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.     

Experimental and computational growth morphology of two polymorphs of a yellow isoxazolone dye

We report on the crystal structures and the experimentally found and the computationally predicted growth morphologies of two polymorphs of a yellow isoxazolone dye. The stable polymorph I has a blocklike habit, and the metastable polymorph II grows as fine needles, nucleating only by heterogeneous or contact nucleation. The habits of both polymorphs depend on the supersaturation during growth. The experimental observations are compared with predictions of the attachment energy model and kinetic Monte Carlo lattice simulations in which the growth is modeled as an "atomistic process", governed by surface energetics. These Monte Carlo simulations correctly predict the shape and the dependence on supersaturation of the crystal morphology for both polymorphs: for polymorph I, a strong dependence on supersaturation is found from the simulations. For polymorph II, the order of morphological importance is reproduced correctly, as well as the needlelike morphology.     

Potential polymorphs of aspirin

Aspirin is only found experimentally in one crystal structure. In this article, the method of Karfunkel and Gdanitz is used to predict potential polymorphs of aspirin. The known structure, containing a nonplanar conformer is found, along with a number of other low energy structures, many of which are based on a planar conformer. Semiempirical and ab initio calculations show that the planar conformer is less stable than the experimentally known one. Force field calculations suggest that the planar conformer is more stable. The lattice energy of the experimentally known crystal structure is 1.4 kcal/mol lower than any of the potential crystal structures, even though there are a number of structures with lower total (lattice+intramolecular) energies. Conformational maps indicate that another stable conformation occurs within a few kilocalories per mole of the known structure. Polymorphs are predicted for this conformer, but it is found to pack poorly. It is proposed that routes to producing polymorphs of aspirin might be found if consideration is given to promoting the stability of the planar conformer with appropriate solvents or additives. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 262–273, 1999     

Molecular Shape and Crystal Packing: a Study of C12H12 Isomers,Real and Imaginary

Isomeric C₁₂H₁₂ hydrocarbon molecules with widely different constitution and shape are analysed for their packing ability. Some correspond to known compounds with known crystal structures, but some are invented hypothetical molecules designed to have low packing efficiency. For each isomer, a large number of close‐packed, low‐energy crystal structures was generated by computer, with lattice energies within a range of a few kJ mol⁻¹. Molecules with linear chains, triple bonds and Me groups tend to have larger molecular volume, lower lattice energy and lower crystal density than cyclic or cage isomers. The calculated crystal structures for each isomer show an inverse relationship between packing energy and cell volume. Although the slope dE/dV varies from molecule to molecule, the product of slope and free space stays roughly constant; less efficient crystal packings thus appear to be less sensitive to an increase in cell volume. Lattice‐vibrational frequencies and the corresponding contributions to thermal vibrational entropy were estimated for real and virtual crystal structures. For a given isomer, as expected, a higher entropy goes with a larger cell volume, but different isomers show different entropy/volume relationships. At 300 K, TΔS differences among computational polymorphs may compete with ΔH differences, thus making the lattice‐vibrational entropy estimation a relevant factor in crystal‐structure prediction.     

Conformational, concomitant polymorphs of 4,4-diphenyl-2,5-cyclohexadienone: conformation and lattice energy compensation in the kinetic and thermodynamic forms

4,4-Diphenyl-2,5-cyclohexadienone (1) crystallized as four conformational polymorphs and a record number of 19 crystallographically independent molecules have been characterized by low-temperature X-ray diffraction: form A (P2(1), Z'=1), form B (P1, Z'=4), form C (P1, Z'=12), and form D (Pbca, Z'=2). We have now confirmed by variable-temperature powder X-ray diffraction that form A is the thermodynamic polymorph and B is the kinetic form of the enantiotropic system A-D. Differences in the packing of the molecules in these polymorphs result from different acidic C-H donors approaching the C=O acceptor in C-H...O chains and in synthons I-III, depending on the molecular conformation. The strength of the C-HO interaction in a particular structure correlates with the number of symmetry-independent conformations (Z') in that polymorph, that is, a short C-HO interaction leads to a high Z' value. Molecular conformation (Econf) and lattice energy (Ulatt) contributions compensate each other in crystal structures A, B, and D resulting in very similar total energies: Etotal of the stable form A=1.22 kcal mol(-1), the metastable form B=1.49 kcal mol(-1), and form D=1.98 kcal mol(-1). Disappeared polymorph C is postulated as a high-Z', high-energy precursor of kinetic form B. Thermodynamic form A matches with the third lowest energy frame based on the value of Ulatt determined in the crystal structure prediction (Cerius2, COMPASS) by full-body minimization. Re-ranking the calculated frames on consideration of both Econf (Spartan 04) and Ulatt energies gives a perfect match of frame #1 with stable structure A. Diphenylquinone 1 is an experimental benchmark used to validate accurate crystal structure energies of the kinetic and thermodynamic polymorphs separated by <0.3 kcal mol(-1) (approximately 1.3 kJ mol(-1)).     

Phonon, IR, and Raman spectra, NMR parameters, and elastic constant calculations for AlH3 polymorphs

The electronic structure, lattice dynamics, and mechanical properties of AlH(3) phases have been studied by density functional calculations. The chemical bonding in different polymorphs of AlH(3) are evaluated on the basis of electronic structures, charge density analysis, and atomic charges, as well as bond overlap population analysis and the Born effective charges. The phonon dispersion relations and phonon density of states of all the polymorphs of AlH(3) are calculated by direct force-constant method. Application of pressure induces seqauence of phase transitions in β-AlH(3) which are understood from the phonon dispersive curves of the involved phases. The previously predicted phases (Chem. Mater. 2008, 20, 5997) are found to be dynamically stable. The calculated single crystal elastic constants reveal that all the studied AlH(3) polymorphs are easily compressible. The chemical bonding of these polymorphs have noticeable covalent character (except the hp2 phase) according to the present chemical bonding analyses. For all these polymorphs, the NMR-related parameters, such as isotropic chemical shielding, quadrupolar coupling constant, and quadrupolar asymmetry, are also calculated. All IR- and Raman-active phonon frequencies, as well as the corresponding intensities, are calculated for all the AlH(3) polymorphs and are compared with available experimental results.     

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.     

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.     

Synthesis and crystal structure determination of a new pressure-induced iridium ditelluride phase, m-IrTe2, and comparison of the crystal structures and relative stabilities of various IrTe2 polymorphs

The new monoclinic IrTe2 phase m-IrTe2 was synthesized under pressure, and its structure was determined by X-ray powder diffraction. The relative stabilities of the three known and three hypothetical IrTe2 polymorphs were discussed on the basis of tight binding electronic band structure calculations. m-IrTe2 exhibits structural features of both CdI2- and pyrite-type IrTe2 phases and is expected to be nearly as stable as that of the CdI2-type IrTe2. The hypothetical IrS2- and ramsdellite-type IrTe2 phases are predicted to be more stable than the CdI2-type IrTe2.     

Isomorphism of anhydrous tetrahedral halides and silicon chalcogenides: energy landscape of crystalline BeF2, BeCl2, SiO2, and SiS2

We employ periodic density functional theory calculations to compare the structural chemistry of silicon chalcogenides (silica, silicon sulfide) and anhydrous tetrahedral halides (beryllium fluoride, beryllium chloride). Despite the different formal oxidation states of the elements involved, the divalent halides are known experimentally to form crystal structures similar to known SiX2 frameworks; the rich polymorphic chemistry of SiO2 is however not matched by divalent halides, for which a very limited number of polymorphs are currently known. The calculated energy landscapes yield a quantitative match between the relative polymorphic stability in the SiO2/BeF2 pair, and a semiquantitative match for the SiS2/BeCl2 pair. The experimentally observed polymorphs are found to lie lowest in energy for each composition studied. For the two BeX2 compounds studied, polymorphs not yet synthesized are predicted to lie very low in energy, either slightly above or even in between the energy of the experimentally observed polymorphs. The experimental lack of polymorphism for tetrahedral halide materials thus does not appear to stem from a lack of low-energy polymorphs but more likely is the result of a lack of experimental exploration. Our calculations further indicate that the rich polymorphic chemistry of SiO2 can be potentially matched, if not extended, by BeF2, provided that milder synthetic conditions similar to those employed in zeolite synthesis are developed for BeF2. Finally, our work demonstrates that both classes of materials show the same behavior upon replacement of the 2p anion with the heavier 3p anion from the same group; the thermodynamic preference shifts from structures with large rings to structures with larger fractions of small two and three membered rings.     

Solid‐State Behaviour of the Dichlorobenzenes: Actual,Semi‐Virtual and Virtual Crystallography

The crystal structures of the low‐melting 1,2‐ and 1,3‐dichlorobenzene isomers have been determined by X‐ray analysis and in situ crystallisation techniques. Attempts to predict these structures in advance by force‐field calculations were not successful, although the known crystal structures of two of the three polymorphs of the 1,4‐isomer were successfully `a posteriori' predicted. Calculated lattice energies were supplemented with estimated lattice‐vibrational entropies obtained in the rigid‐body approximation. Energy calculations for actual and virtual crystal structures indicate that the higher melting point of the 1,4‐isomer can be largely attributed to more efficient crystal packing.     

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.     

First-principles study of lattice dynamics and thermodynamics of TiO2 polymorphs

The structural, phonon, and thermodynamic properties of six TiO(2) polymorphs, i.e., rutile, anatase, columbite, baddeleyite, orthorhombic I, and cotunnite, have been systematically investigated by density functional theory. The predicted volumes, bulk modulus, and Debye temperature are in good agreement with experiments. The phonon dispersions of the TiO(2) polymorphs were studied by the supercell approach, whereas the long-range dipole-dipole interactions were calculated by linear response theory to reproduce the LO-TO splitting, making accurate prediction of phonon frequencies for the polar material TiO(2). The calculated phonon dispersions show that all TiO(2) polymorphs are dynamically stable at ambient pressure, indicating the high-pressure phases might be quenched to ambient conditions as ultrahard materials. Furthermore, the finite temperature thermodynamic properties of TiO(2) polymorphs were predicted accurately from the obtained phonon density of states, which is critical in the future study of the pressure-temperature phase diagram of TiO(2). The calculated Gibbs energies reveal that rutile is more stable than anatase at ambient pressure. We derived the Gibbs energy and heat capacity functions for all TiO(2) polymorphs for use in thermodynamic modeling of phase equilibria.     

Wettability of paracetamol polymorphic forms I and II

It is well known that different forms of solid-state polymorphic materials exhibit diverse physicochemical properties. The variations in the wetting and surface energetics of a pair of organic polymorphic solids are reported in detail here for the first time. The growth of macroscopic single crystals (facet area >1 cm(2)) of paracetamol has enabled for the first time the direct measurement of advancing contact angles, theta(A) for water and diiodomethane on a range of specific facets for two polymorphs; forms I and II. Not only was the wetting behavior found to be anisotropic, as has been recently reported, but the differing polymorphic forms exhibited significant variations in their wetting behavior for the same Miller indexed faces. The (001), (010), and (110) faces were studied, and the observed wettability data differed confirming the independence of facet wettability and Miller indices for both polymorphs. theta(A) was found to be very sensitive to the local surface chemistry for each facet examined, which in turn is a direct consequence of the molecular packing and structure within the crystal lattice. On the basis of the theta(A) value of water, the hydrophilicity rankings for the facet surfaces of form II examined is: (010) approximately (110) > (001). This experimental study highlights complex surface chemistry of polymorphic solids in which anisotropic surface energies were observed for both forms of paracetamol, strongly suggesting that such anisotropic wetting behavior is the norm for organic crystalline solids. Furthermore, the same Miller indexed facets for forms I and II exhibited very different surface chemical behavior, such that it was not possible to infer understanding about one form based upon knowledge of another form.     

Evolutionary Algorithm-based Crystal Structure Prediction for Gold(I) Fluoride

Solid gold(I) fluoride remains as an unsynthesized and uncharacterized compound. We have performed a search for potential gold(I) fluoride crystal structures using USPEX evolutionary algorithm and dispersion-corrected hybrid density functional methods. Over 4000 AuF crystal structures have been investigated. Behavior of the AuF crystal structures under pressure was studied up to 25 GPa, and we also evaluated the thermodynamic stability of the hypothetical AuF crystal structures with respect to AuF₃, AuF₅, and Au₃F₈. Mixed-valence compound Au₃[AuF₄] with Au atoms in various formal oxidation states emerged as the thermodynamically most stable AuF species.     

Crystallization near glass transition: transition from diffusion-controlled to diffusionless crystal growth studied with seven polymorphs

A remarkable property of certain glass-forming liquids is that a fast mode of crystal growth is activated near the glass transition temperature Tg and continues in the glassy state. This growth mode, termed GC (glass-crystal), is so fast that it is not limited by molecular diffusion in the bulk liquid. We have studied the GC mode by growing seven polymorphs from the liquid of ROY, currently the top system for the number of coexisting polymorphs of known structures. Some polymorphs did not show GC growth, while others did, with the latter having higher density and more isotropic molecular packing. The polymorphs not showing GC growth grew as compact spherulites at all temperatures; their growth rates near Tg decreased smoothly with falling temperature. The polymorphs showing GC growth changed growth morphologies with temperature, from faceted single crystals near the melting points, to fiber-like crystals near Tg, and to compact spherulites in the GC mode; in the GC mode, they grew at rates 3-4 orders of magnitude faster with activation energies 2-fold smaller than the polymorphs not showing GC growth. The GC mode had rates and activation energies similar to those of a polymorphic transformation observed near Tg. The GC mode was disrupted by the onset of the liquid's structural relaxation but could persist well above Tg (up to 1.15 Tg) in the form of fast-growing fibers. We consider various explanations for the GC mode and suggest that it is solid-state transformation enabled by local molecular motions native to the glassy state and disrupted by the liquid's structural relaxation (the alpha process).     

Determination of indomethacin polymorphic contents by chemometric near-infrared spectroscopy and conventional powder X-ray diffractometry

A chemoinfometric method for the quantitative determination of the crystal content of indomethacin (IMC) polymorphs, based on Fourier-transform near-infrared (FT-NIR) spectroscopy, was established. A direct comparison of the data with those collected using the conventional powder X-ray diffraction method was performed. Pure alpha and gamma forms of IMC were prepared using published methods. Powder X-ray diffraction profiles and NIR spectra were recorded for six kinds of standard material with various contents of the gamma form of IMC. Principal component regression (PCR) analyses were performed on the basis of the normalized NIR spectral sets of standard samples with known contents of the gamma form of IMC. A calibration equation was determined to minimize the root mean square error of the prediction. The predicted gamma form contents were reproducible and had a relatively small standard deviation. The values of the gamma form contents predicted by the two methods were in close agreement. The results indicated that NIR spectroscopy provides an accurate quantitative analysis of crystallinity in polymorphs compared with the results obtained by conventional powder X-ray diffractometry.     

Comparison of Experimental Methods and Theoretical Calculations on Crystal Energies of ‘Isoenergetic’ Polymorphs of Cimetidine

The thermodynamic energy relationship between two crystal modifications of cimetidine was investigated and compared with differences in their processing properties with respect to transformation from one modification to the other.The crystal energies of the two modifications A and D were found to be almost identical and therefore the polymorphs are regarded as virtually isoenergetic crystals. This statement is based on DSC measurements of the melting points and of the enthalpies of fusion for the two crystal forms, which enable the calculation of the Gibbs free energy functions. Furthermore, the statement is supported by measurements of the enthalpies of solution in two different solvents. Both DSC and solution experiments reveal a slightly higher stability of the D modification with respect to the A form. In addition, tribomechanical treatment also indicates modification D to be the more stable one, as well as the higher density of the D form. No transformation during DSC at low heating rate was found which could be used in a stability consideration.As the explicit crystal structures of the two modifications are resolved, it was possible to calculate crystal energies theoretically as well. The theoretical results showed a remarkable difference in the crystal energies at zero degree Kelvin. Furthermore, they were just contradicting experimental findings by stating A being more stable than D. Possible reasons for this discrepancy and the feasibility of today's calculation methods with respect to prediction of stability properties are discussed.This revised version was published online in November 2005 with corrections to the Cover Date.     

Utilization of DSC for Pharmaceutical crystal form quantitation

The existence of multiple crystal forms in a drug substance poses interesting development challenges as the material is taken from discovery through formulation, manufacture and market. There are a number of factors why drug substances under development are screened for presence of multiple crystal forms. Different crystal forms may exhibit varied performance properties including bioavailability and solubility, as well as, differences in physical properties such as morphology and melting point. These properties can affect the design of the manufacturing processes for the bulk drug substance, the formulation and the performance of the drug product. This paper will focus on the application of differential scanning calorimetry (DSC) for the quantitation of pharmaceutical crystal forms. Feasibility studies were conducted on several pharmaceutical drug substances which were known to have multiple crystal forms, to determine if quantitative, semi-quantitative or limit of detection tests could be developed. The conclusion from these studies is that polymorphic crystal systems comprised of either close, or melting with decomposing, endotherms, competing transitions, or that contain sample contaminants, may not be optimum candidates for quantitation by DSC. Conversely, crystal systems that contain polymorphs that exhibit well-resolved endothermic or exothermic transitions, for either solvated vs. unsolvated species or both unsolvated, may be excellent candidates for crystal form quantitation by DSC. This revised version was published online in July 2006 with corrections to the Cover Date.