amorphous states. Despite the unique advantages of solid-state NMR spectroscopy, its poor spectral resolution and sensitivity have severely limited the scope of this technique. Fortunately, the recent developments in probe technology that mechanically rotate the sample fast (100 kHz and above) to obtain "solution-like" NMR spectra of solids with higher resolution and sensitivity have opened numerous avenues for the development of novel NMR techniques and their applications to study a plethora of solids including globular and membrane-associated proteins, self-assembled protein aggregates such as amyloid fibers, RNA, viral assemblies, polymorphic pharmaceuticals, metal-organic framework, bone materials, and inorganic materials. While the ultrafast-MAS continues to be developed, the minute sample quantity and radio frequency requirements, shorter recycle delays enabling fast data acquisition, the feasibility of employing proton detection, enhancement in proton spectral resolution and polarization transfer efficiency, and high sensitivity per unit sample are some of the remarkable benefits of the ultrafast-MAS technology as demonstrated by the reported studies in the literature. Although the very low sample volume and very high RF power could be limitations for some of the systems, the advantages have spurred solid-state NMR investigation into increasingly complex biological and material systems. As ultrafast-MAS NMR techniques are increasingly used in multidisciplinary research areas, further development of instrumentation, probes, and advanced methods are pursued in parallel to overcome the limitations and challenges for widespread applications. This review article is focused on providing timely comprehensive coverage of the major developments on instrumentation, theory, techniques, applications, limitations, and future scope of ultrafast-MAS technology.

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.

Resolving the Chemical Formula of Nesquehonite via NMR Crystallography, DFT Computation, and Complementary Neutron Diffraction

Nesquehonite is a magnesium carbonate mineral relevant to carbon sequestration envisioned for carbon capture and storage of CO₂ . Its chemical formula remains controversial today, assigned as either a hydrated magnesium carbonate [MgCO₃  ⋅ 3H₂ O], or a hydroxy- hydrated- magnesium bicarbonate [Mg(HCO₃ )OH ⋅ 2H₂ O]. The resolution of this controversy is central to understanding this material's thermodynamic, phase, and chemical behavior. In an NMR crystallography study, using rotational-echo double-resonance ¹³ C{¹ H} (REDOR), ¹³ C-¹ H distances are determined with precision, and the combination of ¹³ C static NMR lineshapes and density functional theory (DFT) calculations are used to model different H atomic coordinates. [MgCO₃  ⋅ 3H₂ O] is found to be accurate, and evidence from neutron powder diffraction bolsters these assignments. Refined H positions can help understand how H-bonding stabilizes this structure against dehydration to MgCO₃ . More broadly, these results illustrate the power of NMR crystallography as a technique for resolving questions where X-ray diffraction is inconclusive.

Revealing carbon capture chemistry with 17-oxygen NMR spectroscopy

Carbon dioxide capture is essential to achieve net-zero emissions. A hurdle to the design of improved capture materials is the lack of adequate tools to characterise how CO₂ adsorbs. Solid-state nuclear magnetic resonance (NMR) spectroscopy is a promising probe of CO₂ capture, but it remains challenging to distinguish different adsorption products. Here we perform a comprehensive computational investigation of 22 amine-functionalised metal-organic frameworks and discover that ¹⁷O NMR is a powerful probe of CO₂ capture chemistry that provides excellent differentiation of ammonium carbamate and carbamic acid species. The computational findings are supported by ¹⁷O NMR experiments on a series of CO₂-loaded frameworks that clearly identify ammonium carbamate chain formation and provide evidence for a mixed carbamic acid - ammonium carbamate adsorption mode. We further find that carbamic acid formation is more prevalent in this materials class than previously believed. Finally, we show that our methods are readily applicable to other adsorbents, and find support for ammonium carbamate formation in amine-grafted silicas. Our work paves the way for investigations of carbon capture chemistry that can enable materials design.

Anisotropy, segmental dynamics and polymorphism of crystalline biogenic carboxylic acids

Carboxylic acids of the Krebs cycle possess invaluable biochemical significance. Still, there are severe gaps in the availability of thermodynamic and crystallographic data, as well as ambiguities prevailing in the literature on the thermodynamic characterization and polymorph ranking. Providing an unambiguous description of the structure, thermodynamics and polymorphism of their neat crystalline phases requires a complex multidisciplinary approach. This work presents results of an extensive investigation of the structural anisotropy of the thermal expansion and local dynamics within these crystals, obtained from a beneficial cooperation of NMR crystallography and ab initio calculations of non-covalent interactions. The observed structural anisotropy and spin-lattice relaxation times are traced to large spatial variations in the strength of molecular interactions in the crystal lattice, especially in the orientation of the hydrogen bonds. A completely resolved crystal structure for oxaloacetic acid is reported for the first time. Thanks to multi-instrumental calorimetric effort, this work clarifies phase behavior, determines third-law entropies of the crystals, and states definitive polymorph ranking for succinic and fumaric acids. These thermodynamic observations are then interpreted in terms of first-principles quasi-harmonic calculations of cohesive properties. A sophisticated model capturing electronic, thermal, and configurational-entropic effects on the crystal structure approaches captures the subtle Gibbs energy differences governing polymorph ranking for succinic and fumaric acids, representing another success story of computational chemistry.

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.

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.

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.

To what extent do bond length and angle govern the 13C and 1H NMR response to weak CH⋯O hydrogen bonds? A case study of caffeine and theophylline cocrystals

Weak hydrogen bonds are important structure-directing elements in supramolecular chemistry and biochemistry. We consider here weak CH⋯O hydrogen bonds in a series of cocrystals of theophylline and caffeine and assess to what extent the CH⋯O distance and angle govern the observed ¹³C and ¹H isotropic chemical shifts. Gauge-including projector-augmented wave density functional theory (GIPAW DFT) calculations consistently predict a decrease in the ¹³C and ¹H magnetic shielding constants upon hydrogen bond formation on the order of 2-5 ppm (¹³C) and 1-2 ppm (¹H). These trends are reproduced using the machine-learning approach implemented in ShiftML. Experimental ¹³C and ¹H chemical shifts obtained for powdered samples using one-dimensional NMR spectroscopy as well as heteronuclear correlation (HETCOR) spectroscopy correlate well with the GIPAW DFT results. However, the experimental ¹³C NMR response only correlates moderately well with the hydrogen bond length and angle, while the experimental ¹H chemical shifts only show very weak correlations to these local structural elements. DFT computations on isolated imidazole-formaldehyde models show that the ¹³C and ¹H chemical shifts generally decrease with the C⋯O distance but show no clear dependence on the CH⋯O angle. These results demonstrate that the ¹³C and ¹H response to weak CH⋯O hydrogen bonding is influenced significantly by additional weak contacts within cocrystal heterodimeric units.

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.

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.

High Level Electronic Structure Calculation of Molecular Solid-State NMR Shielding Constants

In this work, we present a quantum mechanics/molecular mechanics (QM/MM) approach for the computation of solid-state nuclear magnetic resonance (SS-NMR) shielding constants (SCs) for molecular crystals. Besides applying standard-DFT functionals like GGAs (PBE), meta-GGAs (TPSS), and hybrids (B3LYP), we apply a double-hybrid (DSD-PBEP86) functional as well as MP2, using the domain-based local pair natural orbital (DLPNO) formalism, to calculate the NMR SCs of six amino acid crystals. All the electronic structure methods used exhibit good correlation of the NMR shieldings with respect to experimental chemical shifts for both ¹H and ¹³C. We also find that local electronic structure is much more important than the long-range electrostatic effects for these systems, implying that cluster approaches using all-electron/Gaussian basis set methods might offer great potential for predictive computations of solid-state NMR parameters for organic solids.

Multi-Component Crystals Containing Urea: Mechanochemical Synthesis and Characterization by 35Cl Solid-State NMR Spectroscopy and DFT Calculations

Mechanochemical synthesis provides new pathways for the rational design of multi-component crystals (MCCs) involving anionic or cationic components, which offer molecular-level architectures unavailable to MCCs comprised of strictly neutral components....

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.

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.

Quantum Mechanical-Based Stability Evaluation of Crystal Structures for HIV-Targeted Drug Cabotegravir

The long-acting parenteral formulation of the HIV integrase inhibitor cabotegravir (GSK744) is currently being developed to prevent HIV infections, benefiting from infrequent dosing and high efficacy. The crystal structure can affect the bioavailability and efficacy of cabotegravir. However, the stability determination of crystal structures of GSK744 have remained a challenge. Here, we introduced an ab initio protocol to determine the stability of the crystal structures of pharmaceutical molecules, which were obtained from crystal structure prediction process starting from the molecular diagram. Using GSK744 as a case study, the ab initio predicted that Gibbs free energy provides reliable further refinement of the predicted crystal structures and presents its capability for becoming a crystal stability determination approach in the future. The proposed work can assist in the comprehensive screening of pharmaceutical design and can provide structural predictions and stability evaluation for pharmaceutical crystals.

Overcoming Metastable CO2 Adsorption in a Bulky Diamine-Appended Metal-Organic Framework

Carbon capture at fossil fuel-fired power plants is a critical strategy to mitigate anthropogenic contributions to global warming, but widespread deployment of this technology is hindered by a lack of energy-efficient materials that can be optimized for CO2 capture from a specific flue gas. As a result of their tunable, step-shaped CO2 adsorption profiles, diamine-functionalized metal-organic frameworks (MOFs) of the form diamine-Mg2(dobpdc) (dobpdc4- = 4,4'-dioxidobiphenyl-3,3'-dicarboxylate) are among the most promising materials for carbon capture applications. Here, we present a detailed investigation of dmen-Mg2(dobpdc) (dmen = 1,2-diamino-2-methylpropane), one of only two MOFs with an adsorption step near the optimal pressure for CO2 capture from coal flue gas. While prior characterization suggested that this material only adsorbs CO2 to half capacity (0.5 CO2 per diamine) at 1 bar, we show that the half-capacity state is actually a metastable intermediate. Under appropriate conditions, the MOF adsorbs CO2 to full capacity, but conversion from the half-capacity structure happens on a very slow time scale, rendering it inaccessible in traditional adsorption measurements. Data from solid-state magic angle spinning nuclear magnetic resonance spectroscopy, coupled with van der Waals-corrected density functional theory, indicate that ammonium carbamate chains formed at half capacity and full capacity adopt opposing configurations, and the need to convert between these states likely dictates the sluggish post-half-capacity uptake. By use of the more symmetric parent framework Mg2(pc-dobpdc) (pc-dobpdc4- = 3,3'-dioxidobiphenyl-4,4'-dicarboxylate), the metastable trap can be avoided and the full CO2 capacity of dmen-Mg2(pc-dobpdc) accessed under conditions relevant for carbon capture from coal-fired power plants.

Accurate fragment-based 51-V chemical shift predictions in molecular crystals

Nuclear magnetic resonance (NMR) spectroscopy plays a crucial role in determining molecular structure for complex biological and pharmaceutical compounds. NMR investigations are increasingly reliant on computation for mapping spectral features to chemical structures. Here we benchmark the accuracy of fragment-based ⁵¹V chemical shielding tensor calculations using a training set comprised of 10 biologically and pharmaceutically relevant oxovanadium complexes. Using our self-consistent reproduction of the Madelung potential (SCRMP) electrostatic embedding model, we demonstrate comparable performance between fragment methods and computationally demanding cluster-based techniques. Specifically, fragment methods employing hybrid density functionals are capable of reproducing the experimental ⁵¹V isotropic chemical shifts with a training set rms error of ~9 ​ppm, representing a 20% improvement over traditional plane wave techniques. We provide training set-derived linear regression models for mapping the absolute shieldings obtained from computation to the experimentally determined chemical shifts using four common density functionals; PBE0, B3LYP, PBE, and BLYP. Finally, we establish the utility of fragment methods and the reported regression parameters examining four oxovanadium structures excluded from the training set including the tetracoordinate oxovanadium silicate [Formula: see text] , VO¹⁵NGlySalbz which contains redox-active ligands, and the solid-state form of the common ⁵¹V NMR reference compound VOCl₃.

Analyzing Discrepancies in Chemical-Shift Predictions of Solid Pyridinium Fumarates

Highly accurate chemical-shift predictions in molecular solids are behind the success and rapid development of NMR crystallography. However, unusually large errors of predicted hydrogen and carbon chemical shifts are sometimes reported. An understanding of these deviations is crucial for the reliability of NMR crystallography. Here, recently reported large deviations of predicted hydrogen and carbon chemical shifts of a series of solid pyridinium fumarates are thoroughly analyzed. The influence of the geometry optimization protocol and of the computational level of NMR calculations on the accuracy of predicted chemical shifts is investigated. Periodic calculations with GGA, meta-GGA and hybrid functionals are employed. Furthermore, molecular corrections at the coupled-cluster singles-and-doubles (CCSD) level are calculated. The effect of nuclear delocalization on the structure and NMR shielding is also investigated. The geometry optimization with a computationally demanding hybrid functional leads to a substantial improvement in proton chemical-shift predictions.

Understanding Correlation Between CO2 Insertion Mechanism and Chain Length of Diamine in Metal-Organic Framework Adsorbents

Although CO₂ insertion is a predominant phenomenon in diamine-functionalized Mg₂ (dobpdc) (dobpdc^4- =4,4-dioxidobiphenyl-3,3'-dicarboxylate) adsorbents, a high-performance metal-organic framework for capturing CO₂ , the fundamental function of the diamine carbon chain length in the mechanism remains unclear. Here, Mg₂ (dobpdc) systems with open metal sites grafted by primary diamines NH₂ -(CH₂ )_n -NH₂ were developed, with en (n=2), pn (n=3), bn (n=4), pen (n=5), hn (n=6), and on (n=8). Based on CO₂ adsorption and IR results, CO₂ insertion is involved in frameworks with n=2 and 3 but not in systems with n≥5. According to NMR data, bn-appended Mg₂ (dobpdc) exhibited three different chemical environments of carbamate units, attributed to different relative conformations of carbon chains upon CO₂ insertion, as validated by first-principles density functional theory (DFT) calculations. For 1-hn and 1-on, DFT calculations indicated that diamine inter-coordinated open metal sites in adjacent chains bridged by carboxylates and phenoxides of dobpdc^4- . Computed CO₂ binding enthalpies for CO₂ insertion (-27.8 kJ mol^-1 for 1-hn and -20.2 kJ mol^-1 for 1-on) were comparable to those for CO₂ physisorption (-19.3 kJ mol^-1 for 1-hn and -20.8 kJ mol^-1 for 1-on). This suggests that CO₂ insertion is likely to compete with CO₂ physisorption on diamines of the framework when n≥5.

Structure determination of an amorphous drug through large-scale NMR predictions

Knowledge of the structure of amorphous solids can direct, for example, the optimization of pharmaceutical formulations, but atomic-level structure determination in amorphous molecular solids has so far not been possible. Solid-state nuclear magnetic resonance (NMR) is among the most popular methods to characterize amorphous materials, and molecular dynamics (MD) simulations can help describe the structure of disordered materials. However, directly relating MD to NMR experiments in molecular solids has been out of reach until now because of the large size of these simulations. Here, using a machine learning model of chemical shifts, we determine the atomic-level structure of the hydrated amorphous drug AZD5718 by combining dynamic nuclear polarization-enhanced solid-state NMR experiments with predicted chemical shifts for MD simulations of large systems. From these amorphous structures we then identify H-bonding motifs and relate them to local intermolecular complex formation energies.

Automated fragmentation quantum mechanical calculation of 13C and 1H chemical shifts in molecular crystals

In this work, the automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach was applied to calculate the ¹³C and ¹H nuclear magnetic resonance (NMR) chemical shifts in molecular crystals. Two benchmark sets of molecular crystals were selected to calculate the NMR chemical shifts. Systematic investigation was conducted to examine the convergence of AF-QM/MM calculations and the impact of various density functionals with different basis sets on the NMR chemical shift prediction. The result demonstrates that the calculated NMR chemical shifts are close to convergence when the distance threshold for the QM region is larger than 3.5 Å. For ¹³C chemical shift calculations, the mPW1PW91 functional is the best density functional among the functionals chosen in this study (namely, B3LYP, B3PW91, M06-2X, M06-L, mPW1PW91, OB98, and OPBE), while the OB98 functional is more suitable for the ¹H NMR chemical shift prediction of molecular crystals. Moreover, with the B3LYP functional, at least a triple-ζ basis set should be utilized to accurately reproduce the experimental ¹³C and ¹H chemical shifts. The employment of diffuse basis functions will further improve the accuracy for ¹³C chemical shift calculations, but not for the ¹H chemical shift prediction. We further proposed a fragmentation scheme of dividing the central molecule into smaller fragments. By comparing with the results of the fragmentation scheme using the entire central molecule as the core region, the AF-QM/MM calculations with the fragmented central molecule can not only achieve accurate results but also reduce the computational cost. Therefore, the AF-QM/MM approach is capable of predicting the ¹³C and ¹H NMR chemical shifts for molecular crystals accurately and effectively, and could be utilized for dealing with more complex periodic systems such as macromolecular polymers and biomacromolecules. The AF-QM/MM program for molecular crystals is available at https://github.com/shiman1995/NMR.

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.

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.

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.

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.

Periodic DFT Calculations-Review of Applications in the Pharmaceutical Sciences

In the introduction to this review the complex chemistry of solid-state pharmaceutical compounds is summarized. It is also explained why the density functional theory (DFT) periodic calculations became recently so popular in studying the solid APIs (active pharmaceutical ingredients). Further, the most popular programs enabling DFT periodic calculations are presented and compared. Subsequently, on the large number of examples, the applications of such calculations in pharmaceutical sciences are discussed. The mentioned topics include, among others, validation of the experimentally obtained crystal structures and crystal structure prediction, insight into crystallization and solvation processes, development of new polymorph synthesis ways, and formulation techniques as well as application of the periodic DFT calculations in the drug analysis.

Selective detection of active pharmaceutical ingredients in tablet formulations using solid-state NMR spectroscopy

Atomic-level characterization of active pharmaceutical ingredients (API) is crucial in pharmaceutical industry because APIs play an important role in physicochemical properties of drug formulations. However, the analysis of targeted APIs in intact tablet formulations is less straightforward due to the coexistence of excipients as major components and different APIs at dilute concentrations (often below 10 ​wt% loading). Although solid-state (ss) NMR spectroscopy is widely used to investigate short-range order, polymorphism, and pseudo-polymorphism in neat pharmaceutical compounds, the analysis of complex drug formulations is often limited by overlapped signals that originate from structurally different APIs and excipients. In particular, such examples are frequently encountered in the analysis of ¹H ssNMR spectra of pharmaceutical formulations. While the high-resolution in ¹H ssNMR spectra can be attained by, for example, high magnetic fields accompanied by fast magic-angle spinning (MAS) approaches, the spectral complexity associated with the mixtures of compounds hinders the accurate determination of chemical shifts and through-space proximities. Here we propose a fast MAS (70 ​kHz) NMR experiment for the selective detection of ¹H signals associated with an API from a severely overlapped NMR spectrum of a tablet formulation. Spectral simplification is achieved by combining (i) symmetry-based dipolar recoupling (SR4₁²) rotational-echo saturation-pulse double-resonance (RESPDOR) with phase-modulate (PM) saturation pulses, (ii) radio frequency-driven recoupling (RFDR), and (iii) double-quantum excitation using Back-to-Back (BaBa) pulse sequence elements. First, ¹H sites in close proximities to ¹⁴N nuclei of an API are excited using a PM-S-RESPDOR sequence, and simultaneously, the other unwanted ¹H signals of excipients are suppressed. Then, ¹H magnetization transfer to adjacent ¹H sites in the API is achieved by spin diffusion process using a RFDR sequence, which polarizes to ¹H sites within the crystalline API regions of the drug formulation. Next, a PM-S-RESPDOR-RFDR sequence is combined with a Back-to-Back (BaBa) sequence to elucidate local-structures and ¹H-¹H proximities of the API in a dosage form. The PM-S-RESPDOR-RFDR-BaBa experiment is employed in one- (1D) and two-dimensional (2D) versions to selectively detect the ¹H ssNMR spectrum of l-cysteine (10.6 ​wt% or 0.11 ​mg) in a commercial formulation, and compared with the spectra of neat l-cysteine recorded using a standard BaBa experiment. The 2D ¹H double-quantum-single-quantum (DQ-SQ) spectrum of the API (l-cysteine)-detected pharmaceutical tablet is in good agreement with the 2D ¹H DQ-SQ spectrum obtained from the pure API molecule. Furthermore, the sensitivity and robustness of the experiment is examined by selectively detecting ¹H{¹⁴N} signals in an amino acid salt, l-histidine^.H₂O^.HCl.

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.

Improving Predicted Nuclear Magnetic Resonance Chemical Shifts Using the Quasi-Harmonic Approximation

Ab initio nuclear magnetic resonance chemical shift prediction plays an important role in the determination or validation of crystal structures. The ability to predict chemical shifts more accurately can translate to increased confidence in the resulting chemical shift or structural assignments. Standard electronic structure predictions for molecular crystal structures neglect thermal expansion, which can lead to an appreciable underestimation of the molar volumes. This study examines this volume error and its impact on 68 ¹³C- and 28 ¹⁵N-predicted chemical shifts taken from 20 molecular crystals. It assesses the ability to recover more realistic room-temperature crystal structures using the quasi-harmonic approximation and how refining the structures impacts the chemical shifts. Several pharmaceutical molecular crystals are also examined in more detail. On the whole, accounting for quasi-harmonic expansion changes the ¹³C and ¹⁵N chemical shifts by 0.5 and 1.0 ppm on average. This, in turn, reduces the root-mean-square errors relative to experiment by 0.3 ppm for ¹³C and 0.7 ppm for ¹⁵N. Although the statistical impacts are modest, changes in individual chemical shifts can reach multiple ppm. Accounting for thermal expansion in molecular crystal chemical shift prediction may not be needed routinely, but the systematic trend toward improved accuracy with the experiment could be useful in cases where discrimination between structural candidates is challenging, as in the pharmaceutical theophylline.

Multiresolution 3D-DenseNet for Chemical Shift Prediction in NMR Crystallography

We have developed a deep learning algorithm for chemical shift prediction for atoms in molecular crystals that utilizes an atom-centered Gaussian density model for the 3D data representation of a molecule. We define multiple channels that describe different spatial resolutions for each atom type that utilizes cropping, pooling, and concatenation to create a multiresolution 3D-DenseNet architecture (MR-3D-DenseNet). Because the training and testing time scale linearly with the number of samples, the MR-3D-DenseNet can exploit data augmentation that takes into account the property of rotational invariance of the chemical shifts, thereby also increasing the size of the training data set by an order of magnitude without additional cost. We obtain very good agreement for ¹³C, ¹⁵N, and ¹⁷O chemical shifts when compared to ab initio quantum chemistry methods, with the highest accuracy found for ¹H chemical shifts that is comparable to the error between the ab initio results and experimental measurements. Principal component analysis (PCA) is used to both understand these greatly improved predictions for ¹H , as well as indicating that chemical shift prediction for ¹³C, ¹⁵N, and ¹⁷O, which have far fewer training environments than the ¹H atom type, will improve once more unique training samples are made available to exploit the deep network architecture.

Water Enables Efficient CO2 Capture from Natural Gas Flue Emissions in an Oxidation-Resistant Diamine-Appended Metal-Organic Framework

Supported by increasingly available reserves, natural gas is achieving greater adoption as a cleaner-burning alternative to coal in the power sector. As a result, carbon capture and sequestration from natural gas-fired power plants is an attractive strategy to mitigate global anthropogenic CO₂ emissions. However, the separation of CO₂ from other components in the flue streams of gas-fired power plants is particularly challenging due to the low CO₂ partial pressure (∼40 mbar), which necessitates that candidate separation materials bind CO₂ strongly at low partial pressures (≤4 mbar) to capture ≥90% of the emitted CO₂. High partial pressures of O₂ (120 mbar) and water (80 mbar) in these flue streams have also presented significant barriers to the deployment of new technologies for CO₂ capture from gas-fired power plants. Here, we demonstrate that functionalization of the metal-organic framework Mg₂(dobpdc) (dobpdc^4- = 4,4'-dioxidobiphenyl-3,3'-dicarboxylate) with the cyclic diamine 2-(aminomethyl)piperidine (2-ampd) produces an adsorbent that is capable of ≥90% CO₂ capture from a humid natural gas flue emission stream, as confirmed by breakthrough measurements. This material captures CO₂ by a cooperative mechanism that enables access to a large CO₂ cycling capacity with a small temperature swing (2.4 mmol CO₂/g with ΔT = 100 °C). Significantly, multicomponent adsorption experiments, infrared spectroscopy, magic angle spinning solid-state NMR spectroscopy, and van der Waals-corrected density functional theory studies suggest that water enhances CO₂ capture in 2-ampd-Mg₂(dobpdc) through hydrogen-bonding interactions with the carbamate groups of the ammonium carbamate chains formed upon CO₂ adsorption, thereby increasing the thermodynamic driving force for CO₂ binding. In light of the exceptional thermal and oxidative stability of 2-ampd-Mg₂(dobpdc), its high CO₂ adsorption capacity, and its high CO₂ capture rate from a simulated natural gas flue emission stream, this material is one of the most promising adsorbents to date for this important separation.

Understanding hydrogen-bonding structures of molecular crystals via electron and NMR nanocrystallography

Understanding hydrogen-bonding networks in nanocrystals and microcrystals that are too small for X-ray diffractometry is a challenge. Although electron diffraction (ED) or electron 3D crystallography are applicable to determining the structures of such nanocrystals owing to their strong scattering power, these techniques still lead to ambiguities in the hydrogen atom positions and misassignments of atoms with similar atomic numbers such as carbon, nitrogen, and oxygen. Here, we propose a technique combining ED, solid-state NMR (SSNMR), and first-principles quantum calculations to overcome these limitations. The rotational ED method is first used to determine the positions of the non-hydrogen atoms, and SSNMR is then applied to ascertain the hydrogen atom positions and assign the carbon, nitrogen, and oxygen atoms via the NMR signals for ¹H, ¹³C, ¹⁴N, and ¹⁵N with the aid of quantum computations. This approach elucidates the hydrogen-bonding networks in l-histidine and cimetidine form B whose structure was previously unknown.

Electron diffraction can be used to determine nanocrystal structures, but is unsuitable for locating hydrogen atoms. Here the authors combine electron diffraction, solid-state NMR and first-principles calculations to resolve the crystal structures and hydrogen-bonding networks of L-histidine and cimetidine form B.

Line narrowing in 1H NMR of powdered organic solids with TOP-CT-MAS experiments at ultra-fast MAS

The residual broadening observed in ¹H spectra of rigid organic solids at natural abundance under 111 kHz magic angle spinning (MAS) is typically a few hundred Hertz. Here we show that refocusable and non-refocusable interactions contribute roughly equally to this residual at high-fields (21.14 T), and suggest that the removal of the non-refocusable part will produce significant increase in spectral resolution. To this end, we demonstrate an experiment for the indirect acquisition of constant-time experiments at ultra-fast MAS (CT-MAS) which verifies this hypothesis. The combination of this experiment with the two-dimensional one pulse (TOP) transformation reduces the experimental time to a fraction of the original cost while retaining the narrowing effects. Results obtained with TOP-CT-MAS at 111 kHz MAS on a sample of β-AspAla yield up to 30% higher resolution spectra than the equivalent one-pulse experiment, in less than 10 min.

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.

Reducing the computational cost of NMR crystallography of organic powders at natural isotopic abundance with the help of 13 C-13 C dipolar couplings

Structure determination of functional organic compounds remains a formidable challenge when the sample exists as a powder. Nuclear magnetic resonance crystallography approaches based on the comparison of experimental and Density Functional Theory (DFT)-computed ¹ H chemical shifts have already demonstrated great potential for structure determination of organic powders, but limitations still persist. In this study, we discuss the possibility of using ¹³ C-¹³ C dipolar couplings quantified on powdered theophylline at natural isotopic abundance with the help of dynamic nuclear polarization, to realize a DFT-free, rapid screening of a pool of structures predicted by ab initio random structure search. We show that although ¹³ C-¹³ C dipolar couplings can identify structures possessing long range structural motifs and unit cell parameters close to those of the true structure, it must be complemented with other data to recover information about the presence and the chemical nature of the supramolecular interactions.

An NMR crystallography investigation of furosemide

This paper presents an NMR crystallography study of three polymorphs of furosemide. Experimental magic-angle spinning (MAS) solid-state NMR spectra are reported for form I of furosemide, and these are assigned using density-functional theory (DFT)-based gauge-including projector augmented wave (GIPAW) calculations. Focusing on the three known polymorphs, we examine the changes to the NMR parameters due to crystal packing effects. We use a recently developed formalism to visualise which regions are responsible for the chemical shielding of particular sites and hence understand the variation in NMR parameters between the three polymorphs.