Progress in Crystal Structure Prediction

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.

Tailoring the dimensionality of metal complexes via ligand modifications

A series of CuII complexes obtained under the same reaction conditions has been analyzed to gain insight into the effect of the ligand composition on the final reaction product. Dipodal ligands containing N-donor imidazole rings and a benzene ring as a spacer with different numbers of methyl substituents on the aromatic rings were selected for the study such as 1,3-bis(imidazol-1-ylmethyl)benzene (L1), 1,3-bis(imidazol-1-ylmethyl)-5-methylbenzene (L2), 1,3-bis(imidazol-1-ylmethyl)-2,4,6-trimethylbenzene (L3), 1,3-bis(2-methylimidazol-1-ylmethyl)-2,4,6-trimethylbenzene (L4). L4 has not been reported previously and was synthesized for this study. The formed metal complexes show the presence of polymeric (ligand with no or one methyl substituent; 1-4), or discrete motifs (3- or 5-methyl substituents; 5-7). The new metal complexes 3, 5 and 6 were analyzed using single-crystal X-ray diffraction and powder diffraction. In addition, the structural analyses were supported by computational methods.

XDM-corrected hybrid DFT with numerical atomic orbitals predicts molecular crystal lattice energies with unprecedented accuracy

Molecular crystals are important for many applications, including energetic materials, organic semiconductors, and the development and commercialization of pharmaceuticals. The exchange-hole dipole moment (XDM) dispersion model has shown good performance in the calculation of relative and absolute lattice energies of molecular crystals, although it has traditionally been applied in combination with plane-wave/pseudopotential approaches. This has limited XDM to use with semilocal functional approximations, which suffer from delocalization error and poor quality conformational energies, and to systems with a few hundreds of atoms at most due to unfavorable scaling. In this work, we combine XDM with numerical atomic orbitals, which enable the efficient use of XDM-corrected hybrid functionals for molecular crystals. We test the new XDM-corrected functionals for their ability to predict the lattice energies of molecular crystals for the X23 set and 13 ice phases, the latter being a particularly stringent test. A composite approach using a XDM-corrected, 25% hybrid functional based on B86bPBE achieves a mean absolute error of 0.48 kcal mol^-1 per molecule for the X23 set and 0.19 kcal mol^-1 for the total lattice energies of the ice phases, compared to recent diffusion Monte-Carlo data. These results make the new XDM-corrected hybrids not only far more computationally efficient than previous XDM implementations, but also the most accurate density-functional methods for molecular crystal lattice energies to date.

Performance of Dispersion-Inclusive Density Functional Theory Methods for Energetic Materials

Molecular crystals of energetic materials (EMs) are denser than typical molecular crystals and are characterized by distinct intermolecular interactions between nitrogen-containing moieties. To assess the performance of dispersion-inclusive density functional theory (DFT) methods, we have compiled a data set of experimental sublimation enthalpies of 31 energetic materials. We evaluate the performance of three methods: the semilocal Perdew-Burke-Ernzerhof (PBE) functional coupled with the pairwise Tkatchenko-Scheffler (TS) dispersion correction, PBE with the many-body dispersion (MBD) method, and the PBE-based hybrid functional (PBE0) with MBD. Zero-point energy contributions and thermal effects are described using the quasi-harmonic approximation (QHA), including explicit treatment of thermal expansion, which we find to be non-negligible for EMs. The lattice energies obtained with PBE0+MBD are the closest to experimental sublimation enthalpies with a mean absolute error of 9.89 kJ/mol. However, the state-of-the-art treatment of vibrational and thermal contributions makes the agreement with experiment worse. Pressure-volume curves are also examined for six representative materials. For pressure-volume curves, all three methods provide reasonable agreement with experimental data with mean absolute relative errors of 3% or less. Most of the intermolecular interactions typical of EMs, namely nitro-amine, nitro-nitro, and nitro-hydrogen interactions, are more sensitive to the choice of the dispersion method than to the choice of the exchange-correlation functional. The exception is π-π stacking interactions, which are also very sensitive to the choice of the functional. Overall, we find that PBE+TS, PBE+MBD, and PBE0+MBD do not perform as well for energetic materials as previously reported for other classes of molecular crystals. This highlights the importance of testing dispersion-inclusive DFT methods for diverse classes of materials and the need for further method development.

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,...

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...

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.

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.

Prediction of lattice energy of benzene crystals: A robust theoretical approach

We present an inexpensive and robust theoretical approach based on the fragment molecular orbital methodology and the spin-ratio scaled second-order Møller-Plesset perturbation theory to predict the lattice energy of benzene crystals within 2 kJ⋅mol^-1 . Inspired by the Harrison method to estimate the Madelung constant, the proposed approach calculates the lattice energy as a sum of two- and three-body interaction energies between a reference molecule and the surrounding molecules arranged in a sphere. The lattice energy converges rapidly at a radius of 13 Å. Adding the corrections to account for a higher correlated level of theory and basis set superposition for the Hartree Fock (HF) level produced a lattice energy of -57.5 kJ⋅mol^-1 for the benzene crystal structure at 138 K. This estimate is within 1.6 kJ⋅mol^-1 off the best theoretical prediction of -55.9 kJ⋅mol^-1 . We applied this approach to calculate lattice energies of the crystal structures of phase I and phase II-polymorphs of benzene-observed at a higher temperature of 295 K. The stability of these polymorphs was correctly predicted, with phase II being energetically preferred by 3.7 kJ⋅mol^-1 over phase I. The proposed approach gives a tremendous potential to predict stability of other molecular crystal polymorphs.

Crystal structure prediction of energetic materials and a twisted arene with Genarris and GAtor

A molecular crystal structure prediction workflow, based on the random structure generator, Genarris, and the genetic algorithm (GA), GAtor, is successfully applied to two energetic materials and a chiral arene.

Validation of the supramolecular synthon preference through DFT and physicochemical property investigations of pyridyl salts of organo-sulfonates

Understanding of the supramolecular synthon competition is sparse and the synthon hierarchy studies are limited. Herein, we validate the synthon preferences in multi-functional organic precursor through DFT and crystallographic studies.

Diabat method for polymorph free energies: Extension to molecular crystals

Lattice-switch Monte Carlo and the related diabat methods have emerged as efficient and accurate ways to compute free energy differences between polymorphs. In this work, we introduce a one-to-one mapping from the reference positions and displacements in one molecular crystal to the positions and displacements in another. Two features of the mapping facilitate lattice-switch Monte Carlo and related diabat methods for computing polymorph free energy differences. First, the mapping is unitary so that its Jacobian does not complicate the free energy calculations. Second, the mapping is easily implemented for molecular crystals of arbitrary complexity. We demonstrate the mapping by computing free energy differences between polymorphs of benzene and carbamazepine. Free energy calculations for thermodynamic cycles, each involving three independently computed polymorph free energy differences, all return to the starting free energy with a high degree of precision. The calculations thus provide a force field independent validation of the method and allow us to estimate the precision of the individual free energy differences.

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.

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

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

The PO13 crystal structure of ROY

A novel pumpkin-orange polymorph of ROY was matched to a predicted structure and refined to PXRD data.

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

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

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

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

Control and prediction of the organic solid state: a challenge to theory and experiment†

The ability of theoretical chemists to quantitatively model the weak forces between organic molecules is being exploited to predict their crystal structures and estimate their physical properties. Evolving crystal structure prediction methods are increasingly being used to aid the design of organic functional materials and provide information about thermodynamically plausible polymorphs of speciality organic materials to aid, for example, pharmaceutical development. However, the increasingly sophisticated experimental studies for detecting the range of organic solid-state behaviours provide many challenges for improving quantitative theories that form the basis for the computer modelling. It is challenging to calculate the relative thermodynamic stability of different organic crystal structures, let alone understand the kinetic effects that determine which polymorphs can be observed and are practically important. However, collaborations between experiment and theory are reaching the stage of devising experiments to target the first crystallization of new polymorphs or create novel organic molecular materials.

Heterogeneous nucleation of polymorphs on polymer surfaces: polymer-molecule interactions using a heterogeneous dielectric solvation model

We have investigated the mechanism of the nucleation of acetaminophen on poly(methyl-methacrylate) and poly(vinyl-acetate) utilizing a combination of quantum mechanical computations and electrostatic models. We have used a heterogeneous dielectric solvation model to determine the stability of different orientations of acetaminophen on polymer surfaces. We find that for the nucleation of acetaminophen on the polymer surfaces in vacuum, the most stable orientation is a flat orientation. For the nucleation process in solution where acetaminophen and the polymer surface are surrounded by a solvent, we find that the heterogeneous dielectric solvation model predicts that a sideways orientation is the most stable orientation.

A crystal structure prediction enigma solved: the gallic acid monohydrate system - surprises at 10 K

The seemingly unpredictable structure of gallic acid monohydrate form IV has been investigated using accurate X-ray diffraction measurements at temperatures of 10 and 123 K. The measurements demonstrate that the structure is commensurately modulated at 10 K and disordered at higher temperatures. Aided by charge-density modeling and periodic DFT calculations we show that the disorder gives a substantial stabilization of the structure.

How many ritonavir cases are there still out there?

The number of dormant ritonavir cases is estimated based on 41 commercial pharmaceutical crystal structure prediction studies.

Ab initio random structure searching of organic molecular solids: assessment and validation against experimental data

This paper explores the capability of using the DFT-D ab initio random structure searching (AIRSS) method to generate crystal structures of organic molecular materials, focusing on a system (m-aminobenzoic acid; m-ABA) that is known from experimental studies to exhibit abundant polymorphism. Within the structural constraints selected for the AIRSS calculations (specifically, centrosymmetric structures with Z = 4 for zwitterionic m-ABA molecules), the method is shown to successfully generate the two known polymorphs of m-ABA (form III and form IV) that have these structural features. We highlight various issues that are encountered in comparing crystal structures generated by AIRSS to experimental powder X-ray diffraction (XRD) data and solid-state magic-angle spinning (MAS) NMR data, demonstrating successful fitting for some of the lowest energy structures from the AIRSS calculations against experimental low-temperature powder XRD data for known polymorphs of m-ABA, and showing that comparison of computed and experimental solid-state NMR parameters allows different hydrogen-bonding motifs to be discriminated.

Exchange-Hole Dipole Dispersion Model for Accurate Energy Ranking in Molecular Crystal Structure Prediction II: Nonplanar Molecules

The crystal structure prediction (CSP) of a given compound from its molecular diagram is a fundamental challenge in computational chemistry with implications in relevant technological fields. A key component of CSP is the method to calculate the lattice energy of a crystal, which allows the ranking of candidate structures. This work is the second part of our investigation to assess the potential of the exchange-hole dipole moment (XDM) dispersion model for crystal structure prediction. In this article, we study the relatively large, nonplanar, mostly flexible molecules in the first five blind tests held by the Cambridge Crystallographic Data Centre. Four of the seven experimental structures are predicted as the energy minimum, and thermal effects are demonstrated to have a large impact on the ranking of at least another compound. As in the first part of this series, delocalization error affects the results for a single crystal (compound X), in this case by detrimentally overstabilizing the π-conjugated conformation of the monomer. Overall, B86bPBE-XDM correctly predicts 16 of the 21 compounds in the five blind tests, a result similar to the one obtained using the best CSP method available to date (dispersion-corrected PW91 by Neumann et al.). Perhaps more importantly, the systems for which B86bPBE-XDM fails to predict the experimental structure as the energy minimum are mostly the same as with Neumann's method, which suggests that similar difficulties (absence of vibrational free energy corrections, delocalization error,...) are not limited to B86bPBE-XDM but affect GGA-based DFT-methods in general. Our work confirms B86bPBE-XDM as an excellent option for crystal energy ranking in CSP and offers a guide to identify crystals (organic salts, conjugated flexible systems) where difficulties may appear.

The application of tailor-made force fields and molecular dynamics for NMR crystallography: a case study of free base cocaine

Motional averaging has been proven to be significant in predicting the chemical shifts in ab initio solid-state NMR calculations, and the applicability of motional averaging with molecular dynamics has been shown to depend on the accuracy of the molecular mechanical force field. The performance of a fully automatically generated tailor-made force field (TMFF) for the dynamic aspects of NMR crystallography is evaluated and compared with existing benchmarks, including static dispersion-corrected density functional theory calculations and the COMPASS force field. The crystal structure of free base cocaine is used as an example. The results reveal that, even though the TMFF outperforms the COMPASS force field for representing the energies and conformations of predicted structures, it does not give significant improvement in the accuracy of NMR calculations. Further studies should direct more attention to anisotropic chemical shifts and development of the method of solid-state NMR calculations.

Generation of crystal structures using known crystal structures as analogues

This analysis attempts to answer the question of whether similar molecules crystallize in a similar manner. An analysis of structures in the Cambridge Structural Database shows that the answer is yes - sometimes they do, particularly for single-component structures. However, one does need to define what we mean by similar in both cases. Building on this observation we then demonstrate how this correlation between shape similarity and packing similarity can be used to generate potential lattices for molecules with no known crystal structure. Simple intermolecular interaction potentials can be used to minimize these potential lattices. Finally we discuss the many limitations of this approach.

Using crystal structure prediction to rationalize the hydration propensities of substituted adamantane hydrochloride salts

The crystal energy landscapes of the salts of two rigid pharmaceutically active molecules reveal that the experimental structure of amantadine hydrochloride is the most stable structure with the majority of low-energy structures adopting a chain hydrogen-bond motif and packings that do not have solvent accessible voids. By contrast, memantine hydrochloride which differs in the substitution of two methyl groups on the adamantane ring has a crystal energy landscape where all structures within 10 kJ mol−1of the global minimum have solvent-accessible voids ranging from 3 to 14% of the unit-cell volume including the lattice energy minimum that was calculated after removing water from the hydrated memantine hydrochloride salt structure. The success in using crystal structure prediction (CSP) to rationalize the different hydration propensities of these substituted adamantane hydrochloride salts allowed us to extend the model to predict under blind test conditions the experimental crystal structures of the previously uncharacterized 1-(methylamino)adamantane base and its corresponding hydrochloride salt. Although the crystal structure of 1-(methylamino)adamantane was correctly predicted as the second ranked structure on the static lattice energy landscape, the crystallization of aZ′ = 3 structure of 1-(methylamino)adamantane hydrochloride reveals the limits of applying CSP when the contents of the crystallographic asymmetric unit are unknown.

Modeling Polymorphic Molecular Crystals with Electronic Structure Theory

Interest in molecular crystals has grown thanks to their relevance to pharmaceuticals, organic semiconductor materials, foods, and many other applications. Electronic structure methods have become an increasingly important tool for modeling molecular crystals and polymorphism. This article reviews electronic structure techniques used to model molecular crystals, including periodic density functional theory, periodic second-order Møller-Plesset perturbation theory, fragment-based electronic structure methods, and diffusion Monte Carlo. It also discusses the use of these models for predicting a variety of crystal properties that are relevant to the study of polymorphism, including lattice energies, structures, crystal structure prediction, polymorphism, phase diagrams, vibrational spectroscopies, and nuclear magnetic resonance spectroscopy. Finally, tools for analyzing crystal structures and intermolecular interactions are briefly discussed.

Fragment-Based Electronic Structure Approach for Computing Nuclear Magnetic Resonance Chemical Shifts in Molecular Crystals

First-principles chemical shielding tensor predictions play a critical role in studying molecular crystal structures using nuclear magnetic resonance. Fragment-based electronic structure methods have dramatically improved the ability to model molecular crystal structures and energetics using high-level electronic structure methods. Here, a many-body expansion fragment approach is applied to the calculation of chemical shielding tensors in molecular crystals. First, the impact of truncating the many-body expansion at different orders and the role of electrostatic embedding are examined on a series of molecular clusters extracted from molecular crystals. Second, the ability of these techniques to assign three polymorphic forms of the drug sulfanilamide to the corresponding experimental (13)C spectra is assessed. This challenging example requires discriminating among spectra whose (13)C chemical shifts differ by only a few parts per million (ppm) across the different polymorphs. Fragment-based PBE0/6-311+G(2d,p) level chemical shielding predictions correctly assign these three polymorphs and reproduce the sulfanilamide experimental (13)C chemical shifts with 1 ppm accuracy. The results demonstrate that fragment approaches are competitive with the widely used gauge-invariant projector augmented wave (GIPAW) periodic density functional theory calculations.

Predicting finite-temperature properties of crystalline carbon dioxide from first principles with quantitative accuracy

The temperature-dependence of the crystalline carbon dioxide (phase I) structure, thermodynamics, and mechanical properties are predicted in excellent agreement with experiment over a 200 K temperature range using high-level electronic structure calculations.

Molecular crystal structures, thermodynamics, and mechanical properties can vary substantially with temperature, and predicting these temperature-dependencies correctly is important for many practical applications in the pharmaceutical industry and other fields. However, most electronic structure predictions of molecular crystal properties neglect temperature and/or thermal expansion, leading to potentially erroneous results. Here, we demonstrate that by combining large basis set second-order Møller–Plesset (MP2) or even coupled cluster singles, doubles, and perturbative triples (CCSD(T)) electronic structure calculations with a quasiharmonic treatment of thermal expansion, experimentally observable properties such as the unit cell volume, heat capacity, enthalpy, entropy, sublimation point and bulk modulus of phase I crystalline carbon dioxide can be predicted in excellent agreement with experiment over a broad range of temperatures. These results point toward a promising future for ab initio prediction of molecular crystal properties at real-world temperatures and pressures.

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

Organic molecules, such as pharmaceuticals, agro-chemicals and pigments, frequently form several crystal polymorphs with different physicochemical properties. Finding polymorphs has long been a purely experimental game of trial-and-error. Here we utilize in silico polymorph screening in combination with rationally planned crystallization experiments to study the polymorphism of the pharmaceutical compound Dalcetrapib, with 10 torsional degrees of freedom one of the most flexible molecules ever studied computationally. The experimental crystal polymorphs are found at the bottom of the calculated lattice energy landscape, and two predicted structures are identified as candidates for a missing, thermodynamically more stable polymorph. Pressure-dependent stability calculations suggested high pressure as a means to bring these polymorphs into existence. Subsequently, one of them could indeed be crystallized in the 0.02 to 0.50 GPa pressure range and was found to be metastable at ambient pressure, effectively derisking the appearance of a more stable polymorph during late-stage development of Dalcetrapib.

Crystal polymorphism can lead to substances with vastly differing physicochemical properties, which has serious implications in the pharmaceutical industry. Here, the authors use in silico polymorph screening to accurately predict the resulting structures under set crystallisation environments.

Crystal Structure Prediction from First Principles: The Crystal Structures of Glycine

Here we present the results of our unbiased searches of glycine polymorphs obtained using the Genetic Algorithms search implemented in Modified Genetic Algorithm for Crystals coupled with the local optimization and energy evaluation provided by Quantum Espresso. We demonstrate that it is possible to predict the crystal structures of a biomedical molecule using solely first principles calculations. We were able to find all the ambient pressure stable glycine polymorphs, which are found in the same energetic ordering as observed experimentally and the agreement between the experimental and predicted structures is of such accuracy that the two are visually almost indistinguishable.

Analysis of the conformational profiles of fenamates shows route towards novel, higher accuracy, force-fields for pharmaceuticals

The conformational barriers of the fenamates which lead to conformational polymorphism can be represented by a novel, physically motivated, model intramolecular potential suitable for extension to other pharmaceuticals.

A mechanophysical phase transition provides a dramatic example of colour polymorphism: the tribochromism of a substituted tri(methylene)tetrahydrofuran-2-one

Background

Derivatives of fulgides have been shown to have interesting photochromic properties. We have synthesised a number of such derivatives and have found, in some cases, that crystals can be made to change colour on crushing, a phenomenon we have termed “tribochromism”. We have studied a number of derivatives by X-ray crystallography, to see if the colour is linked to molecular structure or crystal packing, or both, and our structural results have been supported by calculation of molecular and lattice energies.

Results

A number of 5-dicyanomethylene-4-diphenylmethylene-3-disubstitutedmethylene-tetrahydrofuran-2-one compounds have been prepared and structurally characterised. The compounds are obtained as yellow or dark red crystals, or, in one case, both. In two cases where yellow crystals were obtained, we found that crushing the crystals gave a deep red powder. Structure determinations, including those of the one compound which gave both coloured forms, depending on crystallisation conditions, showed that the yellow crystals contained molecules in which the structure comprised a folded conformation at the diphenylmethylene site, whilst the red crystals contained molecules in a twisted conformation at this site. Lattice energy and molecular conformation energies were calculated for all molecules, and showed that the conformational energy of the molecule in structure IIIa (yellow) is marginally higher, and the conformation thus less stable, than that of the molecule in structure IIIb (red). However, the van der Waals energy for crystal structure IIIa, is slightly stronger than that of structure IIIb – which may be viewed as a hint of a metastable packing preference for IIIa, overcome by the contribution of a more stabilising Coulomb energy to the overall more favourable lattice energy of structure IIIb.

Conclusions

Our studies have shown that the crystal colour is correlated with one of two molecular conformations which are different in energy, but that the less stable conformation can be stabilised by its host crystal lattice.

Graphical abstract

Crystal structure and prediction

The notion of structure is central to the subject of chemistry. This review traces the development of the idea of crystal structure since the time when a crystal structure could be determined from a three-dimensional diffraction pattern and assesses the feasibility of computationally predicting an unknown crystal structure of a given molecule. Crystal structure prediction is of considerable fundamental and applied importance, and its successful execution is by no means a solved problem. The ease of crystal structure determination today has resulted in the availability of large numbers of crystal structures of higher-energy polymorphs and pseudopolymorphs. These structural libraries lead to the concept of a crystal structure landscape. A crystal structure of a compound may accordingly be taken as a data point in such a landscape.

Predicting crystal structures of organic compounds

Organic Crystal Structure Prediction methods generate the thermodynamically plausible crystal structures of a molecule. There are often many more such structures than experimentally observed polymorphs.

Why don't we find more polymorphs?

Crystal structure prediction (CSP) studies are not limited to being a search for the most thermodynamically stable crystal structure, but play a valuable role in understanding polymorphism, as shown by interdisciplinary studies where the crystal energy landscape has been explored experimentally and computationally. CSP usually produces more thermodynamically plausible crystal structures than known polymorphs. This article illustrates some reasons why: because (i) of approximations in the calculations, particularly the neglect of thermal effects (see §1.1); (ii) of the molecular rearrangement during nucleation and growth (see §1.2); (iii) the solid-state structures observed show dynamic or static disorder, stacking faults, other defects or are not crystalline and so represent more than one calculated structure (see §1.3); (iv) the structures are metastable relative to other molecular compositions (see §1.4); (v) the right crystallization experiment has not yet been performed (see §1.5) or (vi) cannot be performed (see §1.6) and the possibility (vii) that the polymorphs are not detected or structurally characterized (see §1.7). Thus, we can only aspire to a general predictive theory for polymorphism, as this appears to require a quantitative understanding of the kinetic factors involved in all possible multi-component crystallizations. For a specific molecule, analysis of the crystal energy landscape shows the potential complexity of its crystallization behaviour.

Crankshafts: using simple, flat C2h-symmetric molecules to direct the assembly of chiral 2D nanopatterns

Linear D2h-symmetric bisisophthalic acids 1 and 2 and related substances have well-defined flattened structures, high affinities for graphite, and strong abilities to engage in specific intermolecular interactions. Their adsorption produces characteristic nanopatterns that reveal how 2D molecular organization can be controlled by reliable interadsorbate interactions such as hydrogen bonds when properly oriented by molecular geometry. In addition, the behavior of these compounds shows how large-scale organization can be obstructed by programming molecules to associate strongly according to competing motifs that have similar stability and can coexist smoothly without creating significant defects. Analogous new bisisophthalic acids 3a and 4a have similar associative properties, and their unique C2h-symmetric crankshaft geometry gives them the added ability to probe the poorly understood effect of chirality on molecular organization. Their adsorption shows how nanopatterns composed predictably of a single enantiomer can be obtained by depositing molecules that can respect established rules of association only by accepting neighbors of the same configuration. In addition, an analysis of the adsorption of crankshaft compounds 3a and 4a and their derivatives by STM reveals directly on the molecular level how kinetics and thermodynamics compete to control the crystallization of chiral compounds. In such ways, detailed studies of the adsorption of properly designed compounds on surfaces are proving to be a powerful way to discover and test rules that broadly govern molecular organization in both 2D and 3D.