Crystallization Force-A Density Functional Theory Concept for Revealing Intermolecular Interactions and Molecular Packing in Organic Crystals

Unsupervised manifold embedding to encode molecular quantum information for supervised learning of chemical data

Molecular representation is critical in chemical machine learning. It governs the complexity of model development and the fulfillment of training data to avoid either over- or under-fitting. As electronic structures and associated attributes are the root cause for molecular interactions and their manifested properties, we have sought to examine the local electron information on a molecular manifold to understand and predict molecular interactions. Our efforts led to the development of a lower-dimensional representation of a molecular manifold, Manifold Embedding of Molecular Surface (MEMS), to embody surface electronic quantities. By treating a molecular surface as a manifold and computing its embeddings, the embedded electronic attributes retain the chemical intuition of molecular interactions. MEMS can be further featurized as input for chemical learning. Our solubility prediction with MEMS demonstrated the feasibility of both shallow and deep learning by neural networks, suggesting that MEMS is expressive and robust against dimensionality reduction.

How great is the stabilization of crowded polyphenylbiphenyls by London dispersion?

Decaphenylbiphenyl (1) and 2,2',4,4',6,6'-hexaphenylbiphenyl (2) are bulky molecules expected to be greatly destabilized by steric crowding. Herein, through a combined experimental and computational approach, we evaluate the molecular energetics of crowded biphenyls. This is complemented by the study of phase equilibria for 1 and 2. Compound 1 shows a rich phase behavior, displaying an unusual interconversion between two polymorphs. Surprisingly, the polymorph with distorted molecules of C₁ symmetry is found to have the highest melting point and to be the one that is preferentially formed. The thermodynamic results also indicate that the polymorph displaying the more regular D₂ molecular geometry has larger heat capacity and is probably the more stable at lower temperatures. The melting and sublimation data clearly reveal the weakening of cohesive forces in crowded biphenyls due to the lower molecular surface area. The experimental quantification of the intramolecular interactions in 1 and 2 indicated, using homodesmotic reactions, a molecular stabilization of about 30 kJ mol^-1. We attribute the origin of this stabilization in both compounds to the existence of two parallel-displaced π⋯π interactions between the ortho-phenyl substituents on each side of the central biphenyl. Computational calculations with dispersion-corrected DFT methods underestimate the stabilization in 1, unless the steric crowding is well balanced in a homodesmotic scheme. This work demonstrates that London dispersion forces are important in crowded aromatic systems, making these molecules considerably more stable than previously thought.

Towards an atomistic understanding of polymorphism in molecular solids

Understanding and controlling polymorphism in molecular solids is a major unsolved problem in crystal engineering. While the ability to calculate accurate lattice energies with atomistic modelling provides valuable insight into the associated energy scales, existing methods cannot connect energy differences to the delicate balances of intra- and intermolecular forces that ultimately determine polymorph stability ordering. We report herein a protocol for applying Quantum Chemical Topology (QCT) to study the key intra- and intermolecular interactions in molecular solids, which we use to compare the three known polymorphs of succinic acid including the recently-discovered γ form. QCT provides a rigorous partitioning of the total energy into contributions associated with topological atoms, and a quantitative and chemically intuitive description of the intra- and intermolecular interactions. The newly-proposed Relative Energy Gradient (REG) method ranks atomistic energy terms (steric, electrostatic and exchange) by their importance in constructing the total energy profile for a chemical process. We find that the conformation of the succinic acid molecule is governed by a balance of large and opposing electrostatic interactions, while the H-bond dimerisation is governed by a combination of electrostatics and sterics. In the solids, an atomistic energy balance emerges that governs the contraction, towards the equilibrium geometry, of a molecular cluster representing the bulk crystal. The protocol we put forward is as general as the capabilities of the underlying quantum-mechanical model and it can provide novel perspectives on polymorphism in a wide range of chemical systems.

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.

Orbital-free quantum crystallography: view on forces in crystals

Quantum theory of atoms in molecules and the orbital-free density functional theory (DFT) are combined in this work to study the spatial distribution of electrostatic and quantum electronic forces acting in stable crystals. The electron distribution is determined by electrostatic electron mutual repulsion corrected for exchange and correlation, their attraction to nuclei and by electron kinetic energy. The latter defines the spread of permissible variations in the electron momentum resulting from the de Broglie relationship and uncertainty principle, as far as the limitations of Pauli principle and the presence of atomic nuclei and other electrons allow. All forces are expressed via kinetic and DFT potentials and then defined in terms of the experimental electron density and its derivatives; hence, this approach may be considered as orbital-free quantum crystallography. The net force acting on an electron in a crystal at equilibrium is zero everywhere, presenting a balance of the kinetic F kin( r ) and potential forces F ( r ). The critical points of both potentials are analyzed and they are recognized as the points at which forces F kin( r ) and F ( r ) individually are zero (the Lagrange points). The positions of these points in a crystal are described according to Wyckoff notations, while their types depend on the considered scalar field. It was found that F ( r ) force pushes electrons to the atomic nuclei, while the kinetic force F kin( r ) draws electrons from nuclei. This favors formation of electron concentration bridges between some of the nearest atoms. However, in a crystal at equilibrium, only kinetic potential v kin( r ) and corresponding force exhibit the electronic shells and atomic-like zero-flux basins around the nuclear attractors. The force-field approach and quantum topological theory of atoms in molecules are compared and their distinctions are clarified.

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.

Charge-Separation-Type Ionic Crystals with Mixed AuI4CoIII2 and AuI4NiIICoIII Hexanuclear Complexes

Treatment of a digold(I) metalloligand, [Au^I₂(dppe)(d-Hpen)₂] (H₂L^Au; d-H₂pen = d-penicillamine, dppe = 1,2-bis(diphenylphosphino)ethane), with a 1:1 mixture of Co(OAc)₂ and Ni(OAc)₂ under aerobic conditions resulted in the formation of three types of hexanuclear complexes: [Co^III₂(L^Au)₂]²⁺, [Ni^IICo^III(L^Au)₂]⁺, and [Ni^II₂(L^Au)₂]. The addition of NaNO₃, M¹NO₃ (M¹ = K, Rb, Cs), and M²(NO₃)₂ (M² = Ca, Sr, Ba) to the reaction mixture led to co-crystallization of [Co^III₂(L^Au)₂]²⁺ and [Ni^IICo^III(L^Au)₂]⁺ as a solid solution to form the charge-separation (CS)-type ionic crystals 1_Na, 1_M1, and 1_M2, respectively, while [Ni^II₂(L^Au)₂] independently crystallized as a single species (2). In 1_Na, [Co^III₂(L^Au)₂]²⁺ and [Ni^IICo^III(L^Au)₂]⁺ cations assemble in a 1:2 ratio to form a cationic supramolecular octahedron accommodating 4 H₃O⁺ ions, while 10 nitrate ions are packed in each hydrophilic tetrahedral interstice of the crystal to form an anionic adamantane cluster. The overall structures of 1_M1 and 1_M2 are very similar to that of 1_Na, having a CS-type structure composed of cationic supramolecular octahedra with a +12 charge and anionic inorganic clusters with a -10 charge. However, 1_M1 contains M¹ ions in place of the H₃O⁺ ions in 1_Na, and furthermore, a novel rhombic dodecahedron cluster composed of 14 nitrate ions, which encapsulates two M² ions, is formed in each hydrophilic tetrahedral interstice in 1_M2.

Iodine Clathrated: A Solid-State Analogue of the Iodine-Starch Complex

Co-crystallizing iodine with a simple dicationic salt (1,8-diammoniumoctane chloride) results in the clathration of the iodine (I₂ ) molecules inside trigonal and hexagonal helical channels of the crystal lattice with 72 wt % overall I₂ loading. The I₂ inside the bigger trigonal channel forms a I-I⋅⋅⋅I-I⋅⋅⋅I-I halogen-bonded infinite helical chain, while the I₂ in the smaller hexagonal channel is disordered. In both channels the I₂ interaction with the channel wall happens through I-I⋅⋅⋅Cl^- halogen bonds. The helical channels in the crystal lattice are constructed via the strong charge-assisted H₂ N⁺ H⋅⋅⋅Cl^- hydrogen bonds between the dications and the chloride anions. The structure shows a marked similarity with the well-known starch-I₂ system, and thus may provide insight for the yet unresolved structure of the I₂ in the helical starch channel.

Chiroptical Properties of Twisted Acenes: Experimental and Computational Study

Acenes that are twisted out of planarity are expected to display chiroptical properties. However, the effect of twisting on the chiroptical properties of acenes has not been investigated computationally or experimentally. Herein, we present a computational investigation of the chiroptical properties of anthracenes to pentacenes, combined with an experimental study using a series of helically locked acenes, twisted to different torsional angles in their enantiopure form. The lowest energy transition, which is relatively weak in acenes, becomes dominant in their circular dichroism spectra upon twisting. We find that the rotational strength of acenes consistently increases with increasing twist. The experimental data obtained from enantiopure tethered twistacenes show the same trend as the calculated result, with a strong Cotton effect and anisotropy factor, rendering twisted acenes as excellent chiroptical materials.

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.

X-ray crystal structures and anti-breast cancer property of 3-tert-butoxycarbonyl-2-arylthiazolidine-4-carboxylic acids

The present article encompasses resolution and X-ray crystallographically confirmed absolute stereochemistry-correlated anticancer activity of diastereomeric 3-(tert-butoxycarbonyl)-2-(2-aryl)thiazolidine-4-carboxylic acids against MCF7 breast cancer cells.

ROY revisited, again: the eighth solved structure

X-ray powder diffraction and crystal structure prediction algorithms are used in synergy to establish the crystal structure of the eighth polymorph of ROY, form R05.

Steric charge

Steric charge is an informative descriptor providing novel insights to appreciate the steric effect and stereoselectivity for chemical processes and transformations.

The Polymorphs of ROY: A Computational Study of Lattice Energies and Conformational Energy Differences

The remarkable structural diversity observed in polymorphs of 5-methyl-2-[(2-nitrophenyl)amino]-3-thiophenecarbonitrile (commonly known as ROY) challenges computational attempts to predict or rationalize their relative stability. This modest study explores the applicability of CE-B3LYP model energy calculation of lattice energies (using experimental crystal structures), supplemented by a systematic approach to account for conformational energy differences. The CE-B3LYP model provides sensible estimates of absolute and relative lattice energies for the polymorphs, provided care is taken to achieve convergence in the summation of pairwise terms. Conformational energy differences based on density functional theory (DFT) energies are shown to be unreliable, but MP2 energies based on DFT-optimized structures show considerable promise.

Computational predictions of glass-forming ability and crystallization tendency of drug molecules

Amorphization is an attractive formulation technique for drugs suffering from poor aqueous solubility as a result of their high lattice energy. Computational models that can predict the material properties associated with amorphization, such as glass-forming ability (GFA) and crystallization behavior in the dry state, would be a time-saving, cost-effective, and material-sparing approach compared to traditional experimental procedures. This article presents predictive models of these properties developed using support vector machine (SVM) algorithm. The GFA and crystallization tendency were investigated by melt-quenching 131 drug molecules in situ using differential scanning calorimetry. The SVM algorithm was used to develop computational models based on calculated molecular descriptors. The analyses confirmed the previously suggested cutoff molecular weight (MW) of 300 for glass-formers, and also clarified the extent to which MW can be used to predict the GFA of compounds with MW < 300. The topological equivalent of Grav3_3D, which is related to molecular size and shape, was a better descriptor than MW for GFA; it was able to accurately predict 86% of the data set regardless of MW. The potential for crystallization was predicted using molecular descriptors reflecting Hückel pi atomic charges and the number of hydrogen bond acceptors. The models developed could be used in the early drug development stage to indicate whether amorphization would be a suitable formulation strategy for improving the dissolution and/or apparent solubility of poorly soluble compounds.

Intermolecular interactions in organic crystals: gaining insight from electronic structure analysis by density functional theory

Conceptual density functional theory is exploited to extend the HSAB (hard and soft acids and bases) principle for investigating the locality and regioselectivity of intermolecular interactions in organic crystals.

The polymorphs of ROY: application of a systematic crystal structure prediction technique

We investigate the ability of current ab initio crystal structure prediction techniques to identify the polymorphs of 5-methyl-2-[(2-nitrophenyl)amino]-3-thiophenecarbonitrile, also known as ROY because of the red, orange and yellow colours of its polymorphs. We use a methodology combining the generation of a large number of structures based on a computationally inexpensive model using the CrystalPredictor global search algorithm, and the further minimization of the most promising of these structures using the CrystalOptimizer local minimization algorithm which employs an accurate, yet efficiently constructed, model based on isolated-molecule quantum-mechanical calculations. We demonstrate that this approach successfully predicts the seven experimentally resolved structures of ROY as lattice-energy minima, with five of these structures being within the 12 lowest energy structures predicted. Some of the other low-energy structures identified are likely candidates for the still unresolved polymorphs of this molecule. The relative stability of the predicted structures only partially matches that of the experimentally resolved polymorphs. The worst case is that of polymorph ON, whose relative energy with respect to Y is overestimated by 6.65 kJ mol(-1). This highlights the need for further developments in the accuracy of the energy calculations.

Polymorph formation and nucleation mechanism of tolfenamic acid in solution: an investigation of pre-nucleation solute association

PURPOSE

Crystallization from solution involves nucleation and growth; growth conditions greatly influence self-association behaviors of solute molecules in these steps, affecting crystal packing of organic molecules. We examined the role of pre-nucleation association to provide insights into the mutual influence between molecular conformation in solution and packing in the solid state.

METHODS

Crystallization experiments of tolfenamic acid were conducted in ethanol under different supersaturation conditions. UV spectroscopy was performed to study self-association of solute molecules in ethanol as a function of concentration. Intermolecular interaction energies of tolfenamic acid dimers were calculated with quantum mechanical methods.

RESULTS

As supersaturation increased, growth of the most stable polymorph outpaced the metastable one, contradicting Ostwald's Rule of Stages. UV spectroscopy measurement suggests solute molecules exist as hydrogen-bonded dimers and more dimers form as total concentration increases. Hydrogen bonding in the most stable form is significantly stronger than that in the metastable form.

CONCLUSIONS

With the fact that molecular conformation is different in the two polymorphs, as concentration increases, solute molecules rearrange their conformations to form stronger hydrogen-bonded dimers in solution, resulting in nucleation of the most stable form.

Polymorphism in molecular solids: an extraordinary system of red, orange, and yellow crystals

Diamond and graphite are polymorphs of each other: they have the same composition but different structures and properties. Many other substances exhibit polymorphism: inorganic and organic, natural and manmade. Polymorphs are encountered in studies of crystallization, phase transition, materials synthesis, and biomineralization and in the manufacture of specialty chemicals. Polymorphs can provide valuable insights into crystal packing and structure-property relationships. 5-Methyl-2-[(2-nitrophenyl)amino]-3-thiophenecarbonitrile, known as ROY for its red, orange, and yellow crystals, has seven polymorphs with solved structures, the largest number in the Cambridge Structural Database. First synthesized by medicinal chemists, ROY has attracted attention from solid-state chemists because it demonstrates the remarkable diversity possible in organic solids. Many structures of ROY polymorphs and their thermodynamic properties are known, making ROY an important model system for testing computational models. Though not the most polymorphic substance on record, ROY is extraordinary in that many of its polymorphs can crystallize simultaneously from the same liquid and are kinetically stable under the same conditions. Studies of ROY polymorphs have revealed a new crystallization mechanism that invalidates the common view that nucleation defines the polymorph of crystallization. A slow-nucleating polymorph can still dominate the product if it grows rapidly and nucleates on another polymorph. Studies of ROY have also helped understand a new, surprisingly fast mode of crystal growth in organic liquids cooled to the glass transition temperature. This growth mode exists only for those polymorphs that have more isotropic, and perhaps more liquid-like, packing. The rich polymorphism of ROY results from a combination of favorable thermodynamics and kinetics. Not only must there be many polymorphs of comparable energies or free energies, many polymorphs must be kinetically stable and crystallize at comparable rates to be observed. This system demonstrates the unique insights that polymorphism provides into solid-state structures and properties, as well as the inadequacy of our current understanding of the phenomenon. Despite many studies of ROY, it is still impossible to predict the next molecule that is equally or more polymorphic. ROY is a lucky gift from medicinal chemists.