Computational modelling of solvent effects in a prolific solvatomorphic porous organic cage

Machine-Learned Potentials by Active Learning from Organic Crystal Structure Prediction Landscapes

A primary challenge in organic molecular crystal structure prediction (CSP) is accurately ranking the energies of potential structures. While high-level solid-state density functional theory (DFT) methods allow for mostly reliable discrimination of the low-energy structures, their high computational cost is problematic because of the need to evaluate tens to hundreds of thousands of trial crystal structures to fully explore typical crystal energy landscapes. Consequently, lower-cost but less accurate empirical force fields are often used, sometimes as the first stage of a hierarchical scheme involving multiple stages of increasingly accurate energy calculations. Machine-learned interatomic potentials (MLIPs), trained to reproduce the results of ab initio methods with computational costs close to those of force fields, can improve the efficiency of the CSP by reducing or eliminating the need for costly DFT calculations. Here, we investigate active learning methods for training MLIPs with CSP datasets. The combination of active learning with the well-developed sampling methods from CSP yields potentials in a highly automated workflow that are relevant over a wide range of the crystal packing space. To demonstrate these potentials, we illustrate efficiently reranking large, diverse crystal structure landscapes to near-DFT accuracy from force field-based CSP, improving the reliability of the final energy ranking. Furthermore, we demonstrate how these potentials can be extended to more accurately model structures far from lattice energy minima through additional on-the-fly training within Monte Carlo simulations.

Experimental Confirmation of a Predicted Porous Hydrogen-Bonded Organic Framework

Hydrogen-bonded organic frameworks (HOFs) with low densities and high porosities are rare and challenging to design because most molecules have a strong energetic preference for close packing. Crystal structure prediction (CSP) can rank the crystal packings available to an organic molecule based on their relative lattice energies. This has become a powerful tool for the a priori design of porous molecular crystals. Previously, we combined CSP with structure-property predictions to generate energy-structure-function (ESF) maps for a series of triptycene-based molecules with quinoxaline groups. From these ESF maps, triptycene trisquinoxalinedione (TH5) was predicted to form a previously unknown low-energy HOF (TH5-A) with a remarkably low density of 0.374 g cm-3 and three-dimensional (3D) pores. Here, we demonstrate the reliability of those ESF maps by discovering this TH5-A polymorph experimentally. This material has a high accessible surface area of 3,284 m2  g-1 , as measured by nitrogen adsorption, making it one of the most porous HOFs reported to date.

Coarse-grained modelling to predict the packing of porous organic cages

How molecules pack has vital ramifications for their applications as functional molecular materials. Small changes in a molecule's functionality can lead to large, non-intuitive, changes in their global solid-state packing, resulting in difficulty in targeted design. Predicting the crystal structure of organic molecules from only their molecular structure is a well-known problem plaguing crystal engineering. Although relevant to the properties of many organic molecules, the packing behaviour of modular porous materials, such as porous organic cages (POCs), greatly impacts the properties of the material. We present a novel way of predicting the solid-state phase behaviour of POCs by using a simplistic model containing the dominant degrees of freedom driving crystalline phase formation. We employ coarse-grained simulations to systematically study how chemical functionality of pseudo-octahedral cages can be used to manipulate the solid-state phase formation of POCs. Our results support those of experimentally reported structures, showing that for cages which pack via their windows forming a porous network, only one phase is formed, whereas when cages pack via their windows and arenes, the phase behaviour is more complex. While presenting a lower computational cost route for predicting molecular crystal packing, coarse-grained models also allow for the development of design rules which we start to formulate through our results.

A data-driven and topological mapping approach for the a priori prediction of stable molecular crystalline hydrates

Predictions of the structures of stoichiometric, fractional, or nonstoichiometric hydrates of organic molecular crystals are immensely challenging due to the extensive search space of different water contents, host molecular placements throughout the crystal, and internal molecular conformations. However, the dry frameworks of these hydrates, especially for nonstoichiometric or isostructural dehydrates, can often be predicted from a standard anhydrous crystal structure prediction (CSP) protocol. Inspired by developments in the field of drug binding, we introduce an efficient data-driven and topologically aware approach for predicting organic molecular crystal hydrate structures through a mapping of water positions within the crystal structure. The method does not require a priori specification of water content and can, therefore, predict stoichiometric, fractional, and nonstoichiometric hydrate structures. This approach, which we term a mapping approach for crystal hydrates (MACH), establishes a set of rules for systematic determination of favorable positions for water insertion within predicted or experimental crystal structures based on considerations of the chemical features of local environments and void regions. The proposed approach is tested on hydrates of three pharmaceutically relevant compounds that exhibit diverse crystal packing motifs and void environments characteristic of hydrate structures. Overall, we show that our mapping approach introduces an advance in the efficient performance of hydrate CSP through generation of stable hydrate stoichiometries at low cost and should be considered an integral component for CSP workflows.

Analogy Powered by Prediction and Structural Invariants: Computationally Led Discovery of a Mesoporous Hydrogen-Bonded Organic Cage Crystal

Mesoporous molecular crystals have potential applications in separation and catalysis, but they are rare and hard to design because many weak interactions compete during crystallization, and most molecules have an energetic preference for close packing. Here, we combine crystal structure prediction (CSP) with structural invariants to continuously qualify the similarity between predicted crystal structures for related molecules. This allows isomorphous substitution strategies, which can be unreliable for molecular crystals, to be augmented by a priori prediction, thus leveraging the power of both approaches. We used this combined approach to discover a rare example of a low-density (0.54 g cm^–3) mesoporous hydrogen-bonded framework (HOF), 3D-CageHOF-1. This structure comprises an organic cage (Cage-3-NH₂) that was predicted to form kinetically trapped, low-density polymorphs via CSP. Pointwise distance distribution structural invariants revealed five predicted forms of Cage-3-NH₂ that are analogous to experimentally realized porous crystals of a chemically different but geometrically similar molecule, T2. More broadly, this approach overcomes the difficulties in comparing predicted molecular crystals with varying lattice parameters, thus allowing for the systematic comparison of energy–structure landscapes for chemically dissimilar molecules.

Expanding the Solid Form Landscape of Bipyridines

Two bipyridine isomers (2,2'- and 4,4'-), used as coformers and ligands in coordination chemistry, were subjected to solid form screening and crystal structure prediction. One anhydrate and a formic acid disolvate were crystallized for 2,2'-bipyridine, whereas multiple solid-state forms, anhydrate, dihydrate, and eight solvates with carboxylic acids, including a polymorphic acetic acid disolvate, were found for the 4,4'-isomer. Seven of the solvates are reported for the first time, and structural information is provided for six of the new solvates. All twelve solid-state forms were investigated comprehensively using experimental [thermal analysis, isothermal calorimetry, X-ray diffraction, gravimetric moisture (de)sorption, and IR spectroscopy] and computational approaches. Lattice and interaction energy calculations confirmed the thermodynamic driving force for disolvate formation, mediated by the absence of H-bond donor groups of the host molecules. The exposed location of the N atoms in 4,4'-bipyridine facilitates the accommodation of bigger carboxylic acids and leads to higher conformational flexibility compared to 2,2'-bipyridine. For the 4,4'-bipyridine anhydrate ↔ hydrate interconversion hardly any hysteresis and a fast transformation kinetics are observed, with the critical relative humidity being at 35% at room temperature. The computed anhydrate crystal energy landscapes have the 2,2'-bipyridine as the lowest energy structure and the 4,4'-bipyridine among the low-energy structures and suggest a different crystallization behavior of the two compounds.

Accelerating computational discovery of porous solids through improved navigation of energy-structure-function maps

While energy-structure-function (ESF) maps are a powerful new tool for in silico materials design, the cost of acquiring an ESF map for many properties is too high for routine integration into high-throughput virtual screening workflows. Here, we propose the next evolution of the ESF map. This uses parallel Bayesian optimization to selectively acquire energy and property data, generating the same levels of insight at a fraction of the computational cost. We use this approach to obtain a two orders of magnitude speedup on an ESF study that focused on the discovery of molecular crystals for methane capture, saving more than 500,000 central processing unit hours from the original protocol. By accelerating the acquisition of insight from ESF maps, we pave the way for the use of these maps in automated ultrahigh-throughput screening pipelines by greatly reducing the opportunity risk associated with the choice of system to calculate.

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.

Structure prediction of crystals, surfaces and nanoparticles

We review the current techniques used in the prediction of crystal structures and their surfaces and of the structures of nanoparticles. The main classes of search algorithm and energy function are summarized, and we discuss the growing role of methods based on machine learning. We illustrate the current status of the field with examples taken from metallic, inorganic and organic systems. This article is part of a discussion meeting issue 'Dynamic in situ microscopy relating structure and function'.

Structural variety of heterosynthons in linezolid cocrystals with modified thermal properties

In a search for new crystalline forms of linezolid with modified thermal properties five cocrystals of this wide range antibiotic with aromatic acids were obtained via mechanochemical grinding and analyzed with single crystal X-ray diffraction, solid-state NMR spectroscopy, powder X-ray diffraction and DSC measurements. The coformers used in this study were benzoic acid, p-hydroxybenzoic acid, protocatechuic acid, γ-resorcylic acid and gallic acid. In each of the cocrystals distinct structural features have been found, including a variable amount of water and different heterosynthons, indicating that there is more than one type of intermolecular interaction preferred by the linezolid molecule. Basing on the frequency of the observed supramolecular synthons, the proposed hierarchy of the hydrogen-bond acceptor sites of linezolid (LIN) is C=O_amide > C=O_oxazolidone > C-O-C_morpholine > C-N-C_morpholine > C-O-C_oxazolidone. In addition, aromatic-aromatic interactions were found to be important in the stabilization of the analyzed structures. The obtained cocrystals show modified thermal properties, with four of them having melting points lower than the temperature of the phase transition from linezolid form II to linezolid form III. Such a change in this physicochemical property allows for the future application of melting-based techniques of introducing linezolid into drug delivery systems. In addition a change in water solubility of linezolid upon cocrystalization was evaluated, but only in the case of the cocrystal with protocatechuic acid was there a significant (43%) improvement in solubility in comparison with linezolid.

An Expandable Hydrogen-Bonded Organic Framework Characterized by Three-Dimensional Electron Diffraction

A molecular crystal of a 2-D hydrogen-bonded organic framework (HOF) undergoes an unusual structural transformation after solvent removal from the crystal pores during activation. The conformationally flexible host molecule, ABTPA, adapts its molecular conformation during activation to initiate a framework expansion. The microcrystalline activated phase was characterized by three-dimensional electron diffraction (3D ED), which revealed that ABTPA uses out-of-plane anthracene units as adaptive structural anchors. These units change orientation to generate an expanded, lower density framework material in the activated structure. The porous HOF, ABTPA-2, has robust dynamic porosity (SA_BET = 1183 m² g^-1) and exhibits negative area thermal expansion. We use crystal structure prediction (CSP) to understand the underlying energetics behind the structural transformation and discuss the challenges facing CSP for such flexible molecules.

Supramolecular-Macrocycle-Based Crystalline Organic Materials

Supramolecular macrocycles are well known as guest receptors in supramolecular chemistry, especially host-guest chemistry. In addition to their wide applications in host-guest chemistry and related areas, macrocycles have also been employed to construct crystalline organic materials (COMs) owing to their particular structures that combine both rigidity and adaptivity. There are two main types of supramolecular-macrocycle-based COMs: those constructed from macrocycles themselves and those prepared from macrocycles with other organic linkers. This review summarizes recent developments in supramolecular-macrocycle-based COMs, which are categorized by various types of macrocycles, including cyclodextrins, calixarenes, resorcinarenes, pyrogalloarenes, cucurbiturils, pillararenes, and others. Effort is made to focus on the structures of supramolecular-macrocycle-based COMs and their structure-function relationships. In addition, the application of supramolecular-macrocycle-based COMs in gas storage or separation, molecular separation, solid-state electrolytes, proton conduction, iodine capture, water or environmental treatment, etc., are also presented. Finally, perspectives and future challenges in the field of supramolecular-macrocycle-based COMs are discussed.

Geometric landscapes for material discovery within energy-structure-function maps

Porous molecular crystals are an emerging class of porous materials formed by crystallisation of molecules with weak intermolecular interactions, which distinguishes them from extended nanoporous materials like metal-organic frameworks (MOFs). To aid discovery of porous molecular crystals for desired applications, energy-structure-function (ESF) maps were developed that combine a priori prediction of both the crystal structure and its functional properties. However, it is a challenge to represent the high-dimensional structural and functional landscapes of an ESF map and to identify energetically favourable and functionally interesting polymorphs among the 1000s to 10 000s of structures typically on a single ESF map. Here, we introduce geometric landscapes, a representation for ESF maps based on geometric similarity, quantified by persistent homology. We show that this representation allows the exploration of complex ESF maps, automatically pinpointing interesting crystalline phases available to the molecule. Furthermore, we show that geometric landscapes can serve as an accountable descriptor for porous materials to predict their performance for gas adsorption applications. A machine learning model trained using this geometric similarity could reach a remarkable accuracy in predicting the materials' performance for methane storage applications.

Mining predicted crystal structure landscapes with high throughput crystallisation: old molecules, new insights

New crystal forms of two well-studied organic molecules are identified in a computationally targeted way, by combining structure prediction with a robotic crystallisation screen, including a ‘hidden’ porous polymorph of trimesic acid.

Organic molecules tend to close pack to form dense structures when they are crystallised from organic solvents. Porous molecular crystals defy this rule: they contain open space, which is typically stabilised by inclusion of solvent in the interconnected pores during crystallisation. The design and discovery of such structures is often challenging and time consuming, in part because it is difficult to predict solvent effects on crystal form stability. Here, we combine crystal structure prediction (CSP) with a robotic crystallisation screen to accelerate the discovery of stable hydrogen-bonded frameworks. We exemplify this strategy by finding new phases of two well-studied molecules in a computationally targeted way. Specifically, we find a new ‘hidden’ porous polymorph of trimesic acid, δ-TMA, that has a guest-free hexagonal pore structure, as well as three new solvent-stabilized diamondoid frameworks of adamantane-1,3,5,7-tetracarboxylic acid (ADTA). Beyond porous solids, this hybrid computational–experimental approach could be applied to a wide range of materials problems, such as organic electronics and drug formulation.

Experimental and computational approaches to rationalise multicomponent supramolecular assemblies: dapsone monosolvates

The monosolvate crystal energy landscapes of dapsone (DDS) including the solvents carbon tetrachloride, acetone, cyclohexanone, dimethyl formamide, tetrahydrofuran, methyl ethyl ketone, 1,2-dichloroethane, 1,4-dioxane, dichloromethane and chloroform were established using experimental and computational approaches. To rationalise and understand solvate formation, solvate stability and desolvation reactions a careful control of the experimental crystallisation and storage conditions, a range of thermoanalytical methods and crystal structure prediction were required. Six of the eight DDS monosolvates are reported and characterised for the first time. Structural similarity and diversity of the at ambient conditions unstable monosolvates were apparent from the computed crystal energy landscapes, which had the experimental packings as lowest energy structures. The computed structures were used as input for Rietveld refinements and isostructurality of four of the monosolvates was confirmed. Packing comparisons of the solvate structures and molecular properties of the solvent molecules indicated that both size/shape of the solvent molecule and the possible DDSsolvent interactions are the important factors for DDS solvate formation. Through the combination of experiment and theory solvate stability and structural features have been rationalised.

Synthesis of a Large, Shape-Flexible, Solvatomorphic Porous Organic Cage

Porous organic cages have emerged over the last 10 years as a subclass of functional microporous materials. However, among all of the organic cages reported, large multicomponent organic cages with 20 components or more are still rare. Here, we present an [8 + 12] porous organic imine cage, CC20, which has an apparent surface area up to 1752 m² g^-1, depending on the crystallization and activation conditions. The cage is solvatomorphic and displays distinct geometrical cage structures, caused by crystal-packing effects, in its crystal structures. This indicates that larger cages can display a certain range of shape flexibility in the solid state, while remaining shape persistent and porous.

Machine-Learned Fragment-Based Energies for Crystal Structure Prediction

Crystal structure prediction involves a search of a complex configurational space for local minima corresponding to stable crystal structures, which can be performed efficiently using atom-atom force fields for the assessment of intermolecular interactions. However, for challenging systems, the limitations in the accuracy of force fields prevent a reliable assessment of the relative thermodynamic stability of potential structures, while the cost of fully quantum mechanical approaches can limit applications of the methods. We present a method to rapidly improve force field lattice energies by correcting two-body interactions with a higher level of theory in a fragment-based approach and predicting these corrections with machine learning. Corrected lattice energies with commonly used density functionals and second order perturbation theory (MP2) all significantly improve the ranking of experimentally known polymorphs where the rigid molecule model is applicable. The relative lattice energies of known polymorphs are also found to systematically improve with the fragment corrections. Predicting two-body interactions with atom-centered symmetry functions in a Gaussian process is found to give highly accurate results using as little as 10-20% of the data for training, reducing the cost of the energy correction by up to an order of magnitude. The machine learning approach opens up the possibility of more widespread use of fragment-based methods in crystal structure prediction, whose increased accuracy at a low computational cost will benefit applications in areas such as polymorph screening and computer-guided materials discovery.

Explaining crystallization preferences of two polyphenolic diastereoisomers by crystal structure prediction

Crystal structure prediction is used to understand the differences in crystallization of catechin and epicatechin, and to explore the predictability of solvate formation.

The interplay among molecular structures, crystal symmetries and lattice energy landscapes revealed using unsupervised machine learning: a closer look at pyrrole azaphenacenes

Using unsupervised machine learning and CSPs to help crystallographers better understand how crystallizations are affected by molecular structures.

Experimental and computational approaches to produce and characterise isostructural solvates

A combination of experiment and theory was applied to rationalise the formation, stability and phase transitions of isostructural dapsone hemisolvates. Critical solvent properties as well as structural and energetic features are discussed.

From serendipity to supramolecular design: assessing the utility of computed crystal form landscapes in inferring the risks of crystal hydration in carboxylic acids

Calculated structural descriptors for predicted anhydrate polymorphs are used to assess the risks of crystal hydration in carboxylic acids.