Dimer or Catemer? Low-Energy Crystal Packings for Small Carboxylic Acids

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.

Construction of a Gaussian Process Regression Model of Formamide for Use in Molecular Simulations

FFLUX, a novel force field based on quantum chemical topology, can perform molecular dynamics simulations with flexible multipole moments that change with geometry. This is enabled by Gaussian process regression machine learning models, which accurately predict atomic energies and multipole moments up to the hexadecapole. We have constructed a model of the formamide monomer at the B3LYP/aug-cc-pVTZ level of theory capable of sub-kJ mol^-1 accuracy, with the maximum prediction error for the molecule being 0.8 kJ mol^-1. This model was used in FFLUX simulations along with Lennard-Jones parameters to successfully optimize the geometry of formamide dimers with errors smaller than 0.1 Å compared to those obtained with D3-corrected B3LYP/aug-cc-pVTZ. Comparisons were also made to a force field constructed with static multipole moments and Lennard-Jones parameters. FFLUX recovers the expected energy ranking of dimers compared to the literature, and changes in C═O and C-N bond lengths associated with hydrogen bonding were found to be consistent with density functional theory.

Efficient Screening of Coformers for Active Pharmaceutical Ingredient Cocrystallization

Controlling the physical properties of solid forms for active pharmaceutical ingredients (APIs) through cocrystallization is an important part of drug product development. However, it is difficult to know a priori which coformers will form cocrystals with a given API, and the current state-of-the-art for cocrystal discovery involves an expensive, time-consuming, and, at the early stages of pharmaceutical development, API material-limited experimental screen. We propose a systematic, high-throughput computational approach primarily aimed at identifying API/coformer pairs that are unlikely to lead to experimentally observable cocrystals and can therefore be eliminated with only a brief experimental check, from any experimental investigation. On the basis of a well-established crystal structure prediction (CSP) methodology, the proposed approach derives its efficiency by not requiring any expensive quantum mechanical calculations beyond those already performed for the CSP investigation of the neat API itself. The approach and assumptions are tested through a computational investigation on 30 potential 1:1 multicomponent systems (cocrystals and solvate) involving 3 active pharmaceutical ingredients and 9 coformers and one solvent. This is complemented with a detailed experimental investigation of all 30 pairs, which led to the discovery of five new cocrystals (three API-coformer combinations, a polymorphic cocrystal example, and one with different stoichiometries) and a cis-aconitic acid polymorph. The computational approach indicates that, for some APIs, a significant proportion of all potential API/coformer pairs could be investigated with only a brief experimental check, thereby saving considerable experimental effort.

How many more polymorphs of ROY remain undiscovered

With 12 crystal forms, 5-methyl-2-[(2-nitrophenyl)amino]-3-thiophenecabonitrile (a.k.a. ROY) holds the current record for the largest number of fully characterized organic crystal polymorphs. Four of these polymorph structures have been reported since 2019, raising the question of how many more ROY polymorphs await future discovery. Employing crystal structure prediction and accurate energy rankings derived from conformational energy-corrected density functional theory, this study presents the first crystal energy landscape for ROY that agrees well with experiment. The lattice energies suggest that the seven most stable ROY polymorphs (and nine of the twelve lowest-energy forms) on the Z′ = 1 landscape have already been discovered experimentally. Discovering any new polymorphs at ambient pressure will likely require specialized crystallization techniques capable of trapping metastable forms. At pressures above 10 GPa, however, a new crystal form is predicted to become enthalpically more stable than all known polymorphs, suggesting that further high-pressure experiments on ROY may be warranted. This work highlights the value of high-accuracy crystal structure prediction for solid-form screening and demonstrates how pragmatic conformational energy corrections can overcome the limitations of conventional density functionals for conformational polymorphs.

Crystal structure prediction suggests that the low-energy polymorphs of ROY have already been found, but a new high-pressure form is predicted.

Synergy of Solid-State NMR, Single-Crystal X-ray Diffraction, and Crystal Structure Prediction Methods: A Case Study of Teriflunomide (TFM)

In this work, for the first time, we present the X-ray diffraction crystal structure and spectral properties of a new, room-temperature polymorph of teriflunomide (TFM), CSD code 1969989. As revealed by DSC, the low-temperature TFM polymorph recently reported by Gunnam et al. undergoes a reversible thermal transition at -40 °C. This reversible process is related to a change in Z' value, from 2 to 1, as observed by variable-temperature ¹H-¹³C cross-polarization (CP) magic-angle spinning (MAS) solid-state NMR, while the crystallographic system is preserved (triclinic). Two-dimensional ¹³C-¹H and ¹H-¹H double-quantum MAS NMR spectra are consistent with the new room-temperature structure, including comparison with GIPAW (gauge-including projector augmented waves) calculated NMR chemical shifts. A crystal structure prediction procedure found both experimental teriflunomide polymorphs in the energetic global minimum region. Differences between the polymorphs are seen for the torsional angle describing the orientation of the phenyl ring relative to the planarity of the TFM molecule. In the low-temperature structure, there are two torsion angles of 4.5 and 31.9° for the two Z' = 2 molecules, while in the room-temperature structure, there is disorder that is modeled with ∼50% occupancy between torsion angles of -7.8 and 28.6°. These observations are consistent with a broad energy minimum as revealed by DFT calculations. PISEMA solid-state NMR experiments show a reduction in the C-H dipolar coupling in comparison to the static limit for the aromatic CH moieties of 75% and 51% at 20 and 40 °C, respectively, that is indicative of ring flips at the higher temperature. Our study shows the power of combining experiments, namely DSC, X-ray diffraction, and MAS NMR, with DFT calculations and CSP to probe and understand the solid-state landscape, and in particular the role of dynamics, for pharmaceutical molecules.

The crystal structure of α-(meta-methoxyphenoxy)-ortho-tolylic acid, C15H14O4

C15H14O4, monoclinic, C2/c (no. 15), a = 27.1122(8) Å, b = 6.4295(2) Å, c = 14.7495(4) Å, β = 91.7070(10)°, V = 2569.96(13) Å3, Z = 8, Rgt (F) = 0.0387, wRref (F 2) = 0.1091, T = 200 K.

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.

Diabat method for polymorph free energies: Extension to molecular crystals

Lattice-switch Monte Carlo and the related diabat methods have emerged as efficient and accurate ways to compute free energy differences between polymorphs. In this work, we introduce a one-to-one mapping from the reference positions and displacements in one molecular crystal to the positions and displacements in another. Two features of the mapping facilitate lattice-switch Monte Carlo and related diabat methods for computing polymorph free energy differences. First, the mapping is unitary so that its Jacobian does not complicate the free energy calculations. Second, the mapping is easily implemented for molecular crystals of arbitrary complexity. We demonstrate the mapping by computing free energy differences between polymorphs of benzene and carbamazepine. Free energy calculations for thermodynamic cycles, each involving three independently computed polymorph free energy differences, all return to the starting free energy with a high degree of precision. The calculations thus provide a force field independent validation of the method and allow us to estimate the precision of the individual free energy differences.

Efficient Screening for Ternary Molecular Ionic Cocrystals Using a Complementary Mechanosynthesis and Computational Structure Prediction Approach

The discovery of molecular ionic cocrystals (ICCs) of active pharmaceutical ingredients (APIs) widens the opportunities for optimizing the physicochemical properties of APIs whilst facilitating the delivery of multiple therapeutic agents. However, ICCs are often observed serendipitously in crystallization screens and the factors dictating their crystallization are poorly understood. We demonstrate here that mechanochemical ball milling is a versatile technique for the reproducible synthesis of ternary molecular ICCs in less than 30 min of grinding with or without solvent. Computational crystal structure prediction (CSP) calculations have been performed on ternary molecular ICCs for the first time and the observed crystal structures of all the ICCs were correctly predicted. Periodic dispersion-corrected DFT calculations revealed that all the ICCs are thermodynamically stable (mean stabilization energy=-2 kJ mol-1 ) relative to the crystallization of a physical mixture of the binary salt and acid. The results suggest that a combined mechanosynthesis and CSP approach could be used to target the synthesis of higher-order molecular ICCs with functional properties.

Can solvated intermediates inform us about nucleation pathways? The case of β-pABA

Using crystallography to search for nucleation pathways: α and β polymorphs of p-aminobenzoic acid.

Accurate and efficient representation of intramolecular energy in ab initio generation of crystal structures. II. Smoothed intramolecular potentials

The application of crystal structure prediction (CSP) to industrially relevant molecules requires the handling of increasingly large and flexible compounds. A revised model for the effect of molecular flexibility on the lattice energy that removes the discontinuities and non-differentiabilities present in earlier models (Sugden et al., 2016), with a view to improving the performance of CSP is presented. The approach is based on the concept of computing a weighted average of local models, and has been implemented within the CrystalPredictor code. Through the comparative investigation of several compounds studied in earlier literature, it is shown that this new model results in large reductions in computational effort (of up to 65%) and in significant increases in reliability. The approach is further applied to investigate, for the first time, the computational polymorphic landscape of flufenamic acid for Z' = 1 structures, resulting in the successful identification of all three experimentally resolved polymorphs within reasonable computational time.

Repulsion-dispersion parameters for the modelling of organic molecular crystals containing N, O, S and Cl

In lattice energy models that combine ab initio and empirical components, it is important to ensure consistency between these components so that meaningful quantitative results are obtained. A method for deriving parameters of atom-atom repulsion dispersion potentials for crystals, tailored to different ab initio models, is presented. It is based on minimization of the sum of squared deviations between experimental and calculated structures and energies. The solution algorithm is designed to avoid convergence to local minima in the parameter space by combining a deterministic low-discrepancy sequence for the generation of multiple initial parameter guesses with an efficient local minimization algorithm. The proposed approach is applied to derive transferable exp-6 potential parameters suitable for use in conjunction with a distributed multipole electrostatics model derived from isolated molecule charge densities calculated at the M06/6-31G(d,p) level of theory. Data for hydrocarbons, azahydrocarbons, oxohydrocarbons, organosulphur compounds and chlorohydrocarbons are used for the estimation. A good fit is achieved for the new set of parameters with a mean absolute error in sublimation enthalpies of 4.1 kJ mol-1 and an average rmsd15 of 0.31 Å. The parameters are found to perform well on a separate cross-validation set of 39 compounds.

Dissecting Porosity in Molecular Crystals: Influence of Geometry, Hydrogen Bonding, and [π···π] Stacking on the Solid-State Packing of Fluorinated Aromatics

Porous molecular crystals are an emerging class of porous materials that is unique in being built from discrete molecules rather than being polymeric in nature. In this study, we examined the effects of molecular structure of the precursors on the formation of porous solid-state structures with a series of 16 rigid aromatics. The majority of these precursors possess pyrazole groups capable of hydrogen bonding, as well as electron-rich aromatics and electron-poor tetrafluorobenzene rings. These precursors were prepared using a combination of Pd- and Cu-catalyzed cross-couplings, careful manipulations of protecting groups on the nitrogen atoms, and solvothermal syntheses. Our study varied the geometry and dimensions of precursors, as well as the presence of groups capable of hydrogen bonding and [π···π] stacking. Thirteen derivatives were crystallographically characterized, and four of them were found to be porous with surface areas between 283 and 1821 m² g^-1. Common to these four porous structures were (a) rigid trigonal geometry, (b) [π···π] stacking of electron-poor tetrafluorobenzenes with electron-rich pyrazoles or tetrazoles, and

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.

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.

Towards the systematic crystallisation of molecular ionic cocrystals: insights from computed crystal form landscapes

The underlying molecular and crystal properties affecting the crystallisation of organic molecular ionic cocrystals (ICCs) are investigated.

Organometallic chemistry meets crystal engineering to give responsive crystalline materials

Dynamically porous crystalline materials have been obtained by engineering organometallic molecules. This feature article deals with organometallic wheel-and-axle compounds, molecules with two relatively bulky groups (wheels) connected by a linear spacer. The wheels are represented by half-sandwich Ru(ii) moieties, while the spacer can be covalent or supramolecular in character. Covalent spacers are obtained using divergent bidentate ligands connecting two [(arene)RuX2] groups. Supramolecular spacers are instead obtained by exploiting the dimerization of COOH or C(O)NH2 groups appended to N-based ligands. A careful choice of ligand functional groups and X ligands leads to the isolation of crystalline materials with remarkable host-guest properties, evidenced by the possibility of reversibly capturing/releasing volatile guests through heterogenous solid-gas reactions. Structural correlations between the crystalline arrangement of the apohost and the host-guest compounds allow us to envisage the structural path followed by the system during the exchange processes.