Are the Crystal Structures of Enantiopure and Racemic Mandelic Acids Determined by Kinetics or Thermodynamics?

Dynamically Switchable Global Chirality in Racemic Polymer Systems

Any polymers composed of racemic segments are obviously optically inactive and lack any chiroptical applications. Here, we present an intriguing method for precisely generating global chirality in racemic copolymer assemblies without any external asymmetrical intervention via step-wise polymerization-induced chiral self-assembly (PICSA). Global supramolecular chirality of the nanoaggregates could be dynamically switched by the two diametrically opposed chiral conflict effects: "first come, first serve" effect and "late-comer lives above" effect, which can be controlled by the precisely specified the number and sequence of enantiomeric segments. Significantly, the supramolecular stacking manners of the racemic mesogenic building units as well as the liquid crystallinity of the solvophobic core play a crucial role for the chiral communication pathway of enantiomeric mesogens. Furthermore, such switchable global chirality in racemic polymers is broadly applicable and well regulable. We propose that this research may challenge the notion that racemic systems lack optical activity while highlighting their potential applications in functional racemic polymer materials and providing insights into the evolution of racemates towards homochirality on early Earth.

Complex isomerism influencing the textural properties of organometallic [Cu(salen)] porous polymers: paramagnetic solid-state NMR characterization and heterogeneous catalysis

Although organometallic porous polymer networks are recognized as promising heterogeneous catalysts, the relationship between ligand/monomer geometry and network parameters is usually not well understood due to the lack of atom-resolved characterization methods for the amorphous network matrix. In this work, a series of copper(II) salen-type metal complexes was synthesized, using trans- and cis-1,2-diaminocyclohexane segments, and thoroughly characterized by single-crystal X-ray diffraction and solution- and solid-state NMR spectroscopy. Terminal ethynyl groups of the complexes were then transformed into polyacetylene chains by coordination chain-growth homopolymerization, resulting in highly porous (458-655 m2 g-1) organometallic polymer networks with a copper(II) ion content of about 12 wt%. The presence of paramagnetic copper(II) moieties in these complexes and respective polymer networks required the application of tailored NMR techniques, which together with X-ray crystallography and DFT calculations of the paramagnetic NMR shifts made it possible to investigate the differences in the complex geometry in liquid, powder and crystalline form and compare it with the complex geometry in polymer networks. All prepared organometallic polymer networks were also tested as heterogeneous catalysts for styrene oxidation with uncommonly high substrate conversions and compared with their low-molecular-weight analogues. The high reusability of such heterogeneous polymer-based catalysts was also proven.

Dynamic Stereochemistry of M8 Pd6 Supramolecular Cages Based on Metal-Center Lability for Differential Chiral Induction, Resolution, and Recognition

A series of isostructural supramolecular cages with a rhombic dodecahedron shape have been assembled with distinct metal-coordination lability (M8 Pd6 -MOC-16, M=Ru2+ , Fe2+ , Ni2+ , Zn2+ ). The chirality transfer between metal centers generally imposes homochirality on individual cages to enable solvent-dependent spontaneous resolution of Δ8 /Λ8 -M8 Pd6 enantiomers; however, their distinguishable stereochemical dynamics manifests differential chiral phenomena governed by the cage stability following the order Ru8 Pd6 >Ni8 Pd6 >Fe8 Pd6 >Zn8 Pd6 . The highly labile Zn centers endow the Zn8 Pd6 cage with conformational flexibility and deformation, enabling intrigue chiral-Δ8 /Λ8 -Zn8 Pd6 to meso-Δ4 Λ4 -Zn8 Pd6 transition induced by anions. The cage stabilization effect differs from inert Ru2+ , metastable Fe2+ /Ni2+ , and labile Zn2+ , resulting in different chiral-guest induction. Strikingly, solvent-mediated host-guest interactions have been revealed for Δ8 /Λ8 -(Ru/Ni/Fe)8 Pd6 cages to discriminate the chiral recognition of the guests with opposite chirality. These results demonstrate a versatile procedure to control the stereochemistry of metal-organic cages based on the dynamic metal centers, thus providing guidance to maneuver cage chirality at a supramolecular level by virtue of the solvent, anion, and guest to benefit practical applications.

Block Copolymer Enabled Synthesis and Assembly of Chiral Metal Oxide Nanoparticle

Chiral metal oxide nanostructures have received tremendous attention in nanotechnological applications owing to their intriguing chiroptical and magnetic properties. Current synthetic methods mostly rely on the use of amino acids or peptides as chiral inducers. Here, we report a general approach to fabricate chiral metal oxide nanostructures with tunable magneto-chiral effects, using block copolymer (BCP) inverse micelle and R/S-mandelic acid (MA). Diverse chiral metal oxide nanostructures are prepared by the selective incorporation of precursors within micellar cores followed by the oxidation process, exhibiting intense chiroptical properties with a g-factor up to 7.0 × 10^-3 in the visible-NIR range for the Cr₂O₃ nanoparticle multilayer. The BCP inverse micelle is found to inhibit the racemization of MA, allowing MA to act as a chiral dopant that imparts chirality to nanostructures via hierarchical chirality transfer. Notably, for paramagnetic nanostructures, magneto-chiroptical modulation is realized by regulating the direction of the external magnetic field. This BCP-driven approach can be extended to the mass production of chiral nanostructures with tunable architectures and optical activities, which may provide insights into the development of chiroptical functional materials.

Crystallization Behavior and Crystallographic Properties of dl-Arabinose and dl-Xylose Diastereomer Sugars

Natural sugar molecules such as xylose and arabinose exhibit sweetness profiles similar to sucrose, which makes them a valuable alternative in low-calorie foods as well as excipients or cocrystallization agents in pharmaceutical formulations. Xylose and arabinose are also chiral diastereomers that can exhibit specific crystallization behavior. In this work, the solid-state landscapes of the chiral pairs of both xylose and arabinose have been investigated to determine whether racemic compounds or conglomerates are formed. Furthermore, single crystals of xylose and arabinose have been grown and characterized by X-ray diffraction and optical microscopy to study their crystallographic properties and relate them to the crystallization behavior. Differential scanning calorimetry (DSC) measurements were used to determine the phase diagrams of the two analyzed chiral systems. The solubilities of the different solid forms of xylose and arabinose were measured in different solvent mixtures by a thermogravimetric method. An analysis was conducted to assess the main thermodynamic parameters and the activity coefficients of the compounds in solution. Finally, slurry experiments in a 50:50 w/w ethanol/water solvent have also been performed to determine the relative stability of each solid form and the kinetics of transformation in this solvent mixture. It was found that dl-arabinose crystallizes as a stable racemic compound, which transforms quickly from its constituent enantiomers when in solution; whereas d- and l-xylose molecules crystallize separately as a conglomerate.

Pressure Dependence of the Crystallization Rate for the S-Enantiomer and a Racemic Mixture of Ibuprofen

This paper examines the pressure effect on the crystallization rate of the pharmaceutically active enantiomerically pure S-enantiomer and the racemic mixture of the well-known drug ibuprofen. Performed experimental studies revealed that at ambient pressure S-ibuprofen crystallizes faster than the racemic mixture. When the pressure increases, the crystallization rate slows down for both systems, but interestingly it is more apparent in the case of the S-enantiomer. It is found that this experimentally observed trend can be understood based on the predictions of the classical nucleation theory. We suggest that the solid-liquid interfacial free energy is the main reason for the observed variations in S- and RS-ibuprofen's stability behaviors. Employing a special method of computational studies, i.e., the capillary fluctuation method, we show that the increase in pressure affects the solid-liquid interfacial free energy for S- and RS-ibuprofen in an entirely different way. Importantly, the detected differences correspond to the experimentally observed variations in the overall crystallization rates.

Control of self-assembly pathways toward conglomerate and racemic supramolecular polymers

Homo- and heterochiral aggregation during crystallization of organic molecules has significance both for fundamental questions related to the origin of life as well as for the separation of homochiral compounds from their racemates in industrial processes. Herein, we analyse these phenomena at the lowest level of hierarchy – that is the self-assembly of a racemic mixture of (R,R)- and (S,S)-PBI into 1D supramolecular polymers. By a combination of UV/vis and NMR spectroscopy as well as atomic force microscopy, we demonstrate that homochiral aggregation of the racemic mixture leads to the formation of two types of supramolecular conglomerates under kinetic control, while under thermodynamic control heterochiral aggregation is preferred, affording a racemic supramolecular polymer. FT-IR spectroscopy and quantum-chemical calculations reveal unique packing arrangements and hydrogen-bonding patterns within these supramolecular polymers. Time-, concentration- and temperature-dependent UV/vis experiments provide further insights into the kinetic and thermodynamic control of the conglomerate and racemic supramolecular polymer formation.

Homo- and heterochiral aggregation is a process of interest to prebiotic and chiral separation chemistry. Here, the authors analyze the self-assembly of a racemic mixture into 1D supramolecular polymers and find homochiral aggregation into conglomerates under kinetic control, while under thermodynamic control a racemic polymer is formed.

Systematic comparison of racemic and enantiopure multicomponent crystals of phenylsuccinic acid—the role of chirality

Comparison of binary cocrystals of chiral and racemic carboxylic acids showed that the introduction of chiral building blocks may lead to the formation of subclasses of multicomponent crystals with unique Z′′/Z^r values combined with complex protonation stages of the molecules.

Melting point–solubility–structure correlations in chiral and racemic model cocrystals

Comparison of chiral and racemic binary cocrystals showed that the chiral building block limits the formation of certain intermolecular interactions, decreases the packing efficiency, lowers the melting point and increases aqueous solubility.

Structural similarity in chiral-achiral multi-component crystals

Understanding the structural similarities between co-crystals formed with racemic mixture and enantiopure chiral components with an achiral co-former.

Intermolecular Interactions in Molecular Organic Crystals upon Relaxation of Lattice Parameters

Crystal structure prediction is based on the assumption that the most thermodynamically stable structure will crystallize first. The existence of other structures such as polymorphs or from counterenantiomers requires an accurate calculation of the electronic energy. Using atom-centered Gaussian basis functions in periodic Density Functional Theory (DFT) calculations in Turbomole, the performance of two dispersion-corrected functionals, PBE-D3 and B97-D, is assessed for molecular organic crystals of the X23 benchmark set. B97-D shows a MAE (mean absolute error) of 4 kJ/mol, compared to 9 kJ/mol for PBE-D3. A strategy for the convergence of lattice energies towards the basis set limit is outlined. A simultaneous minimization of molecular structures and lattice parameters shows that both methods are able to reproduce experimental unit cell parameters to within 4–5%. Calculated lattice energies, however, deviate slightly more from the experiment, i.e., by 0.4 kJ/mol after unit cell optimization for PBE-D3 and 0.5 kJ/mol for B97-D. The accuracy of the calculated lattice energies compared to the experimental values demonstrates the ability of current DFT methods to assist in the quest for possible polymorphs and enantioselective crystallization processes.

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

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

Composite and Low-Cost Approaches for Molecular Crystal Structure Prediction

Molecular crystal structure prediction (CSP) requires evaluating differences in lattice energy between candidate crystal structures accurately and efficiently. In this work, we explore and compare several low-cost alternatives to dispersion-corrected density-functional theory (DFT) in the plane-waves/pseudopotential approximation, the most accurate and general approach used for CSP at present. Three types of low-cost methods are considered: DFT with a small basis set of finite-support numerical orbitals (the SIESTA method), dispersion-corrected Gaussian small or minimal-basis-set Hartree-Fock and DFT with additional empirical corrections (HF-3c and PBEh-3c), and self-consistent-charge dispersion-corrected density-functional tight binding (SCC-DFTB3-D3). In addition, we study the performance of composite methods that comprise a geometry optimization using a low-cost approach followed by a single-point calculation using the accurate but comparatively expensive B86bPBE-XDM functional. All methods were tested for their abilities to produce absolute lattice energies, relative lattice energies, and crystal geometries. We show that assessing various methods by their ability to produce absolute lattice energies can be misleading and that relative lattice energies are a much better indicator of performance in CSP. The EE14 set of relative solubilities of homochiral and heterochiral chiral crystals is proposed for relative lattice-energy benchmarking. Our results show that PBE-D2 plus a DZP basis set of numerical orbitals coupled with a final B86bPBE-XDM single-point calculation gives excellent performance at a fraction of the cost of a full B86bPBE-XDM calculation, although the results are sensitive to the particular details of the computational protocol. The B86bPBE-XDM//PBE-D2/DZP method was subsequently tested in a practical CSP application from our recent work on the crystal structure of the enantiopure and racemate forms of 1-aza[6]helicene, a chiral organic semiconductor. Our results show that this multilevel method is able to correctly reproduce the energy ranking of both crystal forms.

Computational evaluation of metal pentazolate frameworks: inorganic analogues of azolate metal-organic frameworks

Pentazolate is the ultimate all-nitrogen, inorganic member of the azolate series of aromatic 5-membered ring anions. As an azolate ligand, it has the potential to form open framework structures with metal ions, that would be inorganic analogues of azolate metal-organic frameworks formed by its congeners. However, while the low stability and elusive nature of the pentazolate ion have so far prevented the synthesis of such frameworks, computational studies have focused on pentazolate exclusively as a ligand that would form discrete metallocene structures. Encouraged by the recent first isolation and structural characterization of pentazolate salts and metal complexes stable at ambient conditions, we now explore the role of pentazolate as a framework-forming ligand. We report a computational periodic density-functional theory evaluation of the energetics and topological preferences of putative metal pentazolate frameworks, which also revealed a topologically novel framework structure.

The prediction of hole mobility in organic semiconductors and its calibration based on the grain-boundary effect

A new reliable computational model to predict the hole mobility of poly-crystalline organic semiconductors in thin films was developed. Site energy differences and transfer integrals in crystalline morphologies of organic molecules were obtained from quantum chemical calculations, in which periodic boundary conditions were efficiently applied to capture the interactions with the surrounding molecules in the crystalline organic layer. Then the parameters were employed in kinetic Monte Carlo (kMC) simulations to estimate the carrier mobility. Carrier transport in multiple directions has been considered in the kMC simulation to mimic poly-crystalline characteristics under thin-film conditions. Furthermore, the calculated mobility was corrected using a calibration equation based on microscopy images of the thin films to take the effect of grain boundaries into account. As a result, good agreement was observed between the predicted and measured hole mobility values for 21 molecular species: the coefficient of determination (R(2)) was estimated to be 0.83 and the mean absolute error was 1.32 cm(2) V(-1) s(-1). This numerical approach can be applied to any molecules for which crystal structures are available and will provide a rapid and precise way of predicting device performance.

Is zeroth order crystal structure prediction (CSP_0) coming to maturity? What should we aim for in an ideal crystal structure prediction code?

Crystal structure prediction based on searching for the global minimum in the lattice energy (CSP_0) is growing in use for guiding the discovery of new materials, for example, new functional materials, new phases of interest to planetary scientists and new polymorphs relevant to pharmaceutical development. This Faraday Discussion can assess the progress of CSP_0 over the range of types of materials to which CSP is currently and could be applied, which depends on our ability to model the variety of interatomic forces in crystals. The basic hypothesis, that the outcome of crystallisation is determined by thermodynamics, needs examining by considering methods of modelling relative thermodynamic stability not only as a function of pressure and temperature, but also of size, solvent and the presence of heterogeneous templates or impurities (CSP_thd). Given that many important materials persist, and indeed may be formed, when they are not the most thermodynamically stable structure, we need to define what would be required of an ideal CSP code (CSP_aim).

Chiral metal–organic frameworks constructed from four-fold helical chain SBUs for enantioselective recognition of α-hydroxy/amino acids

Three chiral 3D metal–carboxylate frameworks have been successfully synthesized, featuring four-fold helical metal chains as SBUs. Co-MOFs could recognize enantio-selectively α-hydroxy/amino acids by the change of CD signals.

11-Azaartemisinin cocrystals with preserved lactam : acid heterosynthons

The R22(8) lactam : acid hetero-synthon, found in several new 1 : 1 and 2 : 1 cocrystals between the anti-malarial 11-azaartemisinin and organic acids.

Unraveling Complexity in the Solid Form Screening of a Pharmaceutical Salt: Why so Many Forms? Why so Few?

The solid form landscape of 5-HT2a antagonist 3-(4-(benzo[d]isoxazole-3-yl)piperazin-1-yl)-2,2-dimethylpropanoic acid hydrochloride (B5HCl) proved difficult to establish. Many crystalline materials were produced by solid form screening, but few forms readily grew high quality crystals to afford a clear picture or understanding of the solid form landscape. Careful control of crystallization conditions, a range of experimental methods, computational modeling of solvate structures, and crystal structure prediction were required to see potential arrangements of the salt in its crystal forms. Structural diversity in the solid form landscape of B5HCl was apparent in the layer structures for the anhydrate polymorphs (Forms I and II), dihydrate and a family of solvates with alcohols. The alcohol solvates, which provided a distinct packing from the neat forms and the dihydrate, form layers with conserved hydrogen bonding between B5HCl and the solvent, as well as stacking of the aromatic rings. The ability of the alcohol hydrocarbon moieties to efficiently pack between the layers accounted for the difficulty in growing some solvate crystals and the inability of other solvates to crystallize altogether. Through a combination of experiment and computation, the crystallization problems, form stability, and desolvation pathways of B5HCl have been rationalized at a molecular level.

Use of Crystal Structure Informatics for Defining the Conformational Space Needed for Predicting Crystal Structures of Pharmaceutical Molecules

Determining the range of conformations that a flexible pharmaceutical-like molecule could plausibly adopt in a crystal structure is a key to successful crystal structure prediction (CSP) studies. We aim to use conformational information from the crystal structures in the Cambridge Structural Database (CSD) to facilitate this task. The conformations produced by the CSD Conformer Generator are reduced in number by considering the underlying rotamer distributions, an analysis of changes in molecular shape, and a minimal number of molecular ab initio calculations. This method is tested for five pharmaceutical-like molecules where an extensive CSP study has already been performed. The CSD informatics-derived set of crystal structure searches generates almost all the low-energy crystal structures previously found, including all experimental structures. The workflow effectively combines information on individual torsion angles and then eliminates the combinations that are too high in energy to be found in the solid state, reducing the resources needed to cover the solid-state conformational space of a molecule. This provides insights into how the low-energy solid-state and isolated-molecule conformations are related to the properties of the individual flexible torsion angles.

Exchange-Hole Dipole Dispersion Model for Accurate Energy Ranking in Molecular Crystal Structure Prediction

Accurate energy ranking is a key facet to the problem of first-principles crystal-structure prediction (CSP) of molecular crystals. This work presents a systematic assessment of B86bPBE-XDM, a semilocal density functional combined with the exchange-hole dipole moment (XDM) dispersion model, for energy ranking using 14 compounds from the first five CSP blind tests. Specifically, the set of crystals studied comprises 11 rigid, planar compounds and 3 co-crystals. The experimental structure was correctly identified as the lowest in lattice energy for 12 of the 14 total crystals. One of the exceptions is 4-hydroxythiophene-2-carbonitrile, for which the experimental structure was correctly identified once a quasi-harmonic estimate of the vibrational free-energy contribution was included, evidencing the occasional importance of thermal corrections for accurate energy ranking. The other exception is an organic salt, where charge-transfer error (also called delocalization error) is expected to cause the base density functional to be unreliable. Provided the choice of base density functional is appropriate and an estimate of temperature effects is used, XDM-corrected density-functional theory is highly reliable for the energetic ranking of competing crystal structures.

Induction time of a polymorphic transformation

We analyze the processes governing the lifetimes of transient metastable polymorphs, within the context of classical nucleation theory.

Reversible crystal-to-crystal chiral resolution: making/breaking non-bonding S⋯O interactions

Unconventional non-covalent interactions are the key to reversible chiral resolution in polycrystalline samples of a small, achiral molecule.

Toward polarizable AMOEBA thermodynamics at fixed charge efficiency using a dual force field approach: application to organic crystals

First principles prediction of the structure, thermodynamics and solubility of organic molecular crystals, which play a central role in chemical, material, pharmaceutical and engineering sciences, challenges both potential energy functions and sampling methodologies. Here we calculate absolute crystal deposition thermodynamics using a novel dual force field approach whose goal is to maintain the accuracy of advanced multipole force fields (e.g. the polarizable AMOEBA model) while performing more than 95% of the sampling in an inexpensive fixed charge (FC) force field (e.g. OPLS-AA). Absolute crystal sublimation/deposition phase transition free energies were determined using an alchemical path that grows the crystalline state from a vapor reference state based on sampling with the OPLS-AA force field, followed by dual force field thermodynamic corrections to change between FC and AMOEBA resolutions at both end states (we denote the three step path as AMOEBA/FC). Importantly, whereas the phase transition requires on the order of 200 ns of sampling per compound, only 5 ns of sampling was needed for the dual force field thermodynamic corrections to reach a mean statistical uncertainty of 0.05 kcal mol-1. For five organic compounds, the mean unsigned error between direct use of AMOEBA and the AMOEBA/FC dual force field path was only 0.2 kcal mol-1 and not statistically significant. Compared to experimental deposition thermodynamics, the mean unsigned error for AMOEBA/FC (1.4 kcal mol-1) was more than a factor of two smaller than uncorrected OPLS-AA (3.2 kcal mol-1). Overall, the dual force field thermodynamic corrections reduced condensed phase sampling in the expensive force field by a factor of 40, and may prove useful for protein stability or binding thermodynamics in the future.

Prenucleation Self-Assembly and Chiral Discrimination Mechanisms during Solution Crystallisation of Racemic Diprophylline

The crystallisation behaviour of (RS)-diprophylline (DPL) in two different solvents is investigated to assess the incidence of solvated pre-associations on nucleation, crystal growth and chiral discrimination. In the solvated state, Raman spectroscopy shows that dimeric associations similar to those depicted in the crystalline solid solution (ssRII) predominate in isopropanol (IPA), which may account for the systematic spontaneous nucleation of this crystal form from this solvent. By contrast, spontaneous nucleation in DMF yields the stable racemic compound RI, consistently with the distinct features of the Raman spectrum collected in this solvent. A crystal growth study of ssRII in IPA reveals that the crystal habitus is impacted by the solution enantiomeric excess; this is explained by increased competition between homo- and heterochiral pre-associations. This is supported by a molecular modelling study on the enantiomeric selectivity of the DPL crystal lattices. The combination of assessment methods on solution chemistry, nucleation and chiral discrimination provides methodological tools from which the occurrence of solid solutions can be rationalised.

Can computed crystal energy landscapes help understand pharmaceutical solids?

Computational crystal structure prediction (CSP) methods can now be applied to the smaller pharmaceutical molecules currently in drug development. We review the recent uses of computed crystal energy landscapes for pharmaceuticals, concentrating on examples where they have been used in collaboration with industrial-style experimental solid form screening. There is a strong complementarity in aiding experiment to find and characterise practically important solid forms and understanding the nature of the solid form landscape.

Modeling Polymorphic Molecular Crystals with Electronic Structure Theory

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

Diversity in a simple co-crystal: racemic and kryptoracemic behaviour

The first kryptoracemate co-crystal displays structural diversity and a reversible single-crystal to single-crystal transition between two kryptoracemate forms.