Report on the sixth blind test of organic crystal structure prediction methods

Free-energy landscape of polymer-crystal polymorphism

Polymorphism rationalizes how processing can control the final structure of a material. The rugged free-energy landscape and exceedingly slow kinetics in the solid state have so far hampered computational investigations. We report for the first time the free-energy landscape of a polymorphic crystalline polymer, syndiotactic polystyrene. Coarse-grained metadynamics simulations allow us to efficiently sample the landscape at large. The free-energy difference between the two main polymorphs, α and β, is further investigated by quantum-chemical calculations. The results of the two methods are in line with experimental observations: they predict β as the more stable polymorph under standard conditions. Critically, the free-energy landscape suggests how the α polymorph may lead to experimentally observed kinetic traps. The combination of multiscale modeling, enhanced sampling, and quantum-chemical calculations offers an appealing strategy to uncover complex free-energy landscapes with polymorphic behavior.

Rich polymorphism in nicotinamide revealed by melt crystallization and crystal structure prediction

Overprediction is a major limitation of current crystal structure prediction (CSP) methods. It is difficult to determine whether computer-predicted polymorphic structures are artefacts of the calculation model or are polymorphs that have not yet been found. Here, we reported the well-known vitamin nicotinamide (NIC) to be a highly polymorphic compound with nine solved single-crystal structures determined by performing melt crystallization. A CSP calculation successfully identifies all six Z' = 1 and 2 experimental structures, five of which defy 66 years of attempts at being explored using solution crystallization. Our study demonstrates that when combined with our strategy for cultivating single crystals from melt microdroplets, melt crystallization has turned out to be an efficient tool for exploring polymorphic landscapes to better understand polymorphic crystallization and to more effectively test the accuracy of theoretical predictions, especially in regions inaccessible by solution crystallization.

Identifying aspirin polymorphs from combined DFT-based crystal structure prediction and solid-state NMR

A combined experimental and computational approach was used to distinguish between different polymorphs of the pharmaceutical drug aspirin. This method involves the use of ab initio random structure searching (AIRSS), a density functional theory (DFT)-based crystal structure prediction method for the high-accuracy prediction of polymorphic structures, with DFT calculations of nuclear magnetic resonance (NMR) parameters and solid-state NMR experiments at natural abundance. AIRSS was used to predict the crystal structures of form-I and form-II of aspirin. The root-mean-square deviation between experimental and calculated ¹ H chemical shifts was used to identify form-I as the polymorph present in the experimental sample, the selection being successful despite the large similarities between the molecular environments in the crystals of the two polymorphs.

Statistical Mechanical Approximations to More Efficiently Determine Polymorph Free Energy Differences for Small Organic Molecules

Methods to efficiently determine the relative stability of polymorphs of organic crystals are highly desired in crystal structure predictions (CSPs). Current methodologies include calculating the free energy of static lattice phonons, quasi-harmonic approximations (QHA), and computing the full thermodynamic cycle using replica exchange molecular dynamics (REMD). We found that 13 out of the 29 systems minimized from experimental crystal structures restructured to a lower energy minimum when heated and annealed using REMD, a phenomenon that QHA alone cannot capture. Here, we present a series of methods that are intermediate in accuracy and expense between QHA and computing the full thermodynamic cycle, which can save 42-80% of the computational cost and introduces, on this benchmark, a relatively small (0.16 ± 0.04 kcal/mol) error relative to the full thermodynamic cycle. In particular, a method that Boltzmann weights harmonic free energies from along the trajectory of REMD replica exchange appears to be an appropriate intermediate between QHA and the full thermodynamic cycle using MD when screening crystal polymorph stability.

Estimation and prediction of ellipsoidal molecular shapes in organic crystals based on ellipsoid packing

Crystal structure prediction has been one of the fundamental and challenging problems in materials science. It is computationally exhaustive to identify molecular conformations and arrangements in organic molecular crystals due to complexity in intra- and inter-molecular interactions. From a geometrical viewpoint, specific types of organic crystal structures can be characterized by ellipsoid packing. In particular, we focus on aromatic systems which are important for organic semiconductor materials. In this study, we aim to estimate the ellipsoidal molecular shapes of such crystals and predict them from single molecular descriptors. First, we identify the molecular crystals with molecular centroid arrangements that correspond to affine transformations of four basic cubic lattices, through topological analysis of the dataset of crystalline polycyclic aromatic molecules. The novelty of our method is that the topological data analysis is applied to arrangements of molecular centroids intead of those of atoms. For each of the identified crystals, we estimate the intracrystalline molecular shape based on the ellipsoid packing assumption. Then, we show that the ellipsoidal shape can be predicted from single molecular descriptors using a machine learning method. The results suggest that topological characterization of molecular arrangements is useful for structure prediction of organic semiconductor materials.

Minimizing Polymorphic Risk through Cooperative Computational and Experimental Exploration

We combine state-of-the-art computational crystal structure prediction (CSP) techniques with a wide range of experimental crystallization methods to understand and explore crystal structure in pharmaceuticals and minimize the risk of unanticipated late-appearing polymorphs. Initially, we demonstrate the power of CSP to rationalize the difficulty in obtaining polymorphs of the well-known pharmaceutical isoniazid and show that CSP provides the structure of the recently obtained, but unsolved, Form III of this drug despite there being only a single resolved form for almost 70 years. More dramatically, our blind CSP study predicts a significant risk of polymorphism for the related iproniazid. Employing a wide variety of experimental techniques, including high-pressure experiments, we experimentally obtained the first three known nonsolvated crystal forms of iproniazid, all of which were successfully predicted in the CSP procedure. We demonstrate the power of CSP methods and free energy calculations to rationalize the observed elusiveness of the third form of iproniazid, the success of high-pressure experiments in obtaining it, and the ability of our synergistic computational-experimental approach to “de-risk” solid form landscapes.

Multifidelity Statistical Machine Learning for Molecular Crystal Structure Prediction

The prediction of crystal structures from first-principles requires highly accurate energies for large numbers of putative crystal structures. High accuracy of solid state density functional theory (DFT) calculations is often required, but hundreds or more structures can be present in the low energy region of interest, so that the associated computational costs are prohibitive. Here, we apply statistical machine learning to predict expensive hybrid functional DFT (PBE0) calculations using a multifidelity approach to re-evaluate the energies of crystal structures predicted with an inexpensive force field. The method uses an autoregressive Gaussian process, making use of less expensive GGA DFT (PBE) calculations to bridge the gap between the force field and PBE0 energies. The method is benchmarked on the crystal structure landscapes of three small, hydrogen-bonded organic molecules and shown to produce accurate predictions of energies and crystal structure ranking using small numbers of the most expensive calculations; the PBE0 energies can be predicted with errors of less than 1 kJ mol^-1 with between 4.2 and 6.8% of the cost of the full calculations. As the model that we have developed is probabilistic, we discuss how the uncertainties in predicted energies impact the assessment of the energetic ranking of crystal structures.

XO-PBC: An Accurate and Efficient Method for Molecular Crystals

In this work, we propose the XO-PBC method, which combines the eXtended ONIOM method (XO) with the periodic boundary condition (PBC) for the description of molecular crystals. XO-PBC tries to embed a finite cluster cut out from the solid into the periodic environment, making it feasible to employ advanced molecular quantum chemistry methods, which are usually prohibitively expensive for direct PBC calculations. In particular, XO-PBC utilizes the results from force calculations to design the scheme to fragment the molecule when crystals are made of large molecules and to select cluster model systems automatically consisting of dimer up to tetramer interactions for embedding. By applying an appropriate theory to each model, a satisfactory accuracy for the system under study is ensured, while a high efficiency is achieved with massively parallel computing by distributing model systems onto different processors. A comparison of the XO-PBC calculations with the conventional direct PBC calculations at the B3LYP level demonstrates its accuracy at substantially low cost for the description of molecular crystals. The usefulness of the XO-PBC method is further exemplified, showing that XO-PBC is able to predict the lattice energies of various types of molecular crystals within chemical accuracy (<4 kJ/mol) when the doubly hybrid density functional XYG3 is used as the target high level and the periodic PBE as the basic low level. The XO-PBC method provides a general protocol that brings the great predictive power of advanced electronic structure methods from molecular systems to the extended solids.

Ogre: A Python package for molecular crystal surface generation with applications to surface energy and crystal habit prediction

We present Ogre, an open-source code for generating surface slab models from bulk molecular crystal structures. Ogre is written in Python and interfaces with the FHI-aims code to calculate surface energies at the level of density functional theory (DFT). The input of Ogre is the geometry of the bulk molecular crystal. The surface is cleaved from the bulk structure with the molecules on the surface kept intact. A slab model is constructed according to the user specifications for the number of molecular layers and the length of the vacuum region. Ogre automatically identifies all symmetrically unique surfaces for the user-specified Miller indices and detects all possible surface terminations. Ogre includes utilities to analyze the surface energy convergence and Wulff shape of the molecular crystal. We present the application of Ogre to three representative molecular crystals: the pharmaceutical aspirin, the organic semiconductor tetracene, and the energetic material HMX. The equilibrium crystal shapes predicted by Ogre are in agreement with experimentally grown crystals, demonstrating that DFT produces satisfactory predictions of the crystal habit for diverse classes of molecular crystals.

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.

SAPT codes for calculations of intermolecular interaction energies

Symmetry-adapted perturbation theory (SAPT) is a method for calculations of intermolecular (noncovalent) interaction energies. The set of SAPT codes that is described here, the current version named SAPT2020, includes virtually all variants of SAPT developed so far, among them two-body SAPT based on perturbative, coupled cluster, and density functional theory descriptions of monomers, three-body SAPT, and two-body SAPT for some classes of open-shell monomers. The properties of systems governed by noncovalent interactions can be predicted only if potential energy surfaces (force fields) are available. SAPT is the preferred approach for generating such surfaces since it is seamlessly connected to the asymptotic expansion of interaction energy. SAPT2020 includes codes for automatic development of such surfaces, enabling generation of complete dimer surfaces with a rigid monomer approximation for dimers containing about one hundred atoms. These codes can also be used to obtain surfaces including internal degrees of freedom of monomers.

The Exploration of Chemical Reaction Networks

Modern computational chemistry has reached a stage at which massive exploration into chemical reaction space with unprecedented resolution with respect to the number of potentially relevant molecular structures has become possible. Various algorithmic advances have shown that such structural screenings must and can be automated and routinely carried out. This will replace the standard approach of manually studying a selected and restricted number of molecular structures for a chemical mechanism. The complexity of the task has led to many different approaches. However, all of them address the same general target, namely to produce a complete atomistic picture of the kinetics of a chemical process. It is the purpose of this overview to categorize the problems that should be targeted and to identify the principal components and challenges of automated exploration machines so that the various existing approaches and future developments can be compared based on well-defined conceptual principles.

Efficient Screening for Ternary Molecular Ionic Cocrystals Using a Complementary Mechanosynthesis and Computational Structure Prediction Approach

The discovery of molecular ionic cocrystals (ICCs) of active pharmaceutical ingredients (APIs) widens the opportunities for optimizing the physicochemical properties of APIs whilst facilitating the delivery of multiple therapeutic agents. However, ICCs are often observed serendipitously in crystallization screens and the factors dictating their crystallization are poorly understood. We demonstrate here that mechanochemical ball milling is a versatile technique for the reproducible synthesis of ternary molecular ICCs in less than 30 min of grinding with or without solvent. Computational crystal structure prediction (CSP) calculations have been performed on ternary molecular ICCs for the first time and the observed crystal structures of all the ICCs were correctly predicted. Periodic dispersion-corrected DFT calculations revealed that all the ICCs are thermodynamically stable (mean stabilization energy=-2 kJ mol-1 ) relative to the crystallization of a physical mixture of the binary salt and acid. The results suggest that a combined mechanosynthesis and CSP approach could be used to target the synthesis of higher-order molecular ICCs with functional properties.

Exploring the configuration spaces of surface materials using time-dependent diffraction patterns and unsupervised learning

Computational methods for exploring the atomic configuration spaces of surface materials will lead to breakthroughs in nanotechnology and beyond. In order to develop such methods, especially ones utilizing machine learning approaches, descriptors which encode the structural features of the candidate configurations are required. In this paper, we propose the use of time-dependent electron diffraction simulations to create descriptors for the configurations of surface materials. Our proposal utilizes the fact that the sub-femtosecond time-dependence of electron diffraction patterns are highly sensitive to the arrangement of atoms in the surface region of the material, allowing one to distinguish configurations which possess identical symmetry but differ in the locations of the atoms in the unit cell. We demonstrate the effectiveness of this approach by considering the simple cases of copper(111) and an organic self-assembled monolayer system, and use it to search for metastable configurations of these materials.

Overcoming the difficulties of predicting conformational polymorph energetics in molecular crystals via correlated wavefunction methods

Molecular crystal structure prediction is increasingly being applied to study the solid form landscapes of larger, more flexible pharmaceutical molecules. Despite many successes in crystal structure prediction, van der Waals-inclusive density functional theory (DFT) methods exhibit serious failures predicting the polymorph stabilities for a number of systems exhibiting conformational polymorphism, where changes in intramolecular conformation lead to different intermolecular crystal packings. Here, the stabilities of the conformational polymorphs of o-acetamidobenzamide, ROY, and oxalyl dihydrazide are examined in detail. DFT functionals that have previously been very successful in crystal structure prediction perform poorly in all three systems, due primarily to the poor intramolecular conformational energies, but also due to the intermolecular description in oxalyl dihydrazide. In all three cases, a fragment-based dispersion-corrected second-order Møller-Plesset perturbation theory (MP2D) treatment of the crystals overcomes these difficulties and predicts conformational polymorph stabilities in good agreement with experiment. These results highlight the need for methods which go beyond current-generation DFT functionals to make crystal polymorph stability predictions truly reliable.

Elastic properties of the molecular crystals of hydrocarbons from first principles calculations

I studied the elastic properties of oligoacenes and polycyclic aromatic hydrocarbons crystals within the framework of density functional theory with van der Waals interactions. The full sets of elastic constants were computed. The computed parameters have good agreement with experimental data. The study of four forms (α, β, γ and dimeric) demonstrate that the stacking of molecules leads to different character of interaction between molecules. Crystals with dimeric form have lower anisotropy. If symmetry of crystals is the same, the increase in number of aromatic rings results in anisotropy increase.

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.

An Isosymmetric High-Pressure Phase Transition in α-Glycylglycine: A Combined Experimental and Theoretical Study

We investigated the effects of hydrostatic pressure on α-glycylglycine (α-digly) using a combined experimental and theoretical approach. The results of powder X-ray diffraction show a change in compressibility of the axes above 6.7 GPa, but also indicate that the structure remains in the same monoclinic space group, suggesting an isosymmetric phase transition. A noticeable change in the Raman spectra between 6 and 7.5 GPa further supports the observed phase transition. First-principles-based calculations combined with the crystal structure prediction code USPEX predict a number of possible polymorphs at high pressure. An orthorhombic structure with a bent peptide backbone is the lowest enthalpy polymorph above 6.4 GPa; however, it is not consistent with experimental observations. A second monoclinic structure isosymmetric to α-digly, α'-digly, is predicted to become more stable above 11.4 GPa. The partial atomic charges in α'-digly differ from α-digly, and the molecule is bent, possibly indicating different reactivity of α'-digly. The similarity in the lattice parameters predicted from calculations and the axial changes observed experimentally support that the α'-digly phase is likely observed at high pressure. A possible explanation for the isosymmetric phase transition is discussed in terms of relaxing strained hydrogen bonding interactions. Such combined experimental and modeling efforts provide atomic-level insight into how pressure-driven conformational changes alter hydrogen-bonding networks in complicated molecular crystals.

A machine learning based intramolecular potential for a flexible organic molecule

Here, we employ the kernel regression machine learning technique to construct an analytical potential that reproduces the quantum mechanical potential energy surface of a small, flexible, drug-like molecule, 3-(benzyloxy)pyridin-2-amine.

Increasing the performance, trustworthiness and practical value of machine learning models: a case study predicting hydrogen bond network dimensionalities from molecular diagrams

The value of a hydrogen bond network prediction model was improved using a tool to increase prediction trust. Its accuracy could be improved up to 73% or 89% with the compromise that only 34% and 8% of the test examples could be predicted.

Identifying intermolecular atom⋯atom interactions that are not just bonding but also competitive

This highlight criticises the QTAIM method and discusses algorithms for identifying intermolecular interactions that are both bonding and competitive.

Comment on “Polymorphism of levofloxacin: structure, properties and phase transformation” by N. Wei, L. Jia, Z. Shang, J. Gong, S. Wu, J. Wang and W. Tang, CrystEngComm, 2019, , 6196–6207

A comment on a statement made by W. Tang et al. on the levofloxacin polymorphs predicted through CSP studies.

Disappearing disorder

Disorder in crystal structures can disappear, depending on the circumstances, as shown by multi-temperature measurements, aspherical-atom refinement and computational analyses.

Intermolecular Interactions in Molecular Organic Crystals upon Relaxation of Lattice Parameters

Crystal structure prediction is based on the assumption that the most thermodynamically stable structure will crystallize first. The existence of other structures such as polymorphs or from counterenantiomers requires an accurate calculation of the electronic energy. Using atom-centered Gaussian basis functions in periodic Density Functional Theory (DFT) calculations in Turbomole, the performance of two dispersion-corrected functionals, PBE-D3 and B97-D, is assessed for molecular organic crystals of the X23 benchmark set. B97-D shows a MAE (mean absolute error) of 4 kJ/mol, compared to 9 kJ/mol for PBE-D3. A strategy for the convergence of lattice energies towards the basis set limit is outlined. A simultaneous minimization of molecular structures and lattice parameters shows that both methods are able to reproduce experimental unit cell parameters to within 4–5%. Calculated lattice energies, however, deviate slightly more from the experiment, i.e., by 0.4 kJ/mol after unit cell optimization for PBE-D3 and 0.5 kJ/mol for B97-D. The accuracy of the calculated lattice energies compared to the experimental values demonstrates the ability of current DFT methods to assist in the quest for possible polymorphs and enantioselective crystallization processes.

A Karplus Equation for the Conformational Analysis of Organic Molecular Crystals

Vicinal scalar couplings (³ J) are extensively used for the conformational analysis of organic compounds in the liquid state through empirical Karplus equations. In contrast, there are no examples of such use for the structural investigation of solids. With the support of first principles calculations, we demonstrate here that ¹³ C-¹³ C ³ J coupling constants (³ J_CC ) measured on a series of isotopically enriched solid amino acids and sugars can be related to dihedral angles by a simple Karplus-like relationship, and we provide a parameterized Karplus function for the conformational analysis of organic molecular crystals. Under the experimental conditions discussed, torsional angles can be estimated from the experimental ³ J_CC values with an accuracy of 10° using this function. These results open new perspectives towards the use of ³ J_CC as a new analytical tool that could considerably simplify structure determination of functional organic solids.

Tailor-made solvents for pharmaceutical use? Experimental and computational approach for determining solubility in deep eutectic solvents (DES)

A deep eutectic solvent (DES) is a mixture of two or more chemicals that interact via hydrogen bonding and has a melting point far below that of the individual components. DESs have been proposed as alternative solvents for poorly soluble active pharmaceutical ingredients (API). In this study, the solvation capacities of six deep eutectic solvents were compared to water and three conventional pharmaceutical solvents (PEG 300, ethanol and glycerol) for 11 APIs. The experimentally determined solubilities were compared to computational solubilities predicted by the Conductor-like Screening Model for Real Solvents (COSMO-RS). While the conventional pharmaceutical solvents PEG 300 and ethanol were the best solvents for the majority of the studied APIs, API-DES combinations were identified, which exceeded the API solubility found in the conventional pharmaceutical solvents. Furthermore, it was also possible to obtain high solubilities in the DESs relative to water, suggesting DESs to be potential solvents for poorly water soluble APIs. In addition, the relative increase in solubility found in the experimental data could be well predicted ab initio using COSMO-RS. Hence, COSMO-RS may in the future be used to reduce the experimental screening of potential DESs for a given API.

CrystaLattE: Automated computation of lattice energies of organic crystals exploiting the many-body expansion to achieve dual-level parallelism

We present an algorithm to compute the lattice energies of molecular crystals based on the many-body cluster expansion. The required computations on dimers, trimers, etc., within the crystal are independent of each other, leading to a naturally parallel approach. The algorithm exploits the long-range three-dimensional periodic order of crystals to automatically detect and avoid redundant or unnecessary computations. For this purpose, Coulomb-matrix descriptors from machine learning applications are found to be efficient in determining whether two N-mers are identical. The algorithm is implemented as an open-source Python program, CrystaLattE, that uses some of the features of the Quantum Chemistry Common Driver and Databases library. CrystaLattE is initially interfaced with the quantum chemistry package Psi4. With CrystaLattE, we have applied the fast, dispersion-corrected Hartree-Fock method HF-3c to the lattice energy of crystalline benzene. Including all 73 symmetry-unique dimers and 7130 symmetry-unique trimers that can be formed from molecules within a 15 Å cutoff from a central reference monomer, HF-3c plus an Axilrod-Teller-Muto estimate of three-body dispersion exhibits an error of only -1.0 kJ mol^-1 vs the estimated 0 K experimental lattice energy of -55.3 ± 2.2 kJ mol^-1. The convergence of the HF-3c two- and three-body contributions to the lattice energy as a function of intermonomer distance is examined.

Influence of ortho-substituent on the molecular and crystal structures of 2-(N-arylimino)coumarin-3-carboxamide: isotypic and polymorphic structures

During a comprehensive study of a series of 2-(N-arylimino)coumarin-3-carboxamides with the aryl group substituted in the ortho-position by either a halogen atom, a methyl group or a methoxy group, the existence of three groups of isotypic crystal structures has been revealed. The similarity of crystal structures belonging to the same groups was confirmed by the analysis based on the comparison of pairwise interactions energies obtained from quantum chemical calculations. Group I includes unsubstituted, methyl-substituted and polymorphic modification 1 of fluoro-substituted 2-(N-arylimino)coumarin-3-carboxamide. Structures of polymorphic modification 2 of fluoro-substituted derivative, chloro-substituted and polymorphic modification 1 of bromo-substituted 2-(N-arylimino)coumarin-3-carboxamide may represent group II. Group III contains structures of polymorphic modification 2 of bromo-substituted derivative, iodine- and methoxy-substituted 2-(N-arylimino)coumarin-3-carboxamides. Structures of the same type group have extremely close parameters of the unit cell as well as those of molecular and crystal structures. But they are not identical. Polymorphic modifications of fluoro- and bromo-substituted 2-(N-arylimino)coumarin-3-carboxamides belong to different crystal types mainly due to different arrangement of basic structural motifs separated out using quantum chemical calculations.

Intermolecular Interactions in Functional Crystalline Materials: From Data to Knowledge

Intermolecular interactions of organic, inorganic, and organometallic compounds are the key to many composition–structure and structure–property networks. In this review, some of these relations and the tools developed by the Cambridge Crystallographic Data Center (CCDC) to analyze them and design solid forms with desired properties are described. The potential of studies supported by the Cambridge Structural Database (CSD)-Materials tools for investigation of dynamic processes in crystals, for analysis of biologically active, high energy, optical, (electro)conductive, and other functional crystalline materials, and for the prediction of novel solid forms (polymorphs, co-crystals, solvates) are discussed. Besides, some unusual applications, the potential for further development and limitations of the CCDC software are reported.

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.

High throughput scanning of dimer interactions to facilitate confirmation of the molecular stacking mode: a case of 1,3,5-trinitrobenzene and its amino-derivatives

Exactly predicting the packing structures of a given molecule is a crucial topic in crystal engineering, while it remains still challenging, as it requires huge calculations, largely above common computation cost and time limitations. However, current progress in high throughput calculations makes the fast screening of structures and properties feasible. In the present work, we exemplify this by considering a special case of ascertainment of the molecular stacking mode and shear properties of energetic materials. Four energetic π-bonded molecules, 1,3,5-trinitrobenzene, 2,4,6-trinitroaniline, 1,3-diamino-2,4,6-trinitrobenzene and 2,4,6-triamino-1,3,5-trinitrobenzene, with a different number of H atoms replaced by amino groups, are adopted as samples to scan the potential energy surfaces (PESs) of dimers through high throughput calculations. It is found that the parallel stacking mode is the most energetically favored, followed by the T-shaped, coplanar and crossing ones. Such an energetically favored stacking mode is observed in all related π-stacked crystal structures at ambient conditions or low temperatures. It shows that the stacking mode can be ascertained through the PES scanning of dimers, and thereby, the stacking structures and properties related to the stacking mode, like mechanical anisotropism, can be quickly screened by means of high throughput calculations.

Experimental and computational approaches to rationalise multicomponent supramolecular assemblies: dapsone monosolvates

The monosolvate crystal energy landscapes of dapsone (DDS) including the solvents carbon tetrachloride, acetone, cyclohexanone, dimethyl formamide, tetrahydrofuran, methyl ethyl ketone, 1,2-dichloroethane, 1,4-dioxane, dichloromethane and chloroform were established using experimental and computational approaches. To rationalise and understand solvate formation, solvate stability and desolvation reactions a careful control of the experimental crystallisation and storage conditions, a range of thermoanalytical methods and crystal structure prediction were required. Six of the eight DDS monosolvates are reported and characterised for the first time. Structural similarity and diversity of the at ambient conditions unstable monosolvates were apparent from the computed crystal energy landscapes, which had the experimental packings as lowest energy structures. The computed structures were used as input for Rietveld refinements and isostructurality of four of the monosolvates was confirmed. Packing comparisons of the solvate structures and molecular properties of the solvent molecules indicated that both size/shape of the solvent molecule and the possible DDSsolvent interactions are the important factors for DDS solvate formation. Through the combination of experiment and theory solvate stability and structural features have been rationalised.

Plasticity in zwitterionic drugs: the bending properties of Pregabalin and Gabapentin and their hydrates

The investigation of mechanical properties in molecular crystals is emerging as a novel area of interest in crystal engineering. Indeed, good mechanical properties are required to manufacture pharmaceutical and technologically relevant substances into usable products. In such endeavour, bendable single crystals help to correlate microscopic structure to macroscopic properties for potential design. The hydrate forms of two anticonvulsant zwitterionic drugs, Pregabalin and Gabapentin, are two examples of crystalline materials that show macroscopic plasticity. The direct comparison of these structures with those of their anhydrous counterparts, which are brittle, suggests that the presence of water is critical for plasticity. In contrast, structural features such as molecular packing and anisotropic distribution of strong and weak interactions seem less important.

Nine questions on energy decomposition analysis

The paper collects the answers of the authors to the following questions: Is the lack of precision in the definition of many chemical concepts one of the reasons for the coexistence of many partition schemes? Does the adoption of a given partition scheme imply a set of more precise definitions of the underlying chemical concepts? How can one use the results of a partition scheme to improve the clarity of definitions of concepts? Are partition schemes subject to scientific Darwinism? If so, what is the influence of a community's sociological pressure in the "natural selection" process? To what extent does/can/should investigated systems influence the choice of a particular partition scheme? Do we need more focused chemical validation of Energy Decomposition Analysis (EDA) methodology and descriptors/terms in general? Is there any interest in developing common benchmarks and test sets for cross-validation of methods? Is it possible to contemplate a unified partition scheme (let us call it the "standard model" of partitioning), that is proper for all applications in chemistry, in the foreseeable future or even in principle? In the end, science is about experiments and the real world. Can one, therefore, use any experiment or experimental data be used to favor one partition scheme over another? © 2019 Wiley Periodicals, Inc.

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.

A Million Crystal Structures: The Whole Is Greater than the Sum of Its Parts

The founding in 1965 of what is now called the Cambridge Structural Database (CSD) has reaped dividends in numerous and diverse areas of chemical research. Each of the million or so crystal structures in the database was solved for its own particular reason, but collected together, the structures can be reused to address a multitude of new problems. In this Review, which is focused mainly on the last 10 years, we chronicle the contribution of the CSD to research into molecular geometries, molecular interactions, and molecular assemblies and demonstrate its value in the design of biologically active molecules and the solid forms in which they are delivered. Its potential in other commercially relevant areas is described, including gas storage and delivery, thin films, and (opto)electronics. The CSD also aids the solution of new crystal structures. Because no scientific instrument is without shortcomings, the limitations of CSD research are assessed. We emphasize the importance of maintaining database quality: notwithstanding the arrival of big data and machine learning, it remains perilous to ignore the principle of garbage in, garbage out. Finally, we explain why the CSD must evolve with the world around it to ensure it remains fit for purpose in the years ahead.

Accurate and efficient representation of intramolecular energy in ab initio generation of crystal structures. II. Smoothed intramolecular potentials

The application of crystal structure prediction (CSP) to industrially relevant molecules requires the handling of increasingly large and flexible compounds. A revised model for the effect of molecular flexibility on the lattice energy that removes the discontinuities and non-differentiabilities present in earlier models (Sugden et al., 2016), with a view to improving the performance of CSP is presented. The approach is based on the concept of computing a weighted average of local models, and has been implemented within the CrystalPredictor code. Through the comparative investigation of several compounds studied in earlier literature, it is shown that this new model results in large reductions in computational effort (of up to 65%) and in significant increases in reliability. The approach is further applied to investigate, for the first time, the computational polymorphic landscape of flufenamic acid for Z' = 1 structures, resulting in the successful identification of all three experimentally resolved polymorphs within reasonable computational time.

Charge Distributions of Nitro Groups Within Organic Explosive Crystals: Effects on Sensitivity and Modeling

The charge distribution of NO₂ groups within the crystalline polymorphs of energetic materials strongly affects their explosive properties. We use the recently introduced basis-space iterated stockholder atom partitioning of high-quality charge distributions to examine the approximations that can be made in modeling polymorphs and their physical properties, using 1,3,5-trinitroperhydro-1,3,5-triazine, trinitrotoluene, 1-3-5-trinitrobenzene, and hexanitrobenzene as exemplars. The NO₂ charge distribution is strongly affected by the neighboring atoms, the rest of the molecules, and also significantly by the NO₂ torsion angle within the possible variations found in observed crystal structures. Thus, the proposed correlations between the molecular electrostatic properties, such as trigger-bond potential or maxima in the electrostatic potential, and impact sensitivity will be affected by the changes in conformation that occur on crystallization. We establish the relationship between the NO₂ torsion angle and the likelihood of occurrence in observed crystal structures, the conformational energy, and the charge and dipole magnitude on each atom, and how this varies with the neighboring groups. We examine the effect of analytically rotating the atomic multipole moments to model changes in torsion angle and establish that this is a viable approach for crystal structures but is not accurate enough to model the relative lattice energies. This establishes the basis of transferability of the NO₂ charge distribution for realistic nonempirical model intermolecular potentials for simulating energetic materials.

High Pressure Hydrocarbons Revisited: From van der Waals Compounds to Diamond

Methane and other hydrocarbons are major components of the mantle regions of icy planets. Several recent computational studies have investigated the high-pressure behaviour of specific hydrocarbons. To develop a global picture of hydrocarbon stability, to identify relevant decomposition reactions, and probe eventual formation of diamond, a complete study of all hydrocarbons is needed. Using density functional theory calculations we survey here all known C-H crystal structures augmented by targeted crystal structure searches to build hydrocarbon phase diagrams in the ground state and at elevated temperatures. We find that an updated pressure-temperature phase diagram for methane is dominated at intermediate pressures by CH 4 :H 2 van der Waals inclusion compounds. We discuss the P-T phase diagram for CH and CH 2 (i.e., polystyrene and polyethylene) to illustrate that diamond formation conditions are strongly composition dependent. Finally, crystal structure searches uncover a new CH 4 (H 2 ) 2 van der Waals compound, the most hydrogen-rich hydrocarbon, stable between 170 and 220 GPa.

Crystal Structure Prediction via Basin-Hopping Global Optimization Employing Tiny Periodic Simulation Cells, with Application to Water-Ice

A crystal structure prediction algorithm for use in periodic boundary conditions with empirical rigid models is presented, which employs (i) unrestricted cutoff radii for the real-space interactions, thus allowing the treatment of even very small unit cells, and (ii) a global-optimization algorithm based on the basin-hopping method of Wales et al. (D. J. Wales and J. P. K. Doye, J. Phys. Chem. A 1997, 101, 5111). The algorithm is then applied to the TIP4P model of water (W. L. Jorgensen et al., J. Chem. Phys. 1983, 79, 926.) in order to find the lowest enthalpy water-ice crystalline structures in the pressure region 0-8000 bar, in unit cells holding in the range of 1-16 molecules, and a database of the 10 lowest enthalpy structures found at pressures 0, 4000, and 8000 bar is presented. The algorithm finds many of the ice polymorphs and, in particular, finds that the lowest energy structure at zero pressure is almost exactly tied between an ice Ic (cubic ice) and ice Ih (hexagonal ice) structure, having near-identical energies.