Validation of experimental molecular crystal structures with dispersion-corrected density functional theory calculations

Development of an anisotropic polarizable model for the all-atom AMOEBA force field

For planar and rigid π-conjugated molecular systems, electrostatic and inductive interactions are pivotal in governing molecular packing structures and electron polarization energies. These electrostatic interactions typically exhibit an anisotropic nature within π-conjugated systems. In this study, we utilize the atoms in molecules (AIM) theory in conjunction with linear response theory to decompose molecular polarizability into distributed atomic polarizability tensors. On the basis of atomic polarizability tensors, we extended an anisotropic polarizable model into the AMOEBA polarizable force field. Both anisotropic and isotropic polarizable models in combination with various density functional theory (DFT)-derived atomic multipoles were applied to optimize the experimental crystals of naphthalene and anthracene. Furthermore, these two types of electrostatic models, coupled with the evolutionary algorithm USPEX program, are utilized to predict the crystal structures of oligoacenes. Our findings demonstrate that the anisotropic polarizable model exhibits superior performance in crystal refinement and crystal structure prediction. This enriched anisotropic polarizable model is seamlessly integrated into the AMOEBA polarizable force field and readily applicable within our modified Tinker program.

Linking solid-state phenomena via energy differences in `archetype crystal structures'

Categorization underlies understanding. Conceptualizing solid-state structures of organic molecules with `archetype crystal structures' bridges established categories of disorder, polymorphism and solid solutions and is herein extended to special position and high-Z' structures. The concept was developed in the context of disorder modelling [Dittrich, B. (2021). IUCrJ, 8, 305-318] and relies on adding quantum chemical energy differences between disorder components to other criteria as an explanation as to why disorder - and disappearing disorder - occurs in an average structure. Part of the concept is that disorder, as probed by diffraction, affects entire molecules, rather than just the parts of a molecule with differing conformations, and the finding that an R·T energy difference between disorder archetypes is usually not exceeded. An illustrative example combining disorder and special positions is the crystal structure of oestradiol hemihydrate analysed here, where its space-group/subgroup relationship is required to explain its disorder of hydrogen-bonded hydrogen atoms. In addition, we show how high-Z' structures can also be analysed energetically and understood via archetypes: high-Z' structures occur when an energy gain from combining different rather than overall alike conformations in a crystal significantly exceeds R·T, and this finding is discussed in the context of earlier explanations in the literature. Twinning is not related to archetype structures since it involves macroscopic domains of the same crystal structure. Archetype crystal structures are distinguished from crystal structure prediction trial structures in that an experimental reference structure is required for them. Categorization into archetype structures also has practical relevance, leading to a new practice of disorder modelling in experimental least-squares refinement alluded to in the above-mentioned publication.

High Temperature Electron Diffraction on Organic Crystals: In Situ Crystal Structure Determination of Pigment Orange 34

Small molecule structures and their applications rely on good knowledge of their atomic arrangements. However, the crystal structures of these compounds and materials, which are often composed of fine crystalline domains, cannot be determined with single-crystal X-ray diffraction. Three-dimensional electron diffraction (3D ED) is already becoming a reliable method for the structure analysis of submicrometer-sized organic materials. The reduction of electron beam damage is essential for successful structure determination and often prevents the analysis of organic materials at room temperature, not to mention high temperature studies. In this work, we apply advanced 3D ED methods at different temperatures enabling the accurate structure determination of two phases of Pigment Orange 34 (C34H28N8O2Cl2), a biphenyl pyrazolone pigment that has been industrially produced for more than 80 years and used for plastics application. The crystal structure of the high-temperature phase, which can be formed during plastic coloration, was determined at 220 °C. For the first time, we were able to observe a reversible phase transition in an industrial organic pigment in the solid state, even with atomic resolution, despite crystallites being submicrometer in size. By localizing hydrogen atoms, we were even able to detect the tautomeric state of the molecules at different temperatures. This demonstrates that precise, fast, and low-dose 3D ED measurements enable high-temperature studies the door for general in situ studies of nanocrystalline materials at the atomic level.

Synthesis and Characterization of Two Novel Naphthalenediimide/Zinc Phosphonate Crystalline Materials Precipitated from Different Solvents

Hybrid naphthalenediimide/zinc phosphonate materials (NDI/Zn) were prepared by mixing solutions of N,N'-bis(2-phosphonoethyl)-1,4,5,8-naphthalenediimide (PNDI) and zinc nitrate, resulting in the precipitation of the desired compounds. Samples precipitated from water and N,N-dimethylformamide (DMF) were produced. The obtained samples had the expected elemental composition, and the presence of naphthalenediimides (NDI) was ascertained by infrared and UV-visible spectroscopy. All the samples were crystalline, according to powder X-ray diffraction. Nitrogen adsorption isotherms showed the presence of porosity in the NDI/Zn samples. Mesopores with a diameter = 4.1 nm were present in the sample from DMF, with total pore volume reaching 0.13 cm3/g.

The structure of magnesium stearate trihydrate determined from a micrometre-sized single crystal using a microfocused synchrotron X-ray beam

Crystalline magnesium stearate has been extensively used as an additive in pharmaceutical and other industries for decades. However, the lack of suitably large crystals has hindered the determination of the crystal structure and thereby a more fundamental understanding of the structure-functionality relationship. Presented here is the structure of magnesium stearate trihydrate as determined from X-ray diffraction data of a micrometre-sized single crystal measured at a fourth-generation synchrotron facility. Despite the small size of the single crystals and the weak diffraction, it was possible to determine the positions of the non-hydrogen atoms reliably. Periodic dispersion-corrected density functional theory calculations were used to obtain the positions of the hydrogen atoms playing an important role in the overall organization of the structure via a hydrogen-bond network.

DFT–Assisted Structure Determination from Powder X-ray Diffraction Data of a New Zonisamide/ϵ-Caprolactam Cocrystal

The crystal structure of a new zonisamide cocrystal, an anticonvulsant drug used to treat the symptoms of epilepsy and Parkinson’s disease, with ϵ-caprolactam is reported herein. The structure has been solved by direct space methodologies from powder X-ray diffraction data. The refinement of the structure was conducted by the Rietveld method assisted by the dispersion-corrected density-functional theory (D-DFT) calculations and periodic boundary conditions. Further analysis of the structure reveals several H-bonded synthons and self–assembled dimers that have been further analyzed by DFT calculations and other computational tools such as molecular electrostatic potential (MEP) surfaces and the quantum theory of “atom-in-molecules” (QTAIM).

Ambiguous structure determination from powder data: four different structural models of 4,11-di-fluoro-quinacridone with similar X-ray powder patterns, fit to the PDF, SSNMR and DFT-D

Four different structural models, which all fit the same X-ray powder pattern, were obtained in the structure determination of 4,11-di-fluoro-quinacridone (C20H10N2O2F2) from unindexed X-ray powder data by a global fit. The models differ in their lattice parameters, space groups, Z, Z', molecular packing and hydrogen bond patterns. The molecules form a criss-cross pattern in models A and B, a layer structure built from chains in model C and a criss-cross arrangement of dimers in model D. Nevertheless, all models give a good Rietveld fit to the experimental powder pattern with acceptable R-values. All molecular geometries are reliable, except for model D, which is slightly distorted. All structures are crystallochemically plausible, concerning density, hydrogen bonds, intermolecular distances etc. All models passed the checkCIF test without major problems; only in model A a missed symmetry was detected. All structures could have probably been published, although 3 of the 4 structures were wrong. The investigation, which of the four structures is actually the correct one, was challenging. Six methods were used: (1) Rietveld refinements, (2) fit of the crystal structures to the pair distribution function (PDF) including the refinement of lattice parameters and atomic coordinates, (3) evaluation of the colour, (4) lattice-energy minimizations with force fields, (5) lattice-energy minimizations by two dispersion-corrected density functional theory methods, and (6) multinuclear CPMAS solid-state NMR spectroscopy (1H, 13C, 19F) including the comparison of calculated and experimental chemical shifts. All in all, model B (perhaps with some disorder) can probably be considered to be the correct one. This work shows that a structure determination from limited-quality powder data may result in totally different structural models, which all may be correct or wrong, even if they are chemically sensible and give a good Rietveld refinement. Additionally, the work is an excellent example that the refinement of an organic crystal structure can be successfully performed by a fit to the PDF, and the combination of computed and experimental solid-state NMR chemical shifts can provide further information for the selection of the most reliable structure among several possibilities.

Solving molecular compounds from powder diffraction data: are results always reliable?

Commentary is given on a paper [Schlesinger et al. (2022). IUCrJ, 9, 406-424.] reporting on ambiguous structure determination from powder data using four different structural models of 4,11-difluoroquinacridone with similar X-ray powder patterns.

A structure determination protocol based on combined analysis of 3D-ED data, powder XRD data, solid-state NMR data and DFT-D calculations reveals the structure of a new polymorph of l-tyrosine

We report the crystal structure of a new polymorph of l-tyrosine (denoted the β polymorph), prepared by crystallization from the gas phase following vacuum sublimation. Structure determination was carried out by combined analysis of three-dimensional electron diffraction (3D-ED) data and powder X-ray diffraction (XRD) data. Specifically, 3D-ED data were required for reliable unit cell determination and space group assignment, with structure solution carried out independently from both 3D-ED data and powder XRD data, using the direct-space strategy for structure solution implemented using a genetic algorithm. Structure refinement was carried out both from powder XRD data, using the Rietveld profile refinement technique, and from 3D-ED data. The final refined structure was validated both by periodic DFT-D calculations, which confirm that the structure corresponds to an energy minimum on the energy landscape, and by the fact that the values of isotropic 13C NMR chemical shifts calculated for the crystal structure using DFT-D methodology are in good agreement with the experimental high-resolution solid-state 13C NMR spectrum. Based on DFT-D calculations using the PBE0-MBD method, the β polymorph is meta-stable with respect to the previously reported crystal structure of l-tyrosine (now denoted the α polymorph). Crystal structure prediction calculations using the AIRSS approach suggest that there are three other plausible crystalline polymorphs of l-tyrosine, with higher energy than the α and β polymorphs.

Structure determination from unindexed powder data from scratch by a global optimization approach using pattern comparison based on cross-correlation functions

A method of ab initio crystal structure determination from powder diffraction data for organic and metal-organic compounds, which does not require prior indexing of the powder pattern, has been developed. Only a reasonable molecular geometry is required, needing knowledge of neither unit-cell parameters nor space group. The structures are solved from scratch by a global fit to the powder data using the new program FIDEL-GO (`FIt with DEviating Lattice parameters - Global Optimization'). FIDEL-GO uses a similarity measure based on cross-correlation functions, which allows the comparison of simulated and experimental powder data even if the unit-cell parameters deviate strongly. The optimization starts from large sets of random structures in various space groups. The unit-cell parameters, molecular position and orientation, and selected internal degrees of freedom are fitted simultaneously to the powder pattern. The optimization proceeds in an elaborate multi-step procedure with built-in clustering of duplicate structures and iterative adaptation of parameter ranges. The best structures are selected for an automatic Rietveld refinement. Finally, a user-controlled Rietveld refinement is performed. The procedure aims for the analysis of a wide range of `problematic' powder patterns, in particular powders of low crystallinity. The method can also be used for the clustering and screening of a large number of possible structure candidates and other application scenarios. Examples are presented for structure determination from unindexed powder data of the previously unknown structures of the nanocrystalline phases of 4,11-difluoro-, 2,9-dichloro- and 2,9-dichloro-6,13-dihydro-quinacridone, which were solved from powder patterns with 14-20 peaks only, and of the coordination polymer dichloro-bis(pyridine-N)copper(II).

SDPD-SX: Combining a single crystal X-ray diffraction setup with advanced powder data structure determination for use in early stage drug discovery

We report a method for routine crystal structure determination on very small (typically 0.1 mg or less) amounts of crystalline material using powder X-ray diffraction data from a laboratory-based single-crystal...

The extensive solid-form landscape of sulfathiazole: geometrical similarity and interaction energies

Sulfathiazole shows one of the most extensive solid-form landscapes known to date for an active pharmaceutical ingredient. A standardised structure set of 5 polymorphs, 59 co-crystals, 29 salts, and 3 other structures is established.

Psilocybin: crystal structure solutions enable phase analysis of prior art and recently patented examples

Psilocybin {systematic name: 3-[2-(dimethylamino)ethyl]-1H-indol-4-yl dihydrogen phosphate} is a zwitterionic tryptamine natural product found in numerous species of fungi known for their psychoactive properties. Following its structural elucidation and chemical synthesis in 1959, purified synthetic psilocybin has been evaluated in clinical trials and has shown promise in the treatment of various mental health disorders. In a recent process-scale crystallization investigation, three crystalline forms of psilocybin were repeatedly observed: Hydrate A, Polymorph A, and Polymorph B. The crystal structure for Hydrate A was solved previously by single-crystal X-ray diffraction. This article presents new crystal structure solutions for the two anhydrates, Polymorphs A and B, based on Rietveld refinement using laboratory and synchrotron X-ray diffraction data, and density functional theory (DFT) calculations. Utilizing the three solved structures, an investigation was conducted via Rietveld method (RM) based quantitative phase analysis (QPA) to estimate the contribution of the three different forms in powder X-ray diffraction (PXRD) patterns provided by different sources of bulk psilocybin produced between 1963 and 2021. Over the last 57 years, each of these samples quantitatively reflect one or more of the hydrate and anhydrate polymorphs. In addition to quantitatively evaluating the composition of each sample, this article evaluates correlations between the crystal forms present, corresponding process methods, sample age, and storage conditions. Furthermore, revision is recommended on characterizations in recently granted patents that include descriptions of crystalline psilocybin inappropriately reported as a single-phase `isostructural variant.' Rietveld refinement demonstrated that the claimed material was composed of approximately 81% Polymorph A and 19% Polymorph B, both of which have been identified in historical samples. In this article, we show conclusively that all published data can be explained in terms of three well-defined forms of psilocybin and that no additional forms are needed to explain the diffraction patterns.

The structure of methanol at 5.09 GPa: the fortuitous formation of a new high-pressure phase

The crystal structure of a new polymorph of methanol (the ε polymorph) has been determined at 5.09 GPa by single crystal X-ray diffraction.

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.

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.

Structure determination of organic compounds by a fit to the pair distribution function from scratch without prior indexing

A method for the ab initio crystal structure determination of organic compounds by a fit to the pair distribution function (PDF), without prior knowledge of lattice parameters and space group, has been developed. The method is called 'PDF-Global-Fit' and is implemented by extension of the program FIDEL (fit with deviating lattice parameters). The structure solution is based on a global optimization approach starting from random structural models in selected space groups. No prior indexing of the powder data is needed. The new method requires only the molecular geometry and a carefully determined PDF. The generated random structures are compared with the experimental PDF and ranked by a similarity measure based on cross-correlation functions. The most promising structure candidates are fitted to the experimental PDF data using a restricted simulated annealing structure solution approach within the program TOPAS, followed by a structure refinement against the PDF to identify the correct crystal structure. With the PDF-Global-Fit it is possible to determine the local structure of crystalline and disordered organic materials, as well as to determine the local structure of unindexable powder patterns, such as nanocrystalline samples, by a fit to the PDF. The success of the method is demonstrated using barbituric acid as an example. The crystal structure of barbituric acid form IV solved and refined by the PDF-Global-Fit is in excellent agreement with the published crystal structure data.

Comparison and evaluation of pair distribution functions, using a similarity measure based on cross-correlation functions

An approach for the comparison of pair distribution functions (PDFs) has been developed using a similarity measure based on cross-correlation functions. The PDF is very sensitive to changes in the local structure, i.e. small deviations in the structure can cause large signal shifts and significant discrepancies between the PDFs. Therefore, a comparison based on pointwise differences (e.g. R values and difference curves) may lead to the assumption that the investigated PDFs as well as the corresponding structural models are not in agreement at all, whereas a careful visual inspection of the investigated structural models and corresponding PDFs may reveal a relatively good match. To quantify the agreement of different PDFs for those cases an alternative approach is introduced: the similarity measure based on cross-correlation functions. In this paper, the power of this application of the similarity measure to the analysis of PDFs is highlighted. The similarity measure is compared with the classical R wp values as representative of the comparison based on pointwise differences as well as with the Pearson product-moment correlation coefficient, using polymorph IV of barbituric acid as an example.

On modelling disordered crystal structures through restraints from molecule-in-cluster computations, and distinguishing static and dynamic disorder

Distinguishing disorder into static and dynamic based on multi-temperature X-ray or neutron diffraction experiments is the current state of the art, but is only descriptive, not predictive. Here, several disordered structures are revisited from the Cambridge Crystallographic Data Center 'drug subset', the Cambridge Structural Database and own earlier work, where experimental intensities of Bragg diffraction data were available. Using the molecule-in-cluster approach, structures with distinguishable conformations were optimized separately, as extracted from available or generated disorder models of the respective disordered crystal structures. Re-combining these 'archetype structures' by restraining positional and constraining displacement parameters for conventional least-squares refinement, based on the optimized geometries, then often achieves a superior fit to the experimental diffraction data compared with relying on experimental information alone. It also simplifies and standardizes disorder refinement. Ten example structures were analysed. It is observed that energy differences between separate disorder conformations are usually within a small energy window of RT (T = crystallization temperature). Further computations classify disorder into static or dynamic, using single experiments performed at one single temperature, and this was achieved for propionamide.

GALLOP: accelerated molecular crystal structure determination from powder diffraction data

A new GPU-accelerated algorithm delivers state-of-the-art performance for molecular crystal structure determination from powder diffraction data.

Hydrogen bonding from crystalline water mediates the hydration/dehydration of mequitazine glycolate

Comparison of crystal structures, dynamic vapor adsorption measurements, lattice energy calculations and structural optimization of the dehydration model were used to evaluate the hydration-dehydration behavior.

Density functional theory predictions of the mechanical properties of crystalline materials

The DFT-predicted mechanical properties of crystalline materials are crucial knowledge for their screening, design, and exploitation.

Rhenium versus cadmium: an alternative structure for a thermally stable cadmium carbonyl compound

An alternative description is provided for the previously reported novel tetranuclear cadmium carbonyl compound, [Cd(CO)3(C6H3Cl)]4. Specifically, consideration of single crystal X-ray diffraction data indicates that the compound is better formulated as the rhenium compound, [Re(CO)3(C4N2H3S)]4. Furthermore, density functional theory calculations predict that, if it were to exist, [Cd(CO)3(C6H3Cl)]4 would have a very different structure to that reported. While it is well known that X-ray diffraction may not reliably distinguish between atoms of similar atomic number (e.g. N/C and Cl/S), it is not generally recognized that two atoms with very different atomic numbers could be misassigned. The misidentification of two elements as diverse as Re and Cd (ΔZ = 27) is unexpected and serves as an important caveat for structure determinations.

Intermolecular interactions and disorder in six isostructural celecoxib solvates

Six isostructural crystalline solvates of the active pharmaceutical ingredient celecoxib {4-[5-(4-methylphenyl)-3-(trifluoromethyl)pyrazol-1-yl]benzenesulfonamide; C17H14F3N3O2S} are described, containing dimethylformamide (DMF, C3H7NO, 1), dimethylacetamide (DMA, C4H9NO, 2), N-methylpyrrolidin-2-one (NMP, C5H9NO, 3), tetramethylurea (TMU, C5H12N2O, 4), 1,3-dimethyl-3,4,5,6-tetrahydropyrimidin-2(1H)-one (DMPU, C6H12N2O, 5) or dimethyl sulfoxide (DMSO, C2H6OS, 6). The host celecoxib structure contains one-dimensional channel voids accommodating the solvent molecules, which accept hydrogen bonds from the NH2 groups of two celecoxib molecules. The solvent binding sites have local twofold rotation symmetry, which is consistent with the point symmetry of the solvent molecule in 4 and 5, but introduces orientational disorder for the solvent molecules in 1, 2, 3 and 6. Despite the isostructurality of 1-6, the unit-cell volume and solvent-accessible void space show significant variation. In particular, 4 and 5 show an enlarged and skewed unit cell, which can be attributed to a specific interaction between an N-CH3 group in the solvent molecule and the toluene group of celecoxib. Intermolecular interaction energies calculated using the PIXEL method show that the total interaction energy between the celecoxib and solvent molecules is broadly correlated with the molecular volume of the solvent, except in 6, where the increased polarity of the S=O bond leads to greater overall stabilization compared to the similarly-sized DMF molecule in 1. In the structures showing disorder, the most stable orientations of the solvent molecules make C-H...O contacts to the S=O groups of celecoxib.

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.

Resolving alternative organic crystal structures using density functional theory and NMR chemical shifts

Alternative (‘repeat’) determinations of organic crystal structures deposited in the Cambridge Structural Database are analysed to characterise the nature and magnitude of the differences between structure solutions obtained by diffraction methods. Of the 3132 structure pairs considered, over 20% exhibited local structural differences exceeding 0.25 Å. In most cases (about 83%), structural optimisation using density functional theory (DFT) resolved the differences. Many of the cases where distinct and chemically significant structural differences remained after optimisation involved differently positioned hydroxyl groups, with obvious implications for the correct description of hydrogen bonding. ¹H and ¹³C chemical shifts from solid-state NMR experiments are proposed as an independent methodology in cases where DFT optimisation fails to resolve discrepancies.

DFT optimisation often resolves conflicting crystal structure determinations, with NMR shifts helping in cases where optimisation diverges to different structures.

Calculation of Diamagnetic Susceptibility Tensors of Organic Crystals: From Coronene to Pharmaceutical Polymorphs

Understanding why crystallization in strong magnetic fields can lead to new polymorphs requires methods to calculate the diamagnetic response of organic molecular crystals. We develop the calculation of the macroscopic diamagnetic susceptibility tensor, χ^cryst, for organic molecular crystals using periodic density functional methods. The crystal magnetic susceptibility tensor, χ^cryst, for all experimentally known polymorphs, and its molecular counterpart, χ^mol, are calculated for flexible pharmaceuticals such as carbamazepine, flufenamic acid, and chalcones, and rigid molecules, such as benzene, pyridine, acridine, anthracene, and coronene, whose molecular magnetic properties have been traditionally studied. A tensor addition method is developed to approximate the crystal diamagnetic susceptibility tensor, χ^cryst, from the molecular one, χ^mol, giving good agreement with those calculated directly using the more costly periodic density functional method for χ^cryst. The response of pharmaceutical molecules and crystals to magnetic fields, as embodied by χ^cryst, is largely determined by the packing in the crystal, as well as the molecular conformation. The anisotropy of χ^cryst can vary considerably between polymorphs though the isotropic terms are fairly constant. The implications for developing a computational method for predicting whether crystallization in a magnetic field could produce a novel or different polymorph are discussed.

Fast energy minimization of the CCDC drug-subset structures by molecule-in-cluster computations allows independent structure validation and model completion

Optimizing structures with computations on clusters of molecules permits generation of structure-specific restraints for refinement and structure validation.

A new crystalline form of αβ-D-lactose prepared by oven drying a concentrated aqueous solution of D-lactose

A new crystalline form of αβ-D-lactose (C₁₂H₂₂O₁₁) has been prepared by the rapid drying of an approximately 40% w/v syrup of D-lactose. Initially identified from its novel powder X-ray diffraction pattern, the monoclinic crystal structure was solved from a microcrystal recovered from the generally polycrystalline mixed-phase residue obtained at the end of the drying step. This is the second crystalline form of αβ-D-lactose to be identified and it has a high degree of structural three-dimensional similarity to the previously identified triclinic form.

Machine-Learned Fragment-Based Energies for Crystal Structure Prediction

Crystal structure prediction involves a search of a complex configurational space for local minima corresponding to stable crystal structures, which can be performed efficiently using atom-atom force fields for the assessment of intermolecular interactions. However, for challenging systems, the limitations in the accuracy of force fields prevent a reliable assessment of the relative thermodynamic stability of potential structures, while the cost of fully quantum mechanical approaches can limit applications of the methods. We present a method to rapidly improve force field lattice energies by correcting two-body interactions with a higher level of theory in a fragment-based approach and predicting these corrections with machine learning. Corrected lattice energies with commonly used density functionals and second order perturbation theory (MP2) all significantly improve the ranking of experimentally known polymorphs where the rigid molecule model is applicable. The relative lattice energies of known polymorphs are also found to systematically improve with the fragment corrections. Predicting two-body interactions with atom-centered symmetry functions in a Gaussian process is found to give highly accurate results using as little as 10-20% of the data for training, reducing the cost of the energy correction by up to an order of magnitude. The machine learning approach opens up the possibility of more widespread use of fragment-based methods in crystal structure prediction, whose increased accuracy at a low computational cost will benefit applications in areas such as polymorph screening and computer-guided materials discovery.

Electron diffraction tomography and X-ray powder diffraction on photoredox catalyst PDI

The crystal structure of photoredox catalyst PDI-iPr was determined by a combination of electron diffraction tomography and XRPD.

Accuracy and reproducibility in crystal structure prediction: the curious case of ROY

Because of excessive electron delocalization, the polymorphs of ROY constitute a surprisingly challenging system for crystal structure prediction.

Four interpenetrating hydrogen-bonded three-dimensional networks in divanillin

The crystal structure of divainillin (systematic name: 6,6'-dihydroxy-5,5'-dimethoxy-[1,1'-biphenyl]-3,3'-dicarbaldehyde), C₁₆H₁₄O₆, was determined from laboratory powder X-ray diffraction data using the software EXPO2013 (direct methods) and WinPSSP (direct-space approach). Divanillin molecules crystallize in the orthorhombic space group Pba2 (No. 32), with two molecules per unit cell (Z' = 1/2). Each divanillin molecule, with twofold symmetry, is linked through strong alcohol-aldehyde hydrogen bonds to four equivalent molecules, defining a three-dimensional hydrogen-bonding network, with rings made up of six divanillin units (a diamond-like arrangement). Each molecule is also connected through π-π interactions to a translation-equivalent molecule along c. Four consecutive molecules stacked along [001] belong to four different three-dimensional hydrogen-bonding networks defining a quadruple array of interpenetrating networks. This complex hydrogen-bonding array is proposed as an explanation for the aging process experienced by divanillin powders.

Synthesis, structural and antimicrobial studies of binary and ternary complexes of a new tridentate thiosemicarbazone

A new thiosemicarbazone ligand was synthesized and characterized using spectroscopic techniques (UV-Vis and IR) and synchrotron x-ray powder diffraction. With M²⁺ = Mn²⁺, Zn²⁺ and Cd²⁺, coordination compounds of the type (M[L]₂) were isolated. In the presence of sodium dithiocarbamate salts (NadiEtdtc.3H₂O = sodium diethyldithiocarbamate trihydrate and Napipdtc = sodium piperidinedithiocarbamate), Zn²⁺ and Cd²⁺ were able to form ternary octahedral complexes where each metal binds a deprotonated (thiosemicarbazone) ligand, a monobasic dithiocarbamate ligand and a water molecule. In vitro biological evaluation tests of the free HL ligand and its metal complexes against selected fungal and bacterial cultures were performed. Compared with HL, the complexes displayed enhanced biological activities and ternary Zn (II) complexes displayed comparable antibacterial activities to the chloramphenicol standard.

Pervasive Delocalisation Error Causes Spurious Proton Transfer in Organic Acid-Base Co-Crystals

Dispersion-corrected density-functional theory (DFT-D) methods have become the workhorse of many computational protocols for molecular crystal structure prediction due to their efficiency and convenience. However, certain limitations of DFT, such as delocalisation error, are often overlooked or are too expensive to remedy in solid-state applications. This error can lead to artificial stabilisation of charge transfer and, in this work, it is found to affect the correct identification of the protonation site in multicomponent acid-base crystals. As such, commonly used DFT-D methods cannot be applied with any reliability to the study of acid-base co-crystals or salts, while hybrid functionals remain too restrictive for routine use. This presents an impetus for the development of new functionals with reduced delocalisation error for solid-state applications; the structures studied herein constitute an excellent benchmark for this purpose.

Azulene revisited: solid-state structure, invariom modeling and lattice-energy minimization of a classical example of disorder

The molecular and solid-state structure of azulene both raise fundamental questions. Therefore, the disordered crystal structure of azulene was re-refined with invariom non-spherical atomic scattering factors from new single-crystal X-ray diffraction data with a resolution of d = 0.45 Å. An unconstrained refinement results in a molecular geometry with C s symmetry. Refinements constrained to fulfill C 2v symmetry, as observed in the gas phase and in high-level ab initio calculations, lead to similar figures of merit and residual densities as unconstrained ones. Such models are consistent with the structures from microwave spectroscopy and electron diffraction, albeit they are not the same. It is shown that for the disorder present in azulene, the invariom model describes valence electron density as successfully as it does for non-disordered structures, although the disorder still leads to high correlations mainly between positional parameters. Lattice-energy minimizations on a variety of ordered model structures using dispersion-corrected DFT calculations reveal that the local deviations from the average structure are small. Despite the molecular dipole moment there is no significant molecular ordering in any spatial direction. A superposition of all ordered model structures leads to a calculated average structure, which explains not only the experimental determined atomic coordinates, but also the apparently unusual experimental anisotropic displacement parameters.

A terahertz study of taurine: Dispersion correction and mode couplings

The low-frequency characteristics of polycrystalline taurine were studied experimentally by terahertz (THz) absorption spectroscopy and theoretically by ab initio density-functional simulations. Full optimizations with semi-empirical dispersion correction were performed in spectral computations and vibrational mode assignments. For comparison, partial optimizations with pure density functional theory were conducted in parallel. Results indicate that adding long-range dispersion correction to the standard DFT better reproduces the measured THz spectra than the popular partial optimizations. The main origins of the observed absorption features were also identified. Moreover, a coupled-oscillators model was proposed to explain the experimental observation of the unusual spectralblue-shift with the increase of temperature. Such coupled-oscillators model not only provides insights into the temperature dynamics of non-bonded interactions but also offers an opportunity to better understand the physical mechanisms behind the unusual THz spectral behaviors in taurine. Particularly, the simulation approach and novel coupled-oscillators model presented in this work are applicable to analyze the THz spectra of other molecular systems.

Lattice thermal expansion and anisotropic displacements in urea, bromomalonic aldehyde, pentachloropyridine, and naphthalene

Anisotropic displacement parameters (ADPs) are commonly used in crystallography, chemistry, and related fields to describe and quantify thermal motion of atoms. Within the very recent years, these ADPs have become predictable by lattice dynamics in combination with first-principles theory. Here, we study four very different molecular crystals, namely, urea, bromomalonic aldehyde, pentachloropyridine, and naphthalene, by first-principles theory to assess the quality of ADPs calculated in the quasi-harmonic approximation. In addition, we predict both the thermal expansion and thermal motion within the quasi-harmonic approximation and compare the predictions with the experimental data. Very reliable ADPs are calculated within the quasi-harmonic approximation for all four cases up to at least 200 K, and they turn out to be in better agreement with the experiment than those calculated within the harmonic approximation. In one particular case, ADPs can even reliably be predicted up to room temperature. Our results also hint at the importance of normal-mode anharmonicity in the calculation of ADPs.

Crystal structures of alkali metal (Group 1) citrate salts

The crystal structures of 16 new alkali metal citrates were determined using powder and/or single crystal techniques. These structures and 12 previously determined citrate structures were optimized using density functional techniques. The central portion of a citrate ion is fairly rigid, while the conformations of the terminal carboxylate groups exhibit no preferences. The citrate–metal bonding is ionic. Trends in metal–citrate coordination are noted. The energy of an O—H...O hydrogen bond is proportional to the square root of the H...acceptor Mulliken overlap population, and a correlation between the hydrogen bond energy and the H...acceptor distance was developed:E(kJ mol−1) = 137.5 (5) − 45.7 (8) (H...A, Å). The hydrogen bond contribution to the crystal energy ranges from 62.815 to 627.6 kJ mol−1 citrate−1and comprises ∼5 to 30% of the crystal energy. The general order of ionization of the three carboxylic acid groups of citric acid is: central, terminal, terminal, although there are a few exceptions. Comparisons of the refined and DFT-optimized structures indicate that crystal structures determined using powder diffraction data may not be as accurate as single-crystal structures.

Elucidating an Amorphous Form Stabilization Mechanism for Tenapanor Hydrochloride: Crystal Structure Analysis Using X-ray Diffraction, NMR Crystallography, and Molecular Modeling

By the combined use of powder and single-crystal X-ray diffraction, solid-state NMR, and molecular modeling, the crystal structures of two systems containing the unusually large tenapanor drug molecule have been determined: the free form, ANHY, and a dihydrochloride salt form, 2HCl. Dynamic nuclear polarization (DNP) assisted solid-state NMR (SSNMR) crystallography investigations were found essential for the final assignment and were used to validate the crystal structure of ANHY. From a structural informatics analysis of ANHY and 2HCl, conformational ring differences in one part of the molecule were observed which influence the relative orientation of a methyl group on a ring nitrogen and thereby impact the crystallizability of the dihydrochloride salt. From quantum chemistry calculations, the dynamics between different ring conformations in tenapanor is predicted to be fast. Addition of HCl to tenapanor results in general in a mixture of protonated ring conformers and hence a statistical mix of diastereoisomers which builds up the amorphous form, a-2HCl. This was qualitatively verified by ¹³C CP/MAS NMR investigations of the amorphous form. Thus, to form any significant amount of the crystalline material 2HCl, which originates from the minor (i.e., energetically less stable) ring conformations, one needs to involve nitrogen deprotonation to allow exchange between the minor and major conformations of ANHY in solution. Thus, by controlling the solution pH value to well below the p K_a of ANHY, the equilibrium between ANHY and 2HCl can be controlled and by this mechanism the crystallization of 2HCl can be avoided and the amorphous form of the dichloride salt can therefore be stabilized.

Evaluating the Energetic Driving Force for Cocrystal Formation

We present a periodic density functional theory study of the stability of 350 organic cocrystals relative to their pure single-component structures, the largest study of cocrystals yet performed with high-level computational methods. Our calculations demonstrate that cocrystals are on average 8 kJ mol^-1 more stable than their constituent single-component structures and are very rarely (<5% of cases) less stable; cocrystallization is almost always a thermodynamically favorable process. We consider the variation in stability between different categories of systems-hydrogen-bonded, halogen-bonded, and weakly bound cocrystals-finding that, contrary to chemical intuition, the presence of hydrogen or halogen bond interactions is not necessarily a good predictor of stability. Finally, we investigate the correlation of the relative stability with simple chemical descriptors: changes in packing efficiency and hydrogen bond strength. We find some broad qualitative agreement with chemical intuition-more densely packed cocrystals with stronger hydrogen bonding tend to be more stable-but the relationship is weak, suggesting that such simple descriptors do not capture the complex balance of interactions driving cocrystallization. Our conclusions suggest that while cocrystallization is often a thermodynamically favorable process, it remains difficult to formulate general rules to guide synthesis, highlighting the continued importance of high-level computation in predicting and rationalizing such systems.

Towards the systematic crystallisation of molecular ionic cocrystals: insights from computed crystal form landscapes

The underlying molecular and crystal properties affecting the crystallisation of organic molecular ionic cocrystals (ICCs) are investigated.