Modular, multi-robot integration of laboratories: an autonomous workflow for solid-state chemistry

Automation can transform productivity in research activities that use liquid handling, such as organic synthesis, but it has made less impact in materials laboratories, which require sample preparation steps and a range of solid-state characterization techniques. For example, powder X-ray diffraction (PXRD) is a key method in materials and pharmaceutical chemistry, but its end-to-end automation is challenging because it involves solid powder handling and sample processing. Here we present a fully autonomous solid-state workflow for PXRD experiments that can match or even surpass manual data quality, encompassing crystal growth, sample preparation, and automated data capture. The workflow involves 12 steps performed by a team of three multipurpose robots, illustrating the power of flexible, modular automation to integrate complex, multitask laboratories.

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.

Pushing Technique Boundaries to Probe Conformational Polymorphism

We present an extensive exploration of the solid-form landscape of chlorpropamide (CPA) using a combined experimental-computational approach at the frontiers of both fields. We have obtained new conformational polymorphs of CPA, placing them into context with known forms using flexible-molecule crystal structure prediction. We highlight the formation of a new polymorph (ζ-CPA) via spray-drying experiments despite its notable metastability (14 kJ/mol) relative to the thermodynamic α-form, and we identify and resolve the ball-milled η-form isolated in 2019. Additionally, we employ impurity- and gel-assisted crystallization to control polymorphism and the formation of novel multicomponent forms. We, thus, demonstrate the power of this collaborative screening approach to observe, rationalize, and control the formation of new metastable forms.

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.

Reducing overprediction of molecular crystal structures via threshold clustering

Crystal structure prediction is becoming an increasingly valuable tool for assessing polymorphism of crystalline molecular compounds, yet invariably, it overpredicts the number of polymorphs. One of the causes for this overprediction is in neglecting the coalescence of potential energy minima, separated by relatively small energy barriers, into a single basin at finite temperature. Considering this, we demonstrate a method underpinned by the threshold algorithm for clustering potential energy minima into basins, thereby identifying kinetically stable polymorphs and reducing overprediction.

Seeking Rules Governing Mixed Molecular Crystallization

Mixed crystals result when components of the structure are randomly replaced by analogues in ratios that can be varied continuously over certain ranges. Mixed crystals are useful because their properties can be adjusted by increments, simply by altering the ratio of components. Unfortunately, no clear rules exist to predict when two compounds are similar enough to form mixed crystals containing substantial amounts of both. To gain further understanding, we have used single-crystal X-ray diffraction, computational methods, and other tools to study mixed crystallizations within a selected set of structurally related compounds. This work has allowed us to begin to clarify the rules governing the phenomenon by showing that mixed crystals can have compositions and properties that vary continuously over wide ranges, even when the individual components do not normally crystallize in the same way. Moreover, close agreement of the results of our experiments and computational modeling demonstrates that reliable predictions about mixed crystallization can be made, despite the complexity of the phenomenon.

Densest plane group packings of regular polygons

Packings of regular convex polygons (n-gons) that are sufficiently dense have been studied extensively in the context of modeling physical and biological systems as well as discrete and computational geometry. Former results were mainly regarding densest lattice or double-lattice configurations. Here we consider all two-dimensional crystallographic symmetry groups (plane groups) by restricting the configuration space of the general packing problem of congruent copies of a compact subset of the two-dimensional Euclidean space to particular isomorphism classes of the discrete group of isometries. We formulate the plane group packing problem as a nonlinear constrained optimization problem. By means of the Entropic Trust Region Packing Algorithm that approximately solves this problem, we examine some known and unknown densest packings of various n-gons in all 17 plane groups and state conjectures about common symmetries of the densest plane group packings for every n-gon.

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.

Surprising Chemistry of 6-Azidotetrazolo[5,1-a]phthalazine: What a Purported Natural Product Reveals about the Polymorphism of Explosives

6-Azidotetrazolo[5,1-a]phthalazine (ATPH) is a nitrogen-rich compound of surprisingly broad interest. It is purported to be a natural product, yet it is closely related to substances developed as explosives and is highly polymorphic despite having a nearly planar structure with little flexibility. Seven solid forms of ATPH have been characterized by single-crystal X-ray diffraction. The structures show diverse patterns of molecular organization, including both stacked sheets and herringbone packing. In all cases, N···N and C-H···N interactions play key roles in ensuring molecular cohesion. The high polymorphism of ATPH appears to arise in part from the ability of virtually every atom of nitrogen and hydrogen in the molecule to take part in close N···N and C-H···N contacts. As a result, adjacent molecules can adopt many different relative orientations that are energetically similar, thereby generating a polymorphic landscape with an unusually high density of potential structures. This landscape has been explored in detail by the computational prediction of crystal structures. Studying ATPH has provided insights into the field of energetic materials, where access to multiple polymorphs can be used to improve performance and clarify how it depends on molecular packing. In addition, our work with ATPH shows how valuable insights into molecular crystallization, often gleaned from statistical analyses of structural databases, can also come from in-depth empirical and theoretical studies of single compounds that show distinctive behavior.

De Novo Crystal Structure Determination from Machine Learned Chemical Shifts

Determination of the three-dimensional atomic-level structure of powdered solids is one of the key goals in current chemistry. Solid-state NMR chemical shifts can be used to solve this problem, but they are limited by the high computational cost associated with crystal structure prediction methods and density functional theory chemical shift calculations. Here, we successfully determine the crystal structures of ampicillin, piroxicam, cocaine, and two polymorphs of the drug molecule AZD8329 using on-the-fly generated machine-learned isotropic chemical shifts to directly guide a Monte Carlo-based structure determination process starting from a random gas-phase conformation.

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.

Inherent Ethyl Acetate Selectivity in a Trianglimine Molecular Solid

Ethyl acetate is an important chemical raw material and solvent. It is also a key volatile organic compound in the brewing industry and a marker for lung cancer. Materials that are highly selective toward ethyl acetate are needed for its separation and detection. Here, we report a trianglimine macrocycle (TAMC) that selectively adsorbs ethyl acetate by forming a solvate. Crystal structure prediction showed this to be the lowest energy solvate structure available. This solvate leaves a metastable, “templated” cavity after solvent removal. Adsorption and breakthrough experiments confirmed that TAMC has adequate adsorption kinetics to separate ethyl acetate from azeotropic mixtures with ethanol, which is a challenging and energy‐intensive industrial separation.

Digital navigation of energy-structure-function maps for hydrogen-bonded porous molecular crystals

Energy-structure-function (ESF) maps can aid the targeted discovery of porous molecular crystals by predicting the stable crystalline arrangements along with their functions of interest. Here, we compute ESF maps for a series of rigid molecules that comprise either a triptycene or a spiro-biphenyl core, functionalized with six different hydrogen-bonding moieties. We show that the positioning of the hydrogen-bonding sites, as well as their number, has a profound influence on the shape of the resulting ESF maps, revealing promising structure-function spaces for future experiments. We also demonstrate a simple and general approach to representing and inspecting the high-dimensional data of an ESF map, enabling an efficient navigation of the ESF data to identify 'landmark' structures that are energetically favourable or functionally interesting. This is a step toward the automated analysis of ESF maps, an important goal for closed-loop, autonomous searches for molecular crystals with useful functions.

Exploration and Optimization in Crystal Structure Prediction: Combining Basin Hopping with Quasi-Random Sampling

We describe the implementation of a Monte Carlo basin hopping (BH) global optimization procedure for the prediction of molecular crystal structures. The BH method is combined with quasi-random (QR) structure generation in a hybrid method for crystal structure prediction, QR-BH, which combines the low-discrepancy sampling provided by QR sequences with BH efficiency at locating low energy structures. Through tests on a set of single-component molecular crystals and co-crystals, we demonstrate that QR-BH provides faster location of low energy structures than pure QR sampling, while maintaining the efficient location of higher energy structures that are important for identifying important polymorphs.

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'.

Minimizing Polymorphic Risk through Cooperative Computational and Experimental Exploration

We combine state-of-the-art computational crystal structure prediction (CSP) techniques with a wide range of experimental crystallization methods to understand and explore crystal structure in pharmaceuticals and minimize the risk of unanticipated late-appearing polymorphs. Initially, we demonstrate the power of CSP to rationalize the difficulty in obtaining polymorphs of the well-known pharmaceutical isoniazid and show that CSP provides the structure of the recently obtained, but unsolved, Form III of this drug despite there being only a single resolved form for almost 70 years. More dramatically, our blind CSP study predicts a significant risk of polymorphism for the related iproniazid. Employing a wide variety of experimental techniques, including high-pressure experiments, we experimentally obtained the first three known nonsolvated crystal forms of iproniazid, all of which were successfully predicted in the CSP procedure. We demonstrate the power of CSP methods and free energy calculations to rationalize the observed elusiveness of the third form of iproniazid, the success of high-pressure experiments in obtaining it, and the ability of our synergistic computational-experimental approach to “de-risk” solid form landscapes.

Multifidelity Statistical Machine Learning for Molecular Crystal Structure Prediction

The prediction of crystal structures from first-principles requires highly accurate energies for large numbers of putative crystal structures. High accuracy of solid state density functional theory (DFT) calculations is often required, but hundreds or more structures can be present in the low energy region of interest, so that the associated computational costs are prohibitive. Here, we apply statistical machine learning to predict expensive hybrid functional DFT (PBE0) calculations using a multifidelity approach to re-evaluate the energies of crystal structures predicted with an inexpensive force field. The method uses an autoregressive Gaussian process, making use of less expensive GGA DFT (PBE) calculations to bridge the gap between the force field and PBE0 energies. The method is benchmarked on the crystal structure landscapes of three small, hydrogen-bonded organic molecules and shown to produce accurate predictions of energies and crystal structure ranking using small numbers of the most expensive calculations; the PBE0 energies can be predicted with errors of less than 1 kJ mol^-1 with between 4.2 and 6.8% of the cost of the full calculations. As the model that we have developed is probabilistic, we discuss how the uncertainties in predicted energies impact the assessment of the energetic ranking of crystal structures.

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.

Evolutionary chemical space exploration for functional materials: computational organic semiconductor discovery

Computational methods, including crystal structure and property prediction, have the potential to accelerate the materials discovery process by enabling structure prediction and screening of possible molecular building blocks prior to their synthesis. However, the discovery of new functional molecular materials is still limited by the need to identify promising molecules from a vast chemical space. We describe an evolutionary method which explores a user specified region of chemical space to identify promising molecules, which are subsequently evaluated using crystal structure prediction. We demonstrate the methods for the exploration of aza-substituted pentacenes with the aim of finding small molecule organic semiconductors with high charge carrier mobilities, where the space of possible substitution patterns is too large to exhaustively search using a high throughput approach. The method efficiently explores this large space, typically requiring calculations on only ∼1% of molecules during a search. The results reveal two promising structural motifs: aza-substituted naphtho[1,2-a]anthracenes with reorganisation energies as low as pentacene and a series of pyridazine-based molecules having both low reorganisation energies and high electron affinities.

Crystal structure determination of an elusive methanol solvate – hydrate of catechin using crystal structure prediction and NMR crystallography

A useful short-cut was developed to limit the number of molecular conformations that need to be regarded in crystal structure prediction calculations, which led to the crystal structure determination of new methanol solvate – hydrate of catechin.

Understanding the formation of apremilast cocrystals

Apremilast (APR), an anti-psoriatic agent, easily forms isostructural cocrystals and solvates with aromatic entities, often disobeying at the same time Kitaigorodsky's rule as to the saturation of possible hydrogen-bonding sites. In this paper the reasons for this peculiar behavior are investigated, employing a joint experimental and theoretical approach. This includes the design of cocrystals with coformers having a high propensity towards the formation of both aromatic-aromatic and hydrogen-bonding interactions, determination of their structure, using solid-state NMR spectroscopy and X-ray crystallography, as well as calculations of stabilization energies of formation of the obtained cocrystals, followed by crystal structure prediction calculations and solubility measurements. The findings indicate that the stabilization energies of cocrystal formation are positive in all cases, which results from strain in the APR conformation in these crystal forms. On the other hand, solubility measurements show that the Gibbs free energy of formation of the apremilast:picolinamide cocrystal is negative, suggesting that the formation of the studied cocrystals is entropy driven. This entropic stabilization is associated with the disorder observed in almost all known cocrystals and solvates of APR.

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.

Rapid Structure Determination of Molecular Solids Using Chemical Shifts Directed by Unambiguous Prior Constraints

NMR-based crystallography approaches involving the combination of crystal structure prediction methods, ab initio calculated chemical shifts and solid-state NMR experiments are powerful methods for crystal structure determination of microcrystalline powders. However, currently structural information obtained from solid-state NMR is usually included only after a set of candidate crystal structures has already been independently generated, starting from a set of single-molecule conformations. Here, we show with the case of ampicillin that this can lead to failure of structure determination. We propose a crystal structure determination method that includes experimental constraints during conformer selection. In order to overcome the problem that experimental measurements on the crystalline samples are not obviously translatable to restrict the single-molecule conformational space, we propose constraints based on the analysis of absent cross-peaks in solid-state NMR correlation experiments. We show that these absences provide unambiguous structural constraints on both the crystal structure and the gas-phase conformations, and therefore can be used for unambiguous selection. The approach is parametrized on the crystal structure determination of flutamide, flufenamic acid, and cocaine, where we reduce the computational cost by around 50%. Most importantly, the method is then shown to correctly determine the crystal structure of ampicillin, which would have failed using current methods because it adopts a high-energy conformer in its crystal structure. The average positional RMSE on the NMR powder structure is ⟨r_av⟩ = 0.176 Å, which corresponds to an average equivalent displacement parameter U_eq = 0.0103 Ų.

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.

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

Crystal structure prediction methods can enable the in silico design of functional molecular crystals, but solvent effects can have a major influence on relative lattice energies, sometimes thwarting predictions. This is particularly true for porous solids, where solvent included in the pores can have an important energetic contribution. We present a Monte Carlo solvent insertion procedure for predicting the solvent filling of porous structures from crystal structure prediction landscapes, tested using a highly solvatomorphic porous organic cage molecule, CC1. Using this method, we can understand why the predicted global energy minimum structure for CC1 is never observed from solvent crystallisation. We also explain the formation of three different solvatomorphs of CC1 from three structurally-similar chlorinated solvents. Calculated solvent stabilisation energies are found to correlate with experimental results from thermogravimetric analysis, suggesting a future computational framework for a priori materials design that factors in solvation effects.

Pervasive Delocalisation Error Causes Spurious Proton Transfer in Organic Acid-Base Co-Crystals

Dispersion-corrected density-functional theory (DFT-D) methods have become the workhorse of many computational protocols for molecular crystal structure prediction due to their efficiency and convenience. However, certain limitations of DFT, such as delocalisation error, are often overlooked or are too expensive to remedy in solid-state applications. This error can lead to artificial stabilisation of charge transfer and, in this work, it is found to affect the correct identification of the protonation site in multicomponent acid-base crystals. As such, commonly used DFT-D methods cannot be applied with any reliability to the study of acid-base co-crystals or salts, while hybrid functionals remain too restrictive for routine use. This presents an impetus for the development of new functionals with reduced delocalisation error for solid-state applications; the structures studied herein constitute an excellent benchmark for this purpose.

Energy-Structure-Function Maps: Cartography for Materials Discovery

Some of the most successful approaches to structural design in materials chemistry have exploited strong directional bonds, whose geometric reliability lends predictability to solid-state assembly. For example, metal-organic frameworks are an important design platform in materials chemistry. By contrast, the structure of molecular crystals is defined by a balance of weaker intermolecular forces, and small changes to the molecular building blocks can lead to large changes in crystal packing. Hence, empirical rules are inherently less reliable for engineering the structures of molecular solids. Energy-structure-function (ESF) maps are a new approach for the discovery of functional organic crystals. These maps fuse crystal-structure prediction with the computation of physical properties to allow researchers to choose the most promising molecule for a given application, prior to its synthesis. ESF maps were used recently to discover a highly porous molecular crystal that has a high methane deliverable capacity and the lowest density molecular crystal reported to date (r = 0.41 g cm^-3 , SA_BET = 3425 m² g^-1 ). Progress in this field is reviewed, with emphasis on the future opportunities and challenges for a design strategy based on computed ESF maps.

Near-Ideal Xylene Selectivity in Adaptive Molecular Pillar[ n]arene Crystals

The energy-efficient separation of alkylaromatic compounds is a major industrial sustainability challenge. The use of selectively porous extended frameworks, such as zeolites or metal–organic frameworks, is one solution to this problem. Here, we studied a flexible molecular material, perethylated pillar[n]arene crystals (n = 5, 6), which can be used to separate C8 alkylaromatic compounds. Pillar[6]arene is shown to separate para-xylene from its structural isomers, meta-xylene and ortho-xylene, with 90% specificity in the solid state. Selectivity is an intrinsic property of the pillar[6]arene host, with the flexible pillar[6]arene cavities adapting during adsorption thus enabling preferential adsorption of para-xylene in the solid state. The flexibility of pillar[6]arene as a solid sorbent is rationalized using molecular conformer searches and crystal structure prediction (CSP) combined with comprehensive characterization by X-ray diffraction and ¹³C solid-state NMR spectroscopy. The CSP study, which takes into account the structural variability of pillar[6]arene, breaks new ground in its own right and showcases the feasibility of applying CSP methods to understand and ultimately to predict the behavior of soft, adaptive molecular crystals.

Machine learning for the structure-energy-property landscapes of molecular crystals

Molecular crystals play an important role in several fields of science and technology. They frequently crystallize in different polymorphs with substantially different physical properties. To help guide the synthesis of candidate materials, atomic-scale modelling can be used to enumerate the stable polymorphs and to predict their properties, as well as to propose heuristic rules to rationalize the correlations between crystal structure and materials properties. Here we show how a recently-developed machine-learning (ML) framework can be used to achieve inexpensive and accurate predictions of the stability and properties of polymorphs, and a data-driven classification that is less biased and more flexible than typical heuristic rules. We discuss, as examples, the lattice energy and property landscapes of pentacene and two azapentacene isomers that are of interest as organic semiconductor materials. We show that we can estimate force field or DFT lattice energies with sub-kJ mol-1 accuracy, using only a few hundred reference configurations, and reduce by a factor of ten the computational effort needed to predict charge mobility in the crystal structures. The automatic structural classification of the polymorphs reveals a more detailed picture of molecular packing than that provided by conventional heuristics, and helps disentangle the role of hydrogen bonded and π-stacking interactions in determining molecular self-assembly. This observation demonstrates that ML is not just a black-box scheme to interpolate between reference calculations, but can also be used as a tool to gain intuitive insights into structure-property relations in molecular crystal engineering.

Evaluating the Energetic Driving Force for Cocrystal Formation

We present a periodic density functional theory study of the stability of 350 organic cocrystals relative to their pure single-component structures, the largest study of cocrystals yet performed with high-level computational methods. Our calculations demonstrate that cocrystals are on average 8 kJ mol^-1 more stable than their constituent single-component structures and are very rarely (<5% of cases) less stable; cocrystallization is almost always a thermodynamically favorable process. We consider the variation in stability between different categories of systems-hydrogen-bonded, halogen-bonded, and weakly bound cocrystals-finding that, contrary to chemical intuition, the presence of hydrogen or halogen bond interactions is not necessarily a good predictor of stability. Finally, we investigate the correlation of the relative stability with simple chemical descriptors: changes in packing efficiency and hydrogen bond strength. We find some broad qualitative agreement with chemical intuition-more densely packed cocrystals with stronger hydrogen bonding tend to be more stable-but the relationship is weak, suggesting that such simple descriptors do not capture the complex balance of interactions driving cocrystallization. Our conclusions suggest that while cocrystallization is often a thermodynamically favorable process, it remains difficult to formulate general rules to guide synthesis, highlighting the continued importance of high-level computation in predicting and rationalizing such systems.

Pasteur's tartaramide/malamide quasiracemates: new entries and departures from near inversion symmetry

Reinvestigating Pasteur's 1853 quasiracemates has led to unexpected departures from centrosymmetric crystal packing and new insight into the role of molecular shape to molecular assembly.

Computationally-Guided Synthetic Control over Pore Size in Isostructural Porous Organic Cages

The physical properties of 3-D porous solids are defined by their molecular geometry. Hence, precise control of pore size, pore shape, and pore connectivity are needed to tailor them for specific applications. However, for porous molecular crystals, the modification of pore size by adding pore-blocking groups can also affect crystal packing in an unpredictable way. This precludes strategies adopted for isoreticular metal-organic frameworks, where addition of a small group, such as a methyl group, does not affect the basic framework topology. Here, we narrow the pore size of a cage molecule, CC3, in a systematic way by introducing methyl groups into the cage windows. Computational crystal structure prediction was used to anticipate the packing preferences of two homochiral methylated cages, CC14-R and CC15-R, and to assess the structure-energy landscape of a CC15-R/CC3-S cocrystal, designed such that both component cages could be directed to pack with a 3-D, interconnected pore structure. The experimental gas sorption properties of these three cage systems agree well with physical properties predicted by computational energy-structure-function maps.

Functional materials discovery using energy-structure-function maps

Molecular crystals cannot be designed in the same manner as macroscopic objects, because they do not assemble according to simple, intuitive rules. Their structures result from the balance of many weak interactions, rather than from the strong and predictable bonding patterns found in metal-organic frameworks and covalent organic frameworks. Hence, design strategies that assume a topology or other structural blueprint will often fail. Here we combine computational crystal structure prediction and property prediction to build energy-structure-function maps that describe the possible structures and properties that are available to a candidate molecule. Using these maps, we identify a highly porous solid, which has the lowest density reported for a molecular crystal so far. Both the structure of the crystal and its physical properties, such as methane storage capacity and guest-molecule selectivity, are predicted using the molecular structure as the only input. More generally, energy-structure-function maps could be used to guide the experimental discovery of materials with any target function that can be calculated from predicted crystal structures, such as electronic structure or mechanical properties.

Clathrate Structure Determination by Combining Crystal Structure Prediction with Computational and Experimental 129 Xe NMR Spectroscopy

An approach is presented for the structure determination of clathrates using NMR spectroscopy of enclathrated xenon to select from a set of predicted crystal structures. Crystal structure prediction methods have been used to generate an ensemble of putative structures of o- and m-fluorophenol, whose previously unknown clathrate structures have been studied by ¹²⁹ Xe NMR spectroscopy. The high sensitivity of the ¹²⁹ Xe chemical shift tensor to the chemical environment and shape of the crystalline cavity makes it ideal as a probe for porous materials. The experimental powder NMR spectra can be used to directly confirm or reject hypothetical crystal structures generated by computational prediction, whose chemical shift tensors have been simulated using density functional theory. For each fluorophenol isomer one predicted crystal structure was found, whose measured and computed chemical shift tensors agree within experimental and computational error margins and these are thus proposed as the true fluorophenol xenon clathrate structures.

Application of computational methods to the design and characterisation of porous molecular materials

Composed from discrete units, porous molecular materials (PMMs) possess properties not observed for conventional, extended solids. Molecular simulations provide crucial understanding for the design and characterisation of these unique materials.

Modelling temperature-dependent properties of polymorphic organic molecular crystals

We present a large-scale study of the temperature-dependence of structures, free energy differences and properties of polymorphic molecular organic crystals. Lattice-vibrational Gibbs free energy differences between 475 pairs of polymorphs of organic molecular crystals have been calculated at 0 K and at their respective melting points, using a highly accurate anisotropic multipole-based force field and including thermal expansion through the use of a (negative) thermal pressure. Re-ranking of the relative thermodynamic stability of the polymorphs in each pair indicates the possibility of an enantiotropic phase transition between the crystal structures, which occurs in 21% of the studied systems. While vibrational contributions to free energies can have a significant effect on thermodynamic stability, the impact of thermal expansion on polymorph free energy differences is generally very small. We also calculate thermal expansion coefficients for the 864 crystal structures and investigate the temperature-dependence of mechanical properties, and pairwise differences in these properties between polymorphs.