Molecular Packing Topology and Interactions to Decipher Mechanical Compliances in Dicyano-Distyrylbenzene Derivatives

Flexible optoelectronics is the need of the hour as the market moves toward wearable and conformable devices. Crystalline π-conjugated materials offer high performance as active materials compared to their amorphous counterpart, but they are typically brittle. This poses a significant challenge that needs to be overcome to unfold their potential in optoelectronic devices. Unveiling the molecular packing topology and identifying interaction descriptors that can accommodate strain offers essential guiding principles for developing conjugated materials as active components in flexible optoelectronics. The molecular packing and interaction topology of eight crystal systems of dicyano-distyrylbenzene derivatives are investigated. Face-to-face π-stacks in an inclined orientation relative to the bending surface can accommodate expansion and compression with minimal molecular motion from their equilibrium positions. This configuration exhibits good compliance towards mechanical strain, while a similar structure with a criss-cross arrangement capable of distributing applied strain equally in opposite directions enhances the flexibility. Molecular arrangements that cannot reversibly undergo expansion and compression exhibit brittleness. In the isometric CT crystals, the disproportionate strength of the interactions along the bending plane and orthogonal directions makes these materials sustain a moderate bending strain. These results provide an updated explanation for the elastic bending in semiconducting π-conjugated crystals.

Improved Description of Intra- and Intermolecular Interactions through Dispersion-Corrected Second-Order Møller-Plesset Perturbation Theory

ConspectusThe quantum chemical modeling of organic crystals and other molecular condensed-phase problems requires computationally affordable electronic structure methods which can simultaneously describe intramolecular conformational energies and intermolecular interactions accurately. To achieve this, we have developed a spin-component-scaled, dispersion-corrected second-order Møller-Plesset perturbation theory (SCS-MP2D) model. SCS-MP2D augments canonical MP2 with a dispersion correction which removes the uncoupled Hartree-Fock dispersion energy present in canonical MP2 and replaces it with a more reliable coupled Kohn-Sham treatment, all evaluated within the framework of Grimme's D3 dispersion model. The spin-component scaling is then used to improve the description of the residual (nondispersion) portion of the correlation energy.The SCS-MP2D model improves upon earlier corrected MP2 models in a few ways. Compared to the highly successful dispersion-corrected MP2C model, which is based solely on intermolecular perturbation theory, the SCS-MP2D dispersion correction improves the description of both inter- and intramolecular interactions. The dispersion correction can also be evaluated with trivial computational cost, and nuclear analytic gradients are computed readily to enable geometry optimizations. In contrast to earlier spin-component scaling MP2 models, the optimal spin-component scaling coefficients are only mildly sensitive to the choice of training data, and a single global parametrization of the model can describe both thermochemistry and noncovalent interactions.The resulting dispersion-corrected, spin-component-scaled MP2 (SCS-MP2D) model predicts conformational energies and intermolecular interactions with accuracy comparable to or better than those of many range-separated and double-hybrid density functionals, as is demonstrated on a variety of benchmark tests. Among the functionals considered here, only the revDSD-PBEP86-D3(BJ) functional gives consistently smaller errors in benchmark tests. The results presented also hint that further improvements of SCS-MP2D may be possible through a more robust fitting procedure for the seven empirical parameters.To demonstrate the performance of SCS-MP2D further, several applications to molecular crystal problems are presented. The three chosen examples all represent cases where density-driven delocalization error causes GGA or hybrid density functionals to artificially stabilize crystals exhibiting more extended π-conjugation. Our pragmatic strategy addresses the delocalization error by combining a periodic density functional theory (DFT) treatment of the infinite lattice with intramolecular/conformational energy corrections computed with SCS-MP2D. For the anticancer drug axitinib, applying the SCS-MP2D conformational energy correction produces crystal polymorph stabilities that are consistent with experiment, in contrast to earlier studies. For the crystal structure prediction of the ROY molecule, so named for its colorful red, orange, and yellow crystals, this approach leads to the first plausible crystal energy landscape, and it reveals that the lowest-energy polymorphs have already been found experimentally. Finally, in the context of photomechanical crystals, which transform light into mechanical work, these techniques are used to predict the structural transformations and extract design principles for maximizing the work performed.

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.

Benchmarking two-body contributions to crystal lattice energies and a range-dependent assessment of approximate methods

Using the many-body expansion to predict crystal lattice energies (CLEs), a pleasantly parallel process, allows for flexibility in the choice of theoretical methods. Benchmark-level two-body contributions to CLEs of 23 molecular crystals have been computed using interaction energies of dimers with minimum inter-monomer separations (i.e., closest contact distances) up to 30 Å. In a search for ways to reduce the computational expense of calculating accurate CLEs, we have computed these two-body contributions with 15 different quantum chemical levels of theory and compared these energies to those computed with coupled-cluster in the complete basis set (CBS) limit. Interaction energies of the more distant dimers are easier to compute accurately and several of the methods tested are suitable as replacements for coupled-cluster through perturbative triples for all but the closest dimers. For our dataset, sub-kJ mol^-1 accuracy can be obtained when calculating two-body interaction energies of dimers with separations shorter than 4 Å with coupled-cluster with single, double, and perturbative triple excitations/CBS and dimers with separations longer than 4 Å with MP2.5/aug-cc-pVDZ, among other schemes, reducing the number of dimers to be computed with coupled-cluster by as much as 98%.

Crystalline Derivatives of Dipyrazolo-1,5-diazocine and Dipyrazolopyrimidine: A Case of Unexpected Synthesis and Isostructural Polymorphism

Pyrazole-phenylmethanimines (Shiff bases), Py–N=CH–Ph, form molecular crystals whose supramolecular and self-assembly properties can be tuned according to the substitution made on the aromatic and pyrazole rings. In pursuit of the first pyrazole-pyridinemethanimine member, Py–N=CH–Pyr, by following the well-known synthetic scheme for these Shiff bases, two hitherto unknown crystalline derivatives of dipyrazolo-1,5-diazocine and dipyrazolopyrimidine were obtained instead, this depending on the use or not of acetic acid as the catalyst. 1,5-diazocine crystallizes in a single P-1 triclinic packing system (Z = 2, Z′ = 1), while dipyrazolopyrimidine exhibits isostructural dimorphic behavior by adopting two (pale pink and yellow) alike P21/c monoclinic systems (both Z = 4, Z′ = 1) as a function of the solvent used. Crystal structures were resolved by means of X-ray diffraction technique and their intramolecular, intermolecular, and supramolecular assemblies analyzed with the assistance of decorated Hirshfeld surfaces and the topology study of electron density using the quantum-theory of atoms in molecules (QTAIM). Although both dipyrazolopyrimidine polymorphs are stabilized by the same type of noncovalent motifs, the pale pink crystal has a slightly more compact structure, with more efficient inter- and intramolecular interactions.

Polymorphic selectivity in crystal nucleation

Crystal nucleation rates have been measured in the supercooled melts of two richly polymorphic glass-forming liquids: ROY and nifedipine (NIF). ROY or 5-methyl-2-[(2-nitrophenyl)amino]-3-thiophenecarbonitrile is known for its crystals of red, orange, and yellow colors and many polymorphs of solved structures (12). Of the many polymorphs, ON (orange needles) nucleates the fastest with the runner up (Y04) trailing by a factor of 103 when compared under the same mobility-limited condition, while the other unobserved polymorphs are slower yet by at least 5 orders of magnitude. Similarly, of the six polymorphs of NIF, [Formula: see text]′ nucleates the fastest, [Formula: see text]′ is slower by a factor of 10, and the rest are slower yet by at least 5 decades. In both systems, the faster-nucleating polymorphs are not built from the lowest-energy conformers, while they tend to have higher energies and lower densities and thus greater similarity to the liquid phase by these measures. The temperature ranges of this study covered the glass transition temperature Tg of each system, and we find no evidence that the nucleation rate is sensitive to the passage of Tg. At the lowest temperatures investigated, the rates of nucleation and growth are proportional to each other, indicating that a similar kinetic barrier controls both processes. The classical nucleation theory provides an accurate description of the observed nucleation rates if the crystal growth rate is used to describe the kinetic barrier for nucleation. The quantitative rates of both nucleation and growth for the competing polymorphs enable prediction of the overall rate of crystallization and its polymorphic outcome.

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.

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.

Portrayal of the color polymorphism in the 5-acetyl-derivative of ROY

A novel derivative of ROY, AcROY, was synthesized and studied in this work, where 3 different colored polymorphs were identified. The observed polymorphism of AcROY is an interesting case of packing-determined color polymorphism.

Spin-component-scaled and dispersion-corrected second-order Møller-Plesset perturbation theory: A path toward chemical accuracy

Second-order Moller-Plesset perturbation theory (MP2) provides a valuable alternative to density functional theory for modeing problems in organic and biological chemistry. However, MP2 suffers from known limitations in the description...

Direct evidence for distinct colour origins in ROY polymorphs

ROY is one of the most well-studied families of crystal structures owing to it being the most polymorphic organic material on record. The various red, orange, and yellow colours of its crystal structures are widely-believed to originate from molecular conformation, though the orange needle (ON) polymorph is thought to be an exception. We report high-pressure, single-crystal X-ray measurements which provide direct experimental evidence that the colour origin in ON is intermolecular, revealing that the molecule undergoes minimal deformation but still exhibits a pronounced, reversible, pale orange → dark red colour change between ambient pressure and 4.18 GPa. Our experimental data are rationalised with band structures, calculated using an accurate hybrid DFT approach, where we are able to account for the variation in colour for five polymorphs of ROY. We highlight the outlier behaviour of ON which shows marked π⋯π stacking interactions that are directly modified through application of pressure. Band structure calculations confirm these intermolecular interactions as the origin of the colour change.

Systematic thermodynamic analysis of apremilast polymorphs via solubility measurement with modeling: Mechanism evaluation through molecular simulation

The polymorphism of apremilast has been investigated. Two polymorphs have been identified and characterized by differential scanning calorimeter, fourier transform infrared spectroscopy, and powder X-ray diffractometer. Solubilities of apremilast forms B and E in three binary solvents of methanol-water, acetonitrile-water, and acetonitrile-methanol have been measured using the static method at a temperature ranging from 288.15 K to 328.15 K under standard atmospheric pressure. Subsequently, the solubility data have been analyzed using the Wilson, NRTL, and UNIQUAC thermodynamic models, respectively. Furthermore, the Gibbs energy of solution and the radial distribution function have been calculated using the molecular simulation method to evaluate the dissolution mechanism. The Gibbs energy of solution reveals that the rank of solute-solvent interaction correlated well with solubility order in binary solvent mixtures, and the radial distribution function indicates that weakening of solvent-solvent interaction led to an increase in solubility.

Prolific Polymorph Generator ROY in Its Liquid and Glass: Two Conformational Populations Mirroring the Crystalline-State Distribution

5-Methyl-2-[(2-nitrophenyl)amino]-3-thiophenecarbonitrile, dubbed ROY for its numerous crystal polymorphs of red, orange, and yellow colors, has been studied in its liquid and glassy state by infrared spectroscopy. Two populations of conformers are observed, whose equilibrium is characterized by ΔH = 2.4 kJ/mol and ΔS = 8.0 J/K/mol. The two populations correspond to the global and local minima of the torsional energy surface and to the conformational preference of the 13 crystal polymorphs. The local minimum features a more coplanar arrangement of the two aromatic rings, greater π conjugation, and lower CN stretch frequency. In the gas phase, the lowest-energy path between the two minima has an energy barrier 3.9 kJ/mol above the global minimum, consistent with the rapid equilibration between the two populations. The relevance of our result for understanding the prolific polymorphism of ROY is discussed.

Understanding Conformational Polymorphism in Ganciclovir: A Holistic Approach

We present a holistic crystallographic study of the antiviral ganciclovir, including insights into its solid-state behavior, which could prove useful during drug development, making the process more sustainable. A newly developed methodology was used incorporating a combination of statistical and thermodynamic approaches, which can be applied to various crystalline materials. We demonstrate how the chemical environment and orientation of a functional group can affect its accessibility for participation in hydrogen bonding. The difference in the nature and strength of intermolecular contacts between the two anhydrous forms, exposed through full interaction maps and Hirshfeld surfaces, leads to the manifestation of conformational polymorphism. Variations in the intramolecular geometry and intermolecular interactions of both forms of ganciclovir were identified as possible predictors for their relative thermodynamic stability. It was shown through energy frameworks how the extensive supramolecular network of contacts in form I causes a higher level of compactness and lower enthalpy relative to form II. The likelihood of the material to exhibit polymorphism was assessed through a hydrogen bond propensity model, which predicted a high probability associated with the formation of other relatively stable forms. However, this model failed to classify the stability of form I appropriately, suggesting that it might not have fully captured the collective impacts which govern polymorphic stability.

ROY Reclaims Its Crown: New Ways To Increase Polymorphic Diversity

Chemical compounds that exist in multiple crystalline forms are said to exhibit polymorphism. Polymorphs have the same composition, but their structures and properties can vary markedly. In many fields, conditions for crystallizing compounds of interest are screened exhaustively to generate as many polymorphs as possible, from which the most advantageous form can be selected. We report new ways to search for polymorphs and increase polymorphic diversity, based on crystallization induced by suitably designed mixed-crystal seeds. The potential of the strategy has been demonstrated by using it to produce new polymorphs of the benchmark compound ROY as single crystals structurally characterized by X-ray diffraction. This allows ROY to reclaim its crown as the most polymorphic compound in the Cambridge Structural Database. More generally, the methods promise to become valuable tools for polymorphic screening in all fields where crystalline solids are used.

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

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

Disorder in molecular crystals justified with the help of statistical mechanics: a case of two enantiomer solid solutions

An elegant statistical mechanics approach has been exploited in combination with accurate quantum chemical calculations to justify the disorder in two previously reported racemic solids.

Structural behaviour of OP-ROY at extreme conditions

A highly-flexible organic molecule, with numerous polymorphs at ambient conditions, shows remarkable metastability, resisting the effects of extreme pressure and temperature.

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.

Conformational trimorphism of bis(2,6-dimesitylphenyl)ditelluride

Besides the previously known α-form (monoclinic, P21/c, Z=4) of bis(2,6-dimesitylphenyl)ditelluride, two new polymorphic modifications, namely the β-form (monoclinic, P21/c, Z=8) and the γ-form (triclinic, P1̅, Z=2), were obtained serendipitously during chemical reactions. In all three modifications, the individual molecules possess significantly different conformations and bond parameters, such as Te–Te bond lengths, C–Te–Te bond angles, C–Te–Te–C torsion angles and intramolecular Menshutkin interactions, which is also reflected in their non-covalent interactions with adjacent molecules in the crystal lattice via London dispersion and electrostatic forces. The interplay between intermolecular and intramolecular forces in these conformational polymorphs was investigated using quantum chemical calculations, which reveal that the β-form should be thermodynamically stable at absolute zero. In contrast, crystallization experiments and thermoanalytical investigations indicate that the α-form is stable at high temperatures and therefore, both forms might be related by enantiotropism.