Combined crystal structure prediction and high-pressure crystallization in rational pharmaceutical polymorph screening

High-Pressure and Temperature Effects on the Clustering Ability of Monohydroxy Alcohols

This study examined the clustering behavior of monohydroxy alcohols, where hydrogen-bonded clusters of up to a hundred molecules on the nanoscale can form. By performing X-ray diffraction experiments at different temperatures and under high pressure, we investigated how these conditions affect the ability of alcohols to form clusters. The pioneering high-pressure experiment performed on liquid alcohols contributes to the emerging knowledge in this field. Implementation of molecular dynamics simulations yielded excellent agreement with the experimental results, enabling the analysis of theoretical models. Here we show that at the same global density achieved either by alteration of pressure or temperature, the local aggregation of molecules at the nanoscale may significantly differ. Surprisingly, high pressure not only promotes the formation of hydrogen-bonded clusters but also induces the serious reorganization of molecules. This research represents a milestone in understanding association under extreme thermodynamic conditions in other hydrogen bonding systems such as water.

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

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

Organic crystal structure prediction via coupled generative adversarial networks and graph convolutional networks

Organic crystal structures exert a profound impact on the physicochemical properties and biological effects of organic compounds. Quantum mechanics (QM)-based crystal structure predictions (CSPs) have somewhat alleviated the dilemma that experimental crystal structure investigations struggle to conduct complete polymorphism studies, but the high computing cost poses a challenge to its widespread application. The present study aims to construct DeepCSP, a feasible pure machine learning framework for minute-scale rapid organic CSP. Initially, based on 177,746 data entries from the Cambridge Crystal Structure Database, a generative adversarial network was built to conditionally generate trial crystal structures under selected feature constraints for the given molecule. Simultaneously, a graph convolutional attention network was used to predict the density of stable crystal structures for the input molecule. Subsequently, the distances between the predicted density and the definition-based calculated density would be considered to be the crystal structure screening and ranking basis, and finally, the density-based crystal structure ranking would be output. Two such distinct algorithms, performing the generation and ranking functionalities, respectively, collectively constitute the DeepCSP, which has demonstrated compelling performance in marketed drug validations, achieving an accuracy rate exceeding 80% and a hit rate surpassing 85%. Inspiringly, the computing speed of the pure machine learning methodology demonstrates the potential of artificial intelligence in advancing CSP research.

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

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

Predicting crystal form stability under real-world conditions

The physicochemical properties of molecular crystals, such as solubility, stability, compactability, melting behaviour and bioavailability, depend on their crystal form1. In silico crystal form selection has recently come much closer to realization because of the development of accurate and affordable free-energy calculations2-4. Here we redefine the state of the art, primarily by improving the accuracy of free-energy calculations, constructing a reliable experimental benchmark for solid-solid free-energy differences, quantifying statistical errors for the computed free energies and placing both hydrate crystal structures of different stoichiometries and anhydrate crystal structures on the same energy landscape, with defined error bars, as a function of temperature and relative humidity. The calculated free energies have standard errors of 1-2 kJ mol-1 for industrially relevant compounds, and the method to place crystal structures with different hydrate stoichiometries on the same energy landscape can be extended to other multi-component systems, including solvates. These contributions reduce the gap between the needs of the experimentalist and the capabilities of modern computational tools, transforming crystal structure prediction into a more reliable and actionable procedure that can be used in combination with experimental evidence to direct crystal form selection and establish control5.

Exploration of the physical states of riboflavin (free base) by mechanical milling

Amorphous riboflavin (free base) could be produced for the first time via high energy ball milling of a commercial crystalline form (Form I). Importantly, this solid state amorphization process allowed to circumvent chemical degradation occurring during melting as well as the lack of suitable solvents, which are required for amorphization via spray- or freeze-drying. The amorphous state of riboflavin was thoroughly characterized, revealing a complex recrystallization pattern upon heating, involving two enantiotropic polymorphic forms (II and III) and a dihydrate. The glass transition temperature (Tg) and heat capacity (Cp) jump of the amorphous form were determined as 144 °C and 0.68 J/g/°C. Moreover, the relative physical stability of the different physical states has been elucidated, e.g., at room temperature: I > II > III. The following rank order was observed for the dissolution rates in water at 37 °C during the first 4 h: amorphous > III ≈ II > I. Afterwards, a dihydrate crystallized from the solutions of amorphous and metastable crystalline riboflavin forms, the solubility of which was well above the solubility of the stable FormI.

Pushing Technique Boundaries to Probe Conformational Polymorphism

We present an extensive exploration of the solid-form landscape of chlorpropamide (CPA) using a combined experimental-computational approach at the frontiers of both fields. We have obtained new conformational polymorphs of CPA, placing them into context with known forms using flexible-molecule crystal structure prediction. We highlight the formation of a new polymorph (ζ-CPA) via spray-drying experiments despite its notable metastability (14 kJ/mol) relative to the thermodynamic α-form, and we identify and resolve the ball-milled η-form isolated in 2019. Additionally, we employ impurity- and gel-assisted crystallization to control polymorphism and the formation of novel multicomponent forms. We, thus, demonstrate the power of this collaborative screening approach to observe, rationalize, and control the formation of new metastable forms.

Review of Applications of Density Functional Theory (DFT) Quantum Mechanical Calculations to Study the High-Pressure Polymorphs of Organic Crystalline Materials

Since its inception, chemistry has been predominated by the use of temperature to generate or change materials, but applications of pressure of more than a few tens of atmospheres for such purposes have been rarely observed. However, pressure is a very effective thermodynamic variable that is increasingly used to generate new materials or alter the properties of existing ones. As computational approaches designed to simulate the solid state are normally tuned using structural data at ambient pressure, applying them to high-pressure issues is a highly challenging test of their validity from a computational standpoint. However, the use of quantum chemical calculations, typically at the level of density functional theory (DFT), has repeatedly been shown to be a great tool that can be used to both predict properties that can be later confirmed by experimenters and to explain, at the molecular level, the observations of high-pressure experiments. This article's main goal is to compile, analyze, and synthesize the findings of works addressing the use of DFT in the context of molecular crystals subjected to high-pressure conditions in order to give a general overview of the possibilities offered by these state-of-the-art calculations.

Ab Initio Crystal Structure Prediction of the Energetic Materials LLM-105, RDX, and HMX

Crystal structure prediction (CSP) is performed for the energetic materials (EMs) LLM-105 and α-RDX, as well as the α and β conformational polymorphs of 1,3,5,7-tetranitro-1,3,5,7-tetraazacyclooctane (HMX), using the genetic algorithm (GA) code, GAtor, and its associated random structure generator, Genarris. Genarris and GAtor successfully generate the experimental structures of all targets. GAtor's symmetric crossover scheme, where the space group symmetries of parent structures are treated as genes inherited by offspring, is found to be particularly effective. However, conducting several GA runs with different settings is still important for achieving diverse samplings of the potential energy surface. For LLM-105 and α-RDX, the experimental structure is ranked as the most stable, with all of the dispersion-inclusive density functional theory (DFT) methods used here. For HMX, the α form was persistently ranked as more stable than the β form, in contrast to experimental observations, even when correcting for vibrational contributions and thermal expansion. This may be attributed to insufficient accuracy of dispersion-inclusive DFT methods or to kinetic effects not considered here. In general, the ranking of some putative structures is found to be sensitive to the choice of the DFT functional and the dispersion method. For LLM-105, GAtor generates a putative structure with a layered packing motif, which is desirable thanks to its correlation with low sensitivity. Our results demonstrate that CSP is a useful tool for studying the ubiquitous polymorphism of EMs and shows promise of becoming an integral part of the EM development pipeline.

Reducing overprediction of molecular crystal structures via threshold clustering

Crystal structure prediction is becoming an increasingly valuable tool for assessing polymorphism of crystalline molecular compounds, yet invariably, it overpredicts the number of polymorphs. One of the causes for this overprediction is in neglecting the coalescence of potential energy minima, separated by relatively small energy barriers, into a single basin at finite temperature. Considering this, we demonstrate a method underpinned by the threshold algorithm for clustering potential energy minima into basins, thereby identifying kinetically stable polymorphs and reducing overprediction.

The Phase Diagram of the API Benzocaine and Its Highly Persistent, Metastable Crystalline Polymorphs

The availability of sufficient amounts of form I of benzocaine has led to the investigation of its phase relationships with the other two existing forms, II and III, using adiabatic calorimetry, powder X-ray diffraction, and high-pressure differential thermal analysis. The latter two forms were known to have an enantiotropic phase relationship in which form III is stable at low-temperatures and high-pressures, while form II is stable at room temperature with respect to form III. Using adiabatic calorimetry data, it can be concluded, that form I is the stable low-temperature, high-pressure form, which also happens to be the most stable form at room temperature; however, due to its persistence at room temperature, form II is still the most convenient polymorph to use in formulations. Form III presents a case of overall monotropy and does not possess any stability domain in the pressure-temperature phase diagram. Heat capacity data for benzocaine have been obtained by adiabatic calorimetry from 11 K to 369 K above its melting point, which can be used to compare to results from in silico crystal structure prediction.

Rational design and topochemical synthesis of polymorphs of a polymer

Packing a polymer in different ways can give polymorphs of the polymer having different properties. β-Turn forming peptides such as 2-aminoisobutyric acid (Aib)-rich peptides adopt several conformations by varying the dihedral angles. Aiming at this, a β-turn-forming peptide monomer would give different polymorphs and these polymorphs upon topochemical polymerization would yield polymorphs of the polymer, we designed an Aib-rich monomer N₃-(Aib)₃-NHCH₂-C[triple bond, length as m-dash]CH. This monomer crystallizes as two polymorphs and one hydrate. In all forms, the peptide adopts β-turn conformations and arranges in a head-to-tail manner with their azide and alkyne units proximally placed in a ready-to-react alignment. On heating, both the polymorphs undergo topochemical azide-alkyne cycloaddition polymerization. Polymorph I polymerized in a single-crystal-to-single-crystal (SCSC) fashion and the single-crystal X-ray diffraction analysis of the polymer revealed its screw-sense reversing helical structure. Polymorph II maintains its crystallinity during polymerization but gradually becomes amorphous upon storage. The hydrate III undergoes a dehydrative transition to polymorph II. Nanoindentation studies revealed that different polymorphs of the monomer and the corresponding polymers exhibited different mechanical properties, in accordance with their crystal packing. This work demonstrates the promising future of the marriage of polymorphism and topochemistry for obtaining polymorphs of polymers.

Vapor Sorption and Halogen-Bond-Induced Solid-Form Rearrangement of a Porous Pharmaceutical

A porous, nonsolvated polymorph of the voltage-gated sodium channel blocker mexiletine hydrochloride absorbs iodine vapor to give a pharmaceutical cocrystal incorporating an I₂Cl^- anion that forms a halogen-π interaction with the mexiletine cations. The most thermodynamically stable form of the compound does not absorb iodine. This example shows that vapor sorption is a potentially useful and underused tool for bringing about changes in pharmaceutical solid form as part of a solid form screening protocol.

Inverse Design of Tetracene Polymorphs with Enhanced Singlet Fission Performance by Property-Based Genetic Algorithm Optimization

The efficiency of solar cells may be improved by using singlet fission (SF), in which one singlet exciton splits into two triplet excitons. SF occurs in molecular crystals. A molecule may crystallize in more than one form, a phenomenon known as polymorphism. Crystal structure may affect SF performance. In the common form of tetracene, SF is experimentally known to be slightly endoergic. A second, metastable polymorph of tetracene has been found to exhibit better SF performance. Here, we conduct inverse design of the crystal packing of tetracene using a genetic algorithm (GA) with a fitness function tailored to simultaneously optimize the SF rate and the lattice energy. The property-based GA successfully generates more structures predicted to have higher SF rates and provides insight into packing motifs associated with improved SF performance. We find a putative polymorph predicted to have superior SF performance to the two forms of tetracene, whose structures have been determined experimentally. The putative structure has a lattice energy within 1.5 kJ/mol of the most stable common form of tetracene.

A phase variety of fluorinated ionic liquids: Molecular conformational and crystal polymorph

Crystal polymorphs of fluorinated ionic liquids (fILs) were examined at low-temperature (LT) by Raman spectroscopy. The fILs were 1-alkyl-3-methylimidazolium perfluorobutanesulfonate, [C_nmim][PFBS] (n = 4, 6, and 8). The cations and anion possess conformational degrees of freedom. Various LT phases were derived from the conformational polymorphs of the cations and the anion. Conformational flexibility depended on alkyl chain length. The crystal polymorphs in the fILs were sensitive to molecular conformations and flexibility.

A theoretical framework for the design of molecular crystal engines

Photomechanical molecular crystals have garnered attention for their ability to transform light into mechanical work, but difficulties in characterizing the structural changes and mechanical responses experimentally have hindered the development of practical organic crystal engines. This study proposes a new computational framework for predicting the solid-state crystal-to-crystal photochemical transformations entirely from first principles, and it establishes a photomechanical engine cycle that quantifies the anisotropic mechanical performance resulting from the transformation. The approach relies on crystal structure prediction, solid-state topochemical principles, and high-quality electronic structure methods. After validating the framework on the well-studied [4 + 4] cycloadditions in 9-methyl anthracene and 9-tert-butyl anthracene ester, the experimentally-unknown solid-state transformation of 9-carboxylic acid anthracene is predicted for the first time. The results illustrate how the mechanical work is done by relaxation of the crystal lattice to accommodate the photoproduct, rather than by the photochemistry itself. The large ∼10⁷ J m^-3 work densities computed for all three systems highlight the promise of photomechanical crystal engines. This study demonstrates the importance of crystal packing in determining molecular crystal engine performance and provides tools and insights to design improved materials in silico.

Phase Transitions and Stabilities among Three Phases of Di-p-tolyl Disulfides

Di-p-tolyl disulfides (p-Tol₂S₂) are employed as load-carrying additives because of their anti-wear and extreme load-bearing qualities. External pressure triggers conformational up-conversion (leads to phase transition) in the molecules of p-Tol₂S₂, by compensating for the stress and absorbing its energy. These features make p-Tol₂S₂ a potential candidate for next-generation energy storage devices. Upon lithiation, MoS₂ expands up to 103% which causes stress and affects battery stability and performance. Therefore, it is essential to study these materials under different physical conditions. In this work, we used density functional theory (DFT) at ωB97XD/6-31G* functional level, to calculate lattice parameters, Gibbs free energies, and vibrational spectra of three phases (i.e., α, β, and γ) of p-Tol₂S₂ under different pressure and temperature conditions. The phase transition between phases α and β occurred at a pressure and temperature of 0.65 GPa and 463 K, respectively. Furthermore, phase transition between phases α and γ was found at a pressure and temperature of 0.35 GPa and 400 K, respectively. Moreover, no phase transition was observed between phases β and γ under the pressure range studied (0 GPa to 5.5 GPa). We also computed and compared the FT-IR spectra of the three phases. These results can guide scientists and chemists in designing more stable battery materials.

Efficient Crystal Structure Prediction for Structurally Related Molecules with Accurate and Transferable Tailor-Made Force Fields

Crystal structure prediction (CSP) his generally used to complement experimental solid form screening and applied to individual molecules in drug development. The fast development of algorithms and computing resources offers the opportunity to use CSP earlier and for a broader range of applications in the drug design cycle. This study presents a novel paradigm of CSP specifically designed for structurally related molecules, referred to as Quick-CSP. The approach prioritizes more accurate physics through robust and transferable tailor-made force fields (TMFFs), such that significant efficiency gains are achieved through the reduction of expensive ab initio calculations. The accuracy of the TMFF is increased by the introduction of electrostatic multipoles, and the fragment-based force field parameterization scheme is demonstrated to be transferable for a family of chemically related molecules. The protocol is benchmarked with structurally related compounds from the Bromodomain and Extraterminal (BET) domain inhibitors series. A new convergence criterion is introduced that aims at performing only as many ab initio optimizations of crystal structures as required to locate the bottom of the crystal energy landscape within a user-defined accuracy. The overall approach provides significant cost savings ranging from three- to eight-fold less than the full-CSP workflow. The reported advancements expand the scope and utility of the underlying CSP building blocks as well as their novel reassembly to other applications earlier in the drug design cycle to guide molecule design and selection.

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

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

Complete resonance assignment of a pharmaceutical drug at natural isotopic abundance from DNP-Enhanced solid-state NMR

Solid-state dynamic nuclear polarization enhanced magic angle spinning (DNP-MAS) NMR measurements coupled with density functional theory (DFT) calculations enable the full resonance assignment of a complex pharmaceutical drug molecule without the need for isotopic enrichment. DNP dramatically enhances the NMR signals, thereby making possible previously intractable two-dimensional correlation NMR spectra at natural abundance. Using inputs from DFT calculations, herein we describe a significant improvement to the structure elucidation process for complex organic molecules. Further, we demonstrate that a series of two-dimensional correlation experiments, including ¹⁵N-¹³C TEDOR, ¹³C-¹³C INADEQUATE/SARCOSY, ¹⁹F-¹³C HETCOR, and ¹H-¹³C HETCOR, can be obtained at natural isotopic abundance within reasonable experiment times, thus enabling a complete resonance assignment of sitagliptin, a pharmaceutical used for the treatment of type 2 diabetes.

High-Pressure Polymorphism in Hydrogen-Bonded Crystals: A Concise Review

High-pressure polymorphism is a developing interdisciplinary field. Pressure up to 20 GPa is a powerful thermodynamic parameter for the study and fabrication of hydrogen-bonded polymorphic systems. This review describes how pressure can be used to explore polymorphism and surveys the reports on examples of compounds that our group has studied at high pressures. Such studies have provided insight into the nature of structure–property relationships, which will enable crystal engineering to design crystals with desired architectures through hydrogen-bonded networks. Experimental methods are also briefly surveyed, along with two methods that have proven to be very helpful in the analysis of high-pressure polymorphs, namely, the ab initio pseudopotential plane–wave density functional method and using Hirshfeld surfaces to construct a graphical overview of intermolecular interactions.

The interplay of intra- and intermolecular errors in modeling conformational polymorphs

Conformational polymorphs of organic molecular crystals represent a challenging test for quantum chemistry because they require careful balancing of the intra- and intermolecular interactions. This study examines 54 molecular conformations from 20 sets of conformational polymorphs, along with the relative lattice energies and 173 dimer interactions taken from six of the polymorph sets. These systems are studied with a variety of van der Waals-inclusive density functionals theory models; dispersion-corrected spin-component-scaled second-order Møller–Plesset perturbation theory (SCS-MP2D); and domain local pair natural orbital coupled cluster singles, doubles, and perturbative triples [DLPNO-CCSD(T)]. We investigate how delocalization error in conventional density functionals impacts monomer conformational energies, systematic errors in the intermolecular interactions, and the nature of error cancellation that occurs in the overall crystal. The density functionals B86bPBE-XDM, PBE-D4, PBE-MBD, PBE0-D4, and PBE0-MBD are found to exhibit sizable one-body and two-body errors vs DLPNO-CCSD(T) benchmarks, and the level of success in predicting the relative polymorph energies relies heavily on error cancellation between different types of intermolecular interactions or between intra- and intermolecular interactions. The SCS-MP2D and, to a lesser extent, ωB97M-V models exhibit smaller errors and rely less on error cancellation. Implications for crystal structure prediction of flexible compounds are discussed. Finally, the one-body and two-body DLPNO-CCSD(T) energies taken from these conformational polymorphs establish the CP1b and CP2b benchmark datasets that could be useful for testing quantum chemistry models in challenging real-world systems with complex interplay between intra- and intermolecular interactions, a number of which are significantly impacted by delocalization error.

Psilocybin: Characterization of the Metastable Zone Width (MSZW), Control of Anhydrous Polymorphs, and Particle Size Distribution (PSD)

Psilocybin, a serotonergic agonist, was granted a "breakthrough therapy" status by the Food and Drug Administration for clinical trials involving major depressive disorder and treatment-resistant depression. The direct phosphorylation of psilocin to psilocybin that uses a fast crystallization associated with a kinetically controlled process resulted in a smaller particle size distribution. Herein, the measurement of the metastable zone width (MSZW) and nucleation induction enabled a thermodynamically controlled crystallization process, which leads to the formation of a crystal structure with stronger interactions, controlled particle size distribution (PSD), and improved impurity profile. Employing a high-resolution inline microscopy viewer allowed the real-time monitoring of the crystallization process and the measurement of the particle size. We also present a comprehensive study of the formation of polymorph B (trihydrate), polymorph A (anhydrate), and polymorph H (anhydrate) using water recrystallization, which indicates that the formation of polymorph B (trihydrate) is independent of the crystallization method. However, polymorphs A and H are dependent on the mode of drying: drying at room temperature under vacuum gives rise to mainly polymorph A, and when heated even at relatively low temperatures, a mixture of polymorphs A and H beings to form.

Crystal structure prediction of N-halide phthalimide compounds: Halogen bond synthon as a touchstone

We address crystal structure prediction problem by combining evolutionary algorithm USPEX (used to predict sets of low-energy crystal structures) and synthon approach (extracting preferable supramolecular synthons from Cambridge Structural Database,...

High-pressure Bandgap Engineering and Amorphization in TiNb2O7 Single Crystals

Titanium niobate (TiNb2O7) possesses excellent photocatalytic, dielectric properties, and lithium-insertion capacity. And high-pressure (HP) is a powerful tool for bandgap engineering aiming at widening their applications. Herein, we report the...

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

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

Accessing a regiospecific isomer and a metastable polymorph through crystal engineering and solid-state reaction

We describe a solid-state Diels–Alder reaction where crystal engineering was used to design a reaction site yielding one regioisomer. Reaction was followed with SCXRD, compared to solution synthesis and rationalised using computational modelling.

How many more polymorphs of ROY remain undiscovered

With 12 crystal forms, 5-methyl-2-[(2-nitrophenyl)amino]-3-thiophenecabonitrile (a.k.a. ROY) holds the current record for the largest number of fully characterized organic crystal polymorphs. Four of these polymorph structures have been reported since 2019, raising the question of how many more ROY polymorphs await future discovery. Employing crystal structure prediction and accurate energy rankings derived from conformational energy-corrected density functional theory, this study presents the first crystal energy landscape for ROY that agrees well with experiment. The lattice energies suggest that the seven most stable ROY polymorphs (and nine of the twelve lowest-energy forms) on the Z′ = 1 landscape have already been discovered experimentally. Discovering any new polymorphs at ambient pressure will likely require specialized crystallization techniques capable of trapping metastable forms. At pressures above 10 GPa, however, a new crystal form is predicted to become enthalpically more stable than all known polymorphs, suggesting that further high-pressure experiments on ROY may be warranted. This work highlights the value of high-accuracy crystal structure prediction for solid-form screening and demonstrates how pragmatic conformational energy corrections can overcome the limitations of conventional density functionals for conformational polymorphs.

Crystal structure prediction suggests that the low-energy polymorphs of ROY have already been found, but a new high-pressure form is predicted.

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

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

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.

Modeling the α- and β-resorcinol phase boundary via combination of density functional theory and density functional tight-binding

The ability to predict not only what organic crystal structures might occur but also the thermodynamic conditions under which they are the most stable would be extremely useful for discovering and designing new organic materials. The present study takes a step in that direction by predicting the temperature- and pressure-dependent phase boundary between the α and β polymorphs of resorcinol using density functional theory (DFT) and the quasi-harmonic approximation. To circumvent the major computational bottleneck associated with computing a well-converged phonon density of states via the supercell approach, a recently developed approximation is employed, which combines a supercell phonon density of states from dispersion-corrected third-order density functional tight binding [DFTB3-D3(BJ)] with frequency corrections derived from a smaller B86bPBE-XDM functional DFT phonon calculation on the crystallographic unit cell. This mixed DFT/DFTB quasi-harmonic approach predicts the lattice constants and unit cell volumes to within 1%-2% at lower pressures. It predicts the thermodynamic phase boundary in almost perfect agreement with the experiment, although this excellent agreement does reflect fortuitous cancellation of errors between the enthalpy and entropy of transition.

Ab initio determination of crystal stability of di-p-tolyl disulfide

With the rapid growth of energy demand and the depletion of existing energy resources, the new materials with superior performances, low costs and environmental friendliness for energy production and storage are explored. Di-p-tolyl disulfide (p-Tol₂S₂) is a typical lubricating material, which has been applied in the field of energy storage. The conformational properties and phase transformations of p-Tol₂S₂ have been studied by pioneers, but their polymorphs and the polymorphism induced crystal structure changes require further analysis. In this study, we perform the crystal structural screening, prediction and optimization of p-Tol₂S₂ crystal with quantum mechanical calculations, i.e., density functional theory (DFT) and second-order Møller–Plesset perturbation (MP2) methods. A series of crystal structures with different molecular arrangements are generated based on the crystal structure screening. As compared to long-established lattice energy calculation, we take an advantage of using more accurate technique, which is Gibbs free energy calculation. It considers the effects of entropy and temperature to predict the crystal structures and energy landscape. By comparing the Gibbs free energies between predicted and experimental structures, we found that phase α is the most stable structure for p-Tol₂S₂ crystal at ambient temperature and standard atmospheric pressure. Furthermore, we provide an efficient method to discriminate different polymorphs that are otherwise difficult to be identified based on the Raman/IR spectra. The proposed work enable us to evaluate the quality of various crystal polymorphs rapidly.

Crystal Structure Prediction Methods for Organic Molecules: State of the Art

The prediction of the crystal structures that a given organic molecule is likely to form is an important theoretical problem of significant interest for the pharmaceutical and agrochemical industries, among others. As evidenced by a series of six blind tests organized over the past 2 decades, methodologies for crystal structure prediction (CSP) have witnessed substantial progress and have now reached a stage of development where they can begin to be applied to systems of practical significance. This article reviews the state of the art in general-purpose methodologies for CSP, placing them within a common framework that highlights both their similarities and their differences. The review discusses specific areas that constitute the main focus of current research efforts toward improving the reliability and widening applicability of these methodologies, and offers some perspectives for the evolution of this technology over the next decade.

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.

Improved quantitative crystal-structure comparison using powder diffractograms via anisotropic volume correction

A new anisotropic volume correction improves quantitative crystal structure comparison. Benchmarking against the 6th crystal structure prediction blind test data results in identification of two previously uncredited matching structures.

Structure prediction of crystals, surfaces and nanoparticles

We review the current techniques used in the prediction of crystal structures and their surfaces and of the structures of nanoparticles. The main classes of search algorithm and energy function are summarized, and we discuss the growing role of methods based on machine learning. We illustrate the current status of the field with examples taken from metallic, inorganic and organic systems. This article is part of a discussion meeting issue 'Dynamic in situ microscopy relating structure and function'.

Generating Cocrystal Polymorphs with Information Entropy Driven by Molecular Dynamics-Based Enhanced Sampling

Predicting structures of organic molecular cocrystals is a challenging task when considering the immense number of possible intermolecular orientations. Use of the Shannon information entropy, constructed from an intermolecular orientational spatial distribution function, to drive a search for crystal structures via enhanced molecular dynamics can be an efficient way to map out a landscape of putative polymorphs. Here, the Shannon entropy is used to generate a set of collective variables for differentiating polymorphs of a 1:1 cocrystal of resorcinol and urea. We show that driven adiabatic free energy dynamics, a particular enhanced-sampling approach, combined with these entropy variables, can transform the stable phase into alternate polymorphs. Density functional theory calculations confirm that a structure obtained from the enhanced molecular dynamics is stable at pressures above 1 GPa. We thus show that enhanced sampling should be considered an integral component of crystal structure searching protocols for systems with multiple independent molecules.

Transforming Computed Energy Landscapes into Experimental Realities: The Role of Structural Rugosity

We exploit the possible link between structural surface roughness and difficulty of crystallisation. Polymorphs with smooth surfaces may nucleate and crystallise more readily than polymorphs with rough surfaces. The concept is applied to crystal structure prediction landscapes and reveals a promising complementary way of ranking putative crystal structures.

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.

Crystal forms in pharmaceutical applications: olanzapine, a gift to crystal chemistry that keeps on giving

This contribution reviews the efforts of many scientists around the world to discover and structurally characterize olanzapine crystal forms, clearing up inconsistencies in the scientific and patent literature and highlighting the challenges in identifying new forms amidst 60+ known polymorphs and solvates. Owing to its remarkable solid-state chemistry, olanzapine has emerged over the last three decades as a popular tool compound for developing new experimental and computational methods for enhanced molecular level understanding of solid-state structure, form diversity and crystallization outcomes. This article highlights the role of olanzapine in advancing the fundamental understanding of crystal forms, interactions within crystal structures, and growth units in molecular crystallization, as well as influencing the way in which drugs are developed today.

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.