Porous isoreticular non-metal organic frameworks.

Metal-organic frameworks (MOFs) are useful synthetic materials that are built by the programmed assembly of metal nodes and organic linkers1. The success of MOFs results from the isoreticular principle2, which allows families of structurally analogous frameworks to be built in a predictable way. This relies on directional coordinate covalent bonding to define the framework geometry. However, isoreticular strategies do not translate to other common crystalline solids, such as organic salts3-5, in which the intermolecular ionic bonding is less directional. Here we show that chemical knowledge can be combined with computational crystal-structure prediction6 (CSP) to design porous organic ammonium halide salts that contain no metals. The nodes in these salt frameworks are tightly packed ionic clusters that direct the materials to crystallize in specific ways, as demonstrated by the presence of well-defined spikes of low-energy, low-density isoreticular structures on the predicted lattice energy landscapes7,8. These energy landscapes allow us to select combinations of cations and anions that will form thermodynamically stable, porous salt frameworks with channel sizes, functionalities and geometries that can be predicted a priori. Some of these porous salts adsorb molecular guests such as iodine in quantities that exceed those of most MOFs, and this could be useful for applications such as radio-iodine capture9-12. More generally, the synthesis of these salts is scalable, involving simple acid-base neutralization, and the strategy makes it possible to create a family of non-metal organic frameworks that combine high ionic charge density with permanent porosity.

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.

Predictive crystallography at scale: mapping, validating, and learning from 1000 crystal energy landscapes.

Computational crystal structure prediction (CSP) is an increasingly powerful technique in materials discovery, due to its ability to reveal trends and permit insight across the possibility space of crystal structures of a candidate molecule, beyond simply the observed structure(s). In this work, we demonstrate the reliability and scalability of CSP methods for small, rigid organic molecules by performing in-depth CSP investigations for over 1000 such compounds, the largest survey of its kind to-date. We show that this highly-efficient force-field-based CSP approach is superbly predictive, locating 99.4% of observed experimental structures, and ranking a large majority of these (74%) as among the most stable possible structures (to within uncertainty due to thermal effects). We present two examples of insights such large predicted datasets can permit, examining the space group preferences of organic molecular crystals and rationalising empirical rules concerning the spontaneous resolution of chiral molecules. Finally, we exploit this large and diverse dataset for developing transferable machine-learned energy potentials for the organic solid state, training a neural network lattice energy correction to force field energies that offers substantial improvements to the already impressive energy rankings, and a MACE equivariant message-passing neural network for crystal structure re-optimisation. We conclude that the excellent performance and reliability of the CSP workflow enables the creation of very large datasets of broad utility and explanatory power in materials design.

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.

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.

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.

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.

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.

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.

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.

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 (SABET = 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.

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'.

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.

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 ⟨rav⟩ = 0.176 Å, which corresponds to an average equivalent displacement parameter Ueq = 0.0103 Å2.

From Concept to Crystals via Prediction: Multi-Component Organic Cage Pots by Social Self-Sorting.

We describe the a priori computational prediction and realization of multi-component cage pots, starting with molecular predictions based on candidate precursors through to crystal structure prediction and synthesis using robotic screening. The molecules were formed by the social self-sorting of a tri-topic aldehyde with both a tri-topic amine and di-topic amine, without using orthogonal reactivity or precursors of the same topicity. Crystal structure prediction suggested a rich polymorphic landscape, where there was an overall preference for chiral recognition to form heterochiral rather than homochiral packings, with heterochiral pairs being more likely to pack window-to-window to form two-component capsules. These crystal packing preferences were then observed in experimental crystal structures.

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.

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.

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

Composed from discrete units, porous molecular materials (PMMs) possess unique properties not observed for conventional, extended, solids, such as solution processibility and permanent porosity in the liquid phase. However, identifying the origin of porosity is not a trivial process, especially for amorphous or liquid phases. Furthermore, the assembly of molecular components is typically governed by a subtle balance of weak intermolecular forces that makes structure prediction challenging. Accordingly, in this review we canvass the crucial role of molecular simulations in the characterisation and design of PMMs. We will outline strategies for modelling porosity in crystalline, amorphous and liquid phases and also describe the state-of-the-art methods used for high-throughput screening of large datasets to identify materials that exhibit novel performance characteristics.

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.