Substitutional and orientational disorder in organic crystals: a symmetry-adapted ensemble model

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.

Polymorphic Solid Solutions in Molecular Crystals: Tips, Tricks, and Switches

Crystal polymorphism has been a topic of much interest for the past 20 years or so, especially since its scientific (and legal) importance to the pharmaceutical industry was realized. By contrast, the formation of solid solutions in molecular crystals has been overlooked despite its long-standing prevalence in the analogous field of inorganic crystals. Wilfully forgotten, crystalline molecular solid solutions may be very common in our world since molecular compounds are rarely produced with 100% purity, and impurities able to form solid solutions are difficult to reject via recrystallization. Given the importance of both polymorphism and solid solutions in molecular crystals, we share here some tips, tricks, and observations to aid in their understanding. First, we propose a nomenclature system fit for the description of molecular crystalline solid solutions capable of polymorphism (tips). Second, we highlight the challenges associated with their experimental and computational characterization (tricks). Third, we show that our recently reported observation that polymorph stabilities can change by virtue of solid solution formation is a general phenomenon, reporting it on a second system (switches). Our work focuses on the historically important compound benzamide forming solid solutions with nicotinamide and 3-fluorobenzamide.

Structural Analysis of Molecular Materials Using the Pair Distribution Function

This is a review of atomic pair distribution function (PDF) analysis as applied to the study of molecular materials. The PDF method is a powerful approach to study short- and intermediate-range order in materials on the nanoscale. It may be obtained from total scattering measurements using X-rays, neutrons, or electrons, and it provides structural details when defects, disorder, or structural ambiguities obscure their elucidation directly in reciprocal space. While its uses in the study of inorganic crystals, glasses, and nanomaterials have been recently highlighted, significant progress has also been made in its application to molecular materials such as carbons, pharmaceuticals, polymers, liquids, coordination compounds, composites, and more. Here, an overview of applications toward a wide variety of molecular compounds (organic and inorganic) and systems with molecular components is presented. We then present pedagogical descriptions and tips for further implementation. Successful utilization of the method requires an interdisciplinary consolidation of material preparation, high quality scattering experimentation, data processing, model formulation, and attentive scrutiny of the results. It is hoped that this article will provide a useful reference to practitioners for PDF applications in a wide realm of molecular sciences, and help new practitioners to get started with this technique.

Static discrete disorder in the crystal structure of iododiflunisal: on the importance of hydrogen bond, halogen bond and π-stacking interactions

We report a combined computational/crystallographic analysis focused on the static discrete disorder shown by the drug iododiflunisal.

Engineering of a kinetically driven phase of phenoxazine by surface crystallisation

Surface crystallisation yields an unknown polymorph of the phenoxazine molecule. Tuning the crystallisation conditions causes a defined crystal growth of either the thermodynamically stable phase or the kinetic phase observed exclusively within thin films.

Multiferroic oxide BFCNT/BFCO heterojunction black silicon photovoltaic devices

Multiferroics are being studied increasingly in applications of photovoltaic devices for the carrier separation driven by polarization and magnetization. In this work, textured black silicon photovoltaic devices are fabricated with Bi6Fe1.6Co0.2Ni0.2Ti3O18/Bi2FeCrO6 (BFCNT/BFCO) multiferroic heterojunction as an absorber and graphene as an anode. The structural and optical analyses showed that the bandgap of Aurivillius-typed BFCNT and double perovskite BFCO are 1.62 ± 0.04 eV and 1.74 ± 0.04 eV respectively, meeting the requirements for the active layer in solar cells. Under the simulated AM 1.5 G illumination, the black silicon photovoltaic devices delivered a photoconversion efficiency (η) of 3.9% with open-circuit voltage (Voc), short-circuit current density (Jsc), and fill factor (FF) of 0.75 V, 10.8 mA cm-2, and 48.3%, respectively. Analyses of modulation of an applied electric and magnetic field on the photovoltaic properties revealed that both polarization and magnetization of multiferroics play an important role in tuning the built-in electric field and the transport mechanisms of charge carriers, thus providing a new idea for the design of future high-performance multiferroic oxide photovoltaic devices.

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.

Switching polymorph stabilities with impurities provides a thermodynamic route to benzamide form III

Almost 200 years ago, benzamide was reported as polymorphic with two of its forms (II and III) found to be difficult to crystallise. In a recent study, it was shown that benzamide form I can easily convert into benzamide form III using mechanochemistry in the presence of nicotinamide. Here we show, experimentally and computationally, that this transformation is the result of a thermodynamic switch between these two polymorphic forms driven by the formation of solid solutions with small amounts of nicotinamide. The presence of nicotinamide in the crystallisation environment promotes the robust and exclusive crystallisation of the elusive form III. These results represent a promising route to the synthesis and utilisation of elusive polymorphs of pharmaceutical interest.

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.

Intramolecular sp2-sp3 Disequalization of Chemically Identical Sulfonamide Nitrogen Atoms: Single Crystal X-Ray Diffraction Characterization, Hirshfeld Surface Analysis and DFT Calculations of N-Substituted Hexahydro-1,3,5-Triazines

In this manuscript, the synthesis and single crystal X-ray diffraction characterization of four N-substituted 1,3,5-triazinanes are reported along with a detailed analysis of the noncovalent interactions observed in the solid state architecture to these compounds, focusing on C–H···π and C–H···O H-bonding interactions. These noncovalent contacts have been characterized energetically by using DFT calculations and also by Hirshfeld surface analysis. In addition, the supramolecular assemblies have been characterized using the quantum theory of “atoms-in-molecules” (QTAIM) and molecular electrostatic potential (MEP) calculations. The XRD analysis revealed a never before observed feature of the crystalline structure of some molecules: symmetrically substituted 1,3,5-triazacyclohexanes possess two chemically identical sulfonamide nitrogen atoms in different sp2 and sp3-hybridizations.

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.

Order and disorder in (E)-[1-(biphenyl-4-yl)ethylidene]hydrazine: a structural, spectroscopic and theoretical study

An unexpected global disorder (co-existing rotational disorder and glide disorder) has been observed during an X-ray investigation of the crystal structure of (E)-[1-(biphenyl-4-yl)ethylidene]hydrazine, C14H14N2, at room temperature. When the temperature decreases to 273 K, the disorder disappears, but the quality of the data set is low. The diffraction data were collected again at 110 K. Differential scanning calorimetry (DSC) analysis and polarizing-microscopy experiments, as well as a fourth set of single-crystal data collected at 283 K, proved that the order–disorder transformation occurs continuously. The analyses of these crystal structures and full-range relaxed potential energy surface scans showed that this kind of global disorder is not very difficult to achieve inside the crystal. Experimental and theoretical studiesviaUV–Vis and fluorescence spectra impart an understanding on the prediction methods of optical properties, which are essential for the rational design of biphenyl-based materials with pre-defined properties.

Theoretical insight into the disordered structure of (Z)-2-[(E)-(4-methoxybenzylidene)hydrazinylidene]-1,2-diphenylethanone: the role of noncovalent interactions

A global glide disorder has been discovered during an X-ray investigation of the crystal structure of (Z)-2-[(E)-(4-methoxybenzylidene)hydrazinylidene]-1,2-diphenylethanone (MHDE, C₂₂H₁₈N₂O₂) at room temperature. In another crystal, however, such disorder disappears (still at room temperature). Even though the disorder may be partly due to the poor quality of the harvested crystal, the structure can shed light on the nature of disorder. With the help of quantum chemical calculations, it is found that the global disorder seems to be connected with the need for stabilization of the somewhat rigid but mobile and unstable molecular structure. The most relevant feature driving the packing of the disordered structure concerns the slight perturbations (such as glide) of two or more disorder components (fractional occupancies) distributed throughout the crystal.

Ab initio prediction of the polymorph phase diagram for crystalline methanol

Organic crystals frequently adopt multiple distinct polymorphs exhibiting different properties. The ability to predict not only what crystal forms might occur, but under what experimental thermodynamic conditions those polymorphs are stable would be immensely valuable to the pharmaceutical industry and others. Starting only from knowledge of the experimental crystal structures, this study successfully predicts the methanol crystal polymorph phase diagram from first-principles quantum chemistry, mapping out the thermodynamic regions of stability for three polymorphs over the range 0-400 K and 0-6 GPa. The agreement between the predicted and experimental phase diagrams corresponds to predicting the relative polymorph free energies to within ∼0.5 kJ mol-1 accuracy, which is achieved by employing fragment-based second-order Møller-Plesset perturbation theory and coupled cluster theory plus a quasi-harmonic treatment of the phonons.

A rough guide to molecular solid solutions: design, synthesis and characterization of mixed crystals

Recent literature on molecular solid solutions is reviewed and general empirical rules to help synthesize mixed crystals are summarised.

Stochastic polarity formation in molecular crystals, composite materials and natural tissues

This topical review summarizes the theoretical and experimental findings obtained over the last 20 years on the subject of growth-induced polarity formation driven by a Markov chain process. When entering the growing surface of a molecular crystal, an inorganic-organic composite or a natural tissue, the building blocks may undergo 180° orientational disorder. Driven by configurational entropy, faulted orientations can promote the conversion of a growing non-polar seed into an object showing polar domains. Similarly, orientational disorder at the interface may change a polar seed into a two-domain state. Analytical theory and Monte Carlo simulations were used to model polarity formation. Scanning pyroelectric, piezoresponse force and phase-sensitive second-harmonic microscopies are methods for investigating the spatial distribution of polarity. Summarizing results from different types of materials, a general principle is provided for obtaining growth-induced polar domains: a non-zero difference in the probabilities for 180° orientational misalignments of building blocks, together with uni-directional growth, along with Markov chain theory, can produce objects showing polar domains.

Organised chaos: entropy in hybrid inorganic-organic systems and other materials

Entropy is one of the fundamental quantities which links emerging research areas like flexibility and defect engineering in inorganic-organic hybrid materials. Additionally, a delicate balance between entropy and enthalpy can lead to intriguing temperature-driven transitions in such materials. Here, we briefly overview traditional material design principles, highlight the role of entropy in the past and discuss how computational methods can help us to understand and quantify entropic effects in inorganic-organic hybrid materials in the future.

An optimized intermolecular force field for hydrogen-bonded organic molecular crystals using atomic multipole electrostatics

We present a re-parameterization of a popular intermolecular force field for describing intermolecular interactions in the organic solid state. Specifically we optimize the performance of the exp-6 force field when used in conjunction with atomic multipole electrostatics. We also parameterize force fields that are optimized for use with multipoles derived from polarized molecular electron densities, to account for induction effects in molecular crystals. Parameterization is performed against a set of 186 experimentally determined, low-temperature crystal structures and 53 measured sublimation enthalpies of hydrogen-bonding organic molecules. The resulting force fields are tested on a validation set of 129 crystal structures and show improved reproduction of the structures and lattice energies of a range of organic molecular crystals compared with the original force field with atomic partial charge electrostatics. Unit-cell dimensions of the validation set are typically reproduced to within 3% with the re-parameterized force fields. Lattice energies, which were all included during parameterization, are systematically underestimated when compared with measured sublimation enthalpies, with mean absolute errors of between 7.4 and 9.0%.

Report on the sixth blind test of organic crystal structure prediction methods

The sixth blind test of organic crystal structure prediction (CSP) methods has been held, with five target systems: a small nearly rigid molecule, a polymorphic former drug candidate, a chloride salt hydrate, a co-crystal and a bulky flexible molecule. This blind test has seen substantial growth in the number of participants, with the broad range of prediction methods giving a unique insight into the state of the art in the field. Significant progress has been seen in treating flexible molecules, usage of hierarchical approaches to ranking structures, the application of density-functional approximations, and the establishment of new workflows and `best practices' for performing CSP calculations. All of the targets, apart from a single potentially disordered Z' = 2 polymorph of the drug candidate, were predicted by at least one submission. Despite many remaining challenges, it is clear that CSP methods are becoming more applicable to a wider range of real systems, including salts, hydrates and larger flexible molecules. The results also highlight the potential for CSP calculations to complement and augment experimental studies of organic solid forms.

Static and lattice vibrational energy differences between polymorphs

Lattice energy, entropy and free energy differences for over 500 pairs of known polymorphs are computed and discussed.

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.

Symmetry and random sampling of symmetry independent configurations for the simulation of disordered solids

A symmetry-adapted algorithm producing uniformly at random the set of symmetry independent configurations (SICs) in disordered crystalline systems or solid solutions is presented here. Starting from Pólya's formula, the role of the conjugacy classes of the symmetry group in uniform random sampling is shown. SICs can be obtained for all the possible compositions or for a chosen one, and symmetry constraints can be applied. The approach yields the multiplicity of the SICs and allows us to operate configurational statistics in the reduced space of the SICs. The present low-memory demanding implementation is briefly sketched. The probability of finding a given SIC or a subset of SICs is discussed as a function of the number of draws and their precise estimate is given. The method is illustrated by application to a binary series of carbonates and to the binary spinel solid solution Mg(Al,Fe)2O4.

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.

On the use of symmetry in configurational analysis for the simulation of disordered solids

The starting point for a quantum mechanical investigation of disordered systems usually implies calculations on a limited subset of configurations, generated by defining either the composition of interest or a set of compositions ranging from one end member to another, within an appropriate supercell of the primitive cell of the pure compound. The way in which symmetry can be used in the identification of symmetry independent configurations (SICs) is discussed here. First, Pólya's enumeration theory is adopted to determine the number of SICs, in the case of both varying and fixed composition, for colors numbering two or higher. Then, De Bruijn's generalization is presented, which allows analysis of the case where the colors are symmetry related, e.g. spin up and down in magnetic systems. In spite of their efficiency in counting SICs, neither Pólya's nor De Bruijn's theory helps in solving the difficult problem of identifying the complete list of SICs. Representative SICs are obtained by adopting an orderly generation approach, based on lexicographic ordering, which offers the advantage of avoiding the (computationally expensive) analysis and storage of all the possible configurations. When the number of colors increases, this strategy can be combined with the surjective resolution principle, which permits the efficient generation of SICs of a problem in |R| colors starting from the ones obtained for the (|R| - 1)-colors case. The whole scheme is documented by means of three examples: the abstract case of a square with C(4v) symmetry and the real cases of the garnet and olivine mineral families.