Progress in crystal structure prediction

The results of the application of a density functional theory method incorporating dispersive corrections in the 2010 crystal structure prediction blind test are reported. The method correctly predicted four out of the six experimental structures. Three of the four correct predictions were found to have the lowest lattice energy of any crystal structure for that molecule. The experimental crystal structures for all six compounds were found during the structure generation phase of the simulations, indicating that the tailor-made force fields used for screening structures were valid and that the structure generation engine, which combines a Monte Carlo parallel tempering algorithm with an efficient lattice energy minimiser, was working effectively. For the three compounds for which the experimental crystal structures did not correspond to the lowest energy structures found, the method for calculating the lattice energy needs to be further refined or there may be other polymorphs that have not yet been found experimentally.     

The prediction, morphology, and mechanical properties of the polymorphs of paracetamol.

The analgesic drug paracetamol (acetaminophen) has two reported metastable polymorphs, one with better tableting properties than the stable form, and another which remains uncharacterized. We have therefore performed a systematic crystal structure prediction search for minima in the lattice energy of crystalline paracetamol. The stable monoclinic form is found as the global lattice-energy minimum, but there are at least a dozen energetically feasible structures found, including the well-characterized metastable orthorhombic phase. Hence, we require additional criteria to reduce the number of hypothetical crystal structures that can be considered as potential polymorphs. For this purpose the elastic properties and vapor growth morphology of the known and predicted structures have been estimated using second-derivative analysis and the attachment-energy model. These inexpensive calculations give reasonable agreement with the available experimental data for the known polymorphs. Some of the hypothetical structures are predicted to have a low growth rate and plate-like morphology, and so are unlikely to be observed. Another is only marginally mechanically stable. Thus, this first consideration of such properties in a crystal-structure prediction study appears to reduce the number of predicted polymorphs while leaving a few candidates for the uncharacterized form.     

Polymorphism in crystalline cinchomeronic acid

The structural relationship between the two crystal forms of cinchomeronic acid (CA 3,4-dicarboxypyridine) has been investigated by single crystal X-ray diffraction, IR and Raman spectroscopy and solid state NMR spectroscopy, showing that the two polymorphs form a monotropic system, with the orthorhombic form I being the thermodynamically stable form, while the monoclinic form II is unstable. In both forms CA crystallizes as a zwitterion and decomposes before melting. The crystal structure and spectroscopic analysis indicate that the difference in stability can be ascribed to the strength of the hydrogen-bonding patterns established by the protonated N-atom and the carboxylic/carboxylate O-atoms.     

Exploration of NVE classical trajectories as a tool for molecular crystal structure prediction, with tests on ice polymorphs

Following an initial Communication [Buch et al., J. Chem. Phys. 123, 051108 (2005)], a new molecular-dynamics-based approach is explored to search for candidate crystal structures of molecular solids corresponding to minima of the enthalpy. The approach is based on the observation of phase transitions in an artificial periodic system with a small unit cell and relies on the existence of an optimal energy range for observing freezing to low-lying minima in the course of classical trajectories. Tests are carried out for O structures of nine H2O-ice polymorphs. NVE trajectories for a range of preimposed box shapes display freezing to the different crystal polymorphs whenever the box dimensions approximate roughly the appropriate unit cell; the exception is ice II for which freezing requires unit cell dimensions close to the correct ones. In an alternate version of the algorithm, an initial box shape is picked at random and subsequently readjusted at short trajectory intervals by enthalpy minimization. Tests reveal the existence of ice forms which are "difficult" and "easy" to locate in this way. The former include ice IV, which is also difficult to crystallize experimentally from the liquid, and ice II, which does not interface with the liquid in the phase diagram. On the other hand, the latter crystal search procedure located successfully the remaining seven ice polymorphs, including ice V, which corresponds to the most complicated structure of all ice phases, with a monoclinic cell of 28 molecules.     

Predictability of the polymorphs of small organic compounds: crystal structure predictions of four benchmark blind test molecules

Predicting the crystal structure of an organic molecule from first principles has been a major challenge in physical chemistry. Recently, the application of Density Functional Theory including a dispersive energy correction (the DFT(d) method) has been shown to be a reliable method for predicting experimental structures based purely on their ranking according to lattice energy. Further validation results of the application of the DFT(d) method to four organic molecules are presented here. The compounds were targets (labelled molecule II, VI, VII and XI) in previous blind tests of crystal structure prediction, and their structures proved difficult to predict. However, this study shows that the DFT(d) approach is capable of predicting the solid state structures of these small molecules. For molecule VII, the most stable (rank 1) predicted crystal structure corresponds to the experimentally observed structure. For molecule VI, the rank 1, 2 and 3 predicted structures correspond to the three experimental polymorphs, forms I, III and II, respectively. For molecules II and XI, their rank 1 predicted structures are energetically more stable than those corresponding to the experimental crystal structures, and were not found amongst the structures submitted by the participants in the blind tests. The rank 1 structure of molecule II is predicted to exist under high pressure, whilst the rank 1 structure predicted for molecule XI has the same space group and hydrogen bonding pattern as observed in the crystal of 1-amino-1-methyl-cyclopropane, which is structurally related to molecule XI. The experimental crystal structure of molecule II corresponds to the rank 4 prediction, 0.8 kJ mol(-1) above the global minimum structure, and the experimental structure of molecule XI corresponds to the rank 2 prediction, 0.4 kJ mol(-1) above the global minimum.     

Challenges of crystal structure prediction of diastereomeric salt pairs

A methodology for the computational prediction of the crystal structures and resolution efficiency for diastereomeric salt pairs is developed by considering the polymorphic system of the diastereomeric salt pair (R)-1-phenylethylammonium (R/S)-2-phenylpropanoate. To alleviate the mathematical complexity of the search for minima in the lattice energy due to the presence of two flexible entities in the asymmetric unit, the range of rigid-body lattice energy global optimizations was guided by a statistical analysis of the Cambridge Structural Database for common ion-pair geometries and ion conformations. A distributed multipole model for the dominant electrostatic interactions and high-level ab initio calculations for the intramolecular energy penalty for conformational distortions are used to quantify the relative stabilities of the p- and n-salt forms. While the ab initio prediction of the known structure of the p-salt as the most stable structure was insensitive to minor changes in the rigid-ion conformations considered, the relative stabilities of the known polymorphs and hypothetical structures of the n-salt were very sensitive. Although this paper provides a significant advance over traditional search algorithms and empirical force fields in determining the structures and relative stabilities of diastereomeric salt pairs, the sensitivity of the computed lattice energies to the fine details of the ion conformations overtaxes current computational models and renders the design of diastereomeric resolution processes by computational chemistry a challenging problem.     

Understanding solid-state reactions of organic crystals with density functional theory-based concepts

Solid-state reactions are commonly observed in organic crystals, including pharmaceutical and agricultural materials, fine chemicals, dyes, explosives, optics, and many other substances. The fact that these reactions are in general highly anisotropic with regard to the initiation and propagation in a crystal has led to this study for investigating the effect of crystal packing on the reaction mechanism and kinetics of organic crystals. We have used electron density-based concepts, including nuclear Fukui function, developed from density functional theory, for elucidating the effect of electronic structures of different polymorphs on the difference in their chemical reactivity. Two polymorphs of flufenamic acid were studied. The calculation results on major reacting faces of the two forms support their reactivity difference with ammonia gas. In addition, we calculated surface energies of reacting faces to discuss how the mechanical difference may affect the propagation of solid-state reaction.     

Polymorphic Characterization and Bioavailability of Nomegestrol Acetate

Polymorph screening is currently one of the most important strategies of innovators and generic companies from both pharmaceutical and intellectual property rights perspectives. Different polymorphs may have varying physicochemical properties which influence the bioavailability. The purpose of this study was to investigate the crystal structures and physicochemical properties of Nomegestrol acetate(NOMAC) polymorphs. Forms I and II(dioxane solvate) were isolated and prepared by systemic crystallization screening in this study, and the forms are reported for the first time. A structural analysis and comparison of all the forms are presented. This study was also the first time to apply a rapid and feasible ultra-highperformance-liquid chromatography(UHPLC)-electrospray ionization(ESI)-tandem mass spectrometry(MS) method to determine plasma levels of NOMAC within 3.0 mins. And this study demonstrated that the optimal crystal Form I displayed higher bioavailability than API indicating that Form I could be an alternative solid form that needs further research.     

A new crystal form of the NSAID dexketoprofen

Dexketoprofen [(2S)‐2‐(3‐benzoylphenyl)propanoic acid], C₁₆H₁₄O₃, is the S‐enantiomer of ketoprofen, a nonsteroidal anti‐inflammatory drug (NSAID) that has analgesic, antipyretic and anti‐inflammatory properties, and finds applications for the short‐term treatment of mild to moderate pain. A new crystalline phase of dexketoprofen is reported. Its solid‐state structure was determined by single‐crystal X‐ray diffraction (SCXRD). The molecular structure of the two independent molecules found in the asymmetric unit of this new phase ( DXKP‐β ) were compared to those of the already known crystal form of dexketoprofen ( DXKP‐α ) and with the S‐enantiomer of the racemic compound. The three different conformers of dexketoprofen found in DXKP‐α and DXKP‐β were then investigated by computational methods. The optimized structures are very close to the corresponding starting geometries and do not differ significantly in energy. The crystal packing of DXKP‐β was studied by means of Hirshfeld surface (HS) analysis; interaction energies were also calculated. A comparison with DXKP‐α shows close similarities between the two crystal forms, i.e. in both cases, molecules assemble through the catemer O—H…O synthon of the carboxylic acid stabilized by additional C—H…O contacts and, accordingly, the interaction energies, as well as the contributions to the HS area, are very similar. Finally, the thermal behaviour of the two polymorphs of dexketoprofen was assessed by means of XRD (both from single crystal and microcrystalline powder) and differential scanning calorimetry (DSC); both crystal forms are stable under the experimental conditions adopted (air, 300–350 K for DXKP‐α and 300–340 K DXKP‐β ) and no solid–solid phase transition occurs between the two crystal forms in the investigated temperature range (from 100 K up to ca 350 K).     

Amyloid Polymorphism in the Protein Folding and Aggregation Energy Landscape

Protein folding involves a large number of steps and conformations in which the folding protein samples different thermodynamic states characterized by local minima. Kinetically trapped on‐ or off‐pathway intermediates are metastable folding intermediates towards the lowest absolute energy minima, which have been postulated to be the natively folded state where intramolecular interactions dominate, and the amyloid state where intermolecular interactions dominate. However, this view largely neglects the rich polymorphism found within amyloid species. We review the protein folding energy landscape in view of recent findings identifying specific transition routes among different amyloid polymorphs. Observed transitions such as twisted ribbon→crystal or helical ribbon→nanotube, and forbidden transitions such helical ribbon?crystal, are discussed and positioned within the protein folding and aggregation energy landscape. Finally, amyloid crystals are identified as the ground state of the protein folding and aggregation energy landscape.     

Investigating the polymorphism in PR179: a combined crystal structure prediction and metadynamics study

The polymorphism of an industrial important pigment (PR179) was studied with a combination of standard crystal structure prediction and metadynamics. The former provided a starting set of candidate polymorphs whose structural and thermal stability were then probed by metadynamics. Moreover, metadynamics allowed for exploring the free energy surface to look for other possible polymorphs that were not included in the original set. Our calculations indicate that two structures have a high structural stability and are therefore good candidates to be found in experiments. The lower energy phase of the two indeed corresponds to the known polymorph, and we suggest that the other might be a metastable polymorph not yet experimentally discovered.     

Combinatorial Crystal Synthesis: Structural Landscape of Phloroglucinol:1,2‐bis(4‐pyridyl)ethylene and Phloroglucinol:Phenazine

A large number of crystal forms, polymorphs and pseudopolymorphs, have been isolated in the phloroglucinol‐dipyridylethylene (PGL:DPE) and phloroglucinol‐phenazine (PGL:PHE) systems. An understanding of the intermolecular interactions and synthon preferences in these binary systems enables one to design a ternary molecular solid that consists of PGL, PHE, and DPE, and also others where DPE is replaced by other heterocycles. Clean isolation of these ternary cocrystals demonstrates synthon amplification during crystallization. These results point to the lesser likelihood of polymorphism in multicomponent crystals compared to single‐component crystals. The appearance of several crystal forms during crystallization of a multicomponent system can be viewed as combinatorial crystal synthesis with synthon selection from a solution library. The resulting polymorphs and pseudopolymorphs that are obtained constitute a crystal structure landscape.     

Molecular Recognition and Crystal Energy Landscapes: An X‐ray and Computational Study of Caffeine and Other Methylxanthines

We introduce a new approach to crystal‐packing analysis, based on the study of mutual recognition modes of entire molecules or of molecular moieties, rather than a search for selected atom–atom contacts, and on the study of crystal energy landscapes over many computer‐generated polymorphs, rather than a quest for the one most stable crystal structure. The computational tools for this task are a polymorph generator and the PIXEL density sums method for the calculation of intermolecular energies. From this perspective, the molecular recognition, crystal packing, and solid‐state phase behavior of caffeine and several methylxanthines (purine‐2,6‐diones) have been analyzed. Many possible crystal structures for anhydrous caffeine have been generated by computer simulation, and the most stable among them is a thermodynamic, ordered equivalent of the disordered phase, revealed by powder X‐ray crystallography. Molecular recognition energies between two caffeine molecules or between caffeine and water have been calculated, and the results reveal the largely predominant mode to be the stacking of parallel caffeine molecules, an intermediately favorable caffeine–water interaction, and many other equivalent energy minima for lateral interactions of much less stabilization power. This last indetermination helps to explain why caffeine does not crystallize easily into an ordered anhydrous structure. In contrast, the mono‐ and dimethylxanthines (theophylline, theobromine, and the 1,7‐isomer, for which we present a single‐crystal X‐ray study and a lattice energy landscape) do crystallize in anhydrous form thanks to the formation of lateral hydrogen bonds.     

Characterization of complicated new polymorphs of chlorothalonil by X-ray diffraction and computer crystal structure prediction

A simultaneous experimental and computational search for polymorphs of chlorothalonil (2,4,5,6-tetrachloro-1,3-benzenedicarbonitrile) has been conducted, leading to the first characterization of forms 2 and 3. The crystal structure prediction study, using a specifically developed anisotropic atom-atom potential for chlorothalonil, gave as the global minimum in the lattice energy a structure that was readily refined against powder diffraction data to the known form 1 (P2(1)/a). The structure of form 2 was solved and refined from powder diffraction data, giving a disordered structure in the Rm (166) space group (Z = 3). It could also be refined against a P1 ordered model, starting from a low-energy hypothetical sheet structure found in the computational search. This shows that the disorder could be associated with the stacking of ordered sheets. The disordered structure for form 2 was later confirmed by single-crystal X-ray diffraction. The structure of form 3, determined from single-crystal diffraction, contains three independent molecules in the asymmetric unit in P2(1) (4) (Z = 6). Powder diffraction showed that this single-herringbone structure was similar to two low-energy structures found in the search. Further analysis confirmed that form 3 has a similar lattice energy and contains elements from both these predicted structures, which can be considered as good approximations to the form 3 structure.     

Disappearing Polymorphs Revisited

Nearly twenty years ago, Dunitz and Bernstein described a selection of intriguing cases of polymorphs that disappear. The inability to obtain a crystal form that has previously been prepared is indeed a frustrating and potentially serious problem for solid‐state scientists. This Review discusses recent occurrences and examples of disappearing polymorphs (as well as the emergence of elusive crystal forms) to demonstrate the enduring relevance of this troublesome, but always captivating, phenomenon in solid‐state research. A number of these instances have been central issues in patent litigations. This Review, therefore, also highlights the complex relationship between crystal chemistry and the law.     

Molecular recognition and crystal energy landscapes: an X-ray and computational study of caffeine and other methylxanthines

We introduce a new approach to crystal-packing analysis, based on the study of mutual recognition modes of entire molecules or of molecular moieties, rather than a search for selected atom-atom contacts, and on the study of crystal energy landscapes over many computer-generated polymorphs, rather than a quest for the one most stable crystal structure. The computational tools for this task are a polymorph generator and the PIXEL density sums method for the calculation of intermolecular energies. From this perspective, the molecular recognition, crystal packing, and solid-state phase behavior of caffeine and several methylxanthines (purine-2,6-diones) have been analyzed. Many possible crystal structures for anhydrous caffeine have been generated by computer simulation, and the most stable among them is a thermodynamic, ordered equivalent of the disordered phase, revealed by powder X-ray crystallography. Molecular recognition energies between two caffeine molecules or between caffeine and water have been calculated, and the results reveal the largely predominant mode to be the stacking of parallel caffeine molecules, an intermediately favorable caffeine-water interaction, and many other equivalent energy minima for lateral interactions of much less stabilization power. This last indetermination helps to explain why caffeine does not crystallize easily into an ordered anhydrous structure. In contrast, the mono- and dimethylxanthines (theophylline, theobromine, and the 1,7-isomer, for which we present a single-crystal X-ray study and a lattice energy landscape) do crystallize in anhydrous form thanks to the formation of lateral hydrogen bonds.     

Ab Initio prediction of possible crystal structures for general organic molecules

The performance of a new crystal packing procedure for the ab initio prediction of possible molecular crystal structures is presented. The method is based upon only molecular information, i.e., no unit cell parameters are assumed to be known. The search for the global crystal energy minimum and all local minima inside an energy window is derived from Monte Carlo simulated annealing methods and has been applied to various organic molecules containing heteroatoms and polar groups. A systematic evaluation of the search method and of the quality of the potential energy function has been established. It is demonstrated that the packing of general organic molecules is possible even with standard force fields like CHARMM provided that the charges defining the electrostatic interactions are based upon physical models rather than transferable empirical parameters. Concepts of crystal packing that were based till now upon assumptions and speculations could be proved or disproved by solving directly the extended global optimization problem related to crystal packing. Crystal structures of molecules as complex as those treated in this article have not been, till now, predicted by a computational approach. In one case, a disagreement between the predicted and experimental structure was evident and, based upon the computations, we suspect that the published structure is the wrong one. © 1992 by John Wiley & Sons, Inc.     

Control over Kinetic and Thermodynamically Driven Pathways of Crystallization to Yield Cofacial and Slipped-Stack Dimers in Single Crystals

Control over the molecular packing in the solid state is of utmost importance in regulating the bulk optical properties of organic semiconductors. The electronic coupling between the molecules makes it possible to improve the properties of the bulk materials. This work reports an example of control over the selective formation of polymorphic single crystals of donor–acceptor-type small-molecule compound 25TR by 1) kinetic or 2) thermodynamic course of crystallisation to yield slipped stack (S) and cofacial (C) dimers in the single crystals. The distinct optical characteristics of the C-dimer and S-dimer are summarised. Both forms show significant excitonic interactions in the solid state, and the S-dimeric form has strong yellowish orange fluorescence, whereas the C-dimeric form is non-fluorescent in the crystalline state. DFT calculations and differential scanning calorimetric experiments revealed that the C-dimer polymorph is the thermodynamically stable form with a free energy offset of 0.43 eV in comparison with the S-dimer. Interestingly, the thermodynamically driven non-fluorescent single crystal was found to be convertible to its fluorescent form irreversibly by thermal trigger. The charge-carrier-transport characteristics of these two polymorphs were computed by using the Marcus–Hush formalism. The computations of the charge-carrier-transport behaviour revealed that the S-dimer ( 25TR_(R) ) is ambipolar, whereas the C-dimer ( 25TR_(Y) ) is predominantly n-type.