Computational polymorph screening reveals late-appearing and poorly-soluble form of rotigotine

Polymorph Identification for Flexible Molecules: Linear Regression Analysis of Experimental and Calculated Solution- and Solid-State NMR Data

The Δδ regression approach of Blade et al. [ J. Phys. Chem. A 2020, 124(43), 8959-8977] for accurately discriminating between solid forms using a combination of experimental solution- and solid-state NMR data with density functional theory (DFT) calculation is here extended to molecules with multiple conformational degrees of freedom, using furosemide polymorphs as an exemplar. As before, the differences in measured 1H and 13C chemical shifts between solution-state NMR and solid-state magic-angle spinning (MAS) NMR (Δδexperimental) are compared to those determined by gauge-including projector augmented wave (GIPAW) calculations (Δδcalculated) by regression analysis and a t-test, allowing the correct furosemide polymorph to be precisely identified. Monte Carlo random sampling is used to calculate solution-state NMR chemical shifts, reducing computation times by avoiding the need to systematically sample the multidimensional conformational landscape that furosemide occupies in solution. The solvent conditions should be chosen to match the molecule's charge state between the solution and solid states. The Δδ regression approach indicates whether or not correlations between Δδexperimental and Δδcalculated are statistically significant; the approach is differently sensitive to the popular root mean squared error (RMSE) method, being shown to exhibit a much greater dynamic range. An alternative method for estimating solution-state NMR chemical shifts by approximating the measured solution-state dynamic 3D behavior with an ensemble of 54 furosemide crystal structures (polymorphs and cocrystals) from the Cambridge Structural Database (CSD) was also successful in this case, suggesting new avenues for this method that may overcome its current dependency on the prior determination of solution dynamic 3D structures.

Is the Local Ion Density Sufficient to Drive NaCl Nucleation from the Melt and Aqueous Solution?

Even though nucleation is ubiquitous in different science and engineering problems, investigating nucleation is extremely difficult due to the complicated ranges of time and length scales involved. In this work, we simulate NaCl nucleation in both molten and aqueous environments using enhanced sampling of all-atom molecular dynamics with deep-learning-based estimation of reaction coordinates. By incorporating various structural order parameters and learning the reaction coordinate as a function thereof, we achieve significantly improved sampling relative to traditional ad hoc descriptions of what drives nucleation, particularly in an aqueous medium. Our results reveal a one-step nucleation mechanism in both environments, with reaction coordinate analysis highlighting the importance of local ion density in distinguishing solid and liquid states. However, although fluctuations in the local ion density are necessary to drive nucleation, they are not sufficient. Our analysis shows that near the transition states, descriptors such as enthalpy and local structure become crucial. Our protocol proposed here enables robust nucleation analysis and phase sampling and could offer insights into nucleation mechanisms for generic small molecules in different environments.

Frontiers of molecular crystal structure prediction for pharmaceuticals and functional organic materials

The reliability of organic molecular crystal structure prediction has improved tremendously in recent years. Crystal structure predictions for small, mostly rigid molecules are quickly becoming routine. Structure predictions for larger, highly flexible molecules are more challenging, but their crystal structures can also now be predicted with increasing rates of success. These advances are ushering in a new era where crystal structure prediction drives the experimental discovery of new solid forms. After briefly discussing the computational methods that enable successful crystal structure prediction, this perspective presents case studies from the literature that demonstrate how state-of-the-art crystal structure prediction can transform how scientists approach problems involving the organic solid state. Applications to pharmaceuticals, porous organic materials, photomechanical crystals, organic semi-conductors, and nuclear magnetic resonance crystallography are included. Finally, efforts to improve our understanding of which predicted crystal structures can actually be produced experimentally and other outstanding challenges are discussed.

Predicting crystal form stability under real-world conditions

The physicochemical properties of molecular crystals, such as solubility, stability, compactability, melting behaviour and bioavailability, depend on their crystal form1. In silico crystal form selection has recently come much closer to realization because of the development of accurate and affordable free-energy calculations2-4. Here we redefine the state of the art, primarily by improving the accuracy of free-energy calculations, constructing a reliable experimental benchmark for solid-solid free-energy differences, quantifying statistical errors for the computed free energies and placing both hydrate crystal structures of different stoichiometries and anhydrate crystal structures on the same energy landscape, with defined error bars, as a function of temperature and relative humidity. The calculated free energies have standard errors of 1-2 kJ mol-1 for industrially relevant compounds, and the method to place crystal structures with different hydrate stoichiometries on the same energy landscape can be extended to other multi-component systems, including solvates. These contributions reduce the gap between the needs of the experimentalist and the capabilities of modern computational tools, transforming crystal structure prediction into a more reliable and actionable procedure that can be used in combination with experimental evidence to direct crystal form selection and establish control5.

Ionic Liquids: New Forms of Active Pharmaceutical Ingredients with Unique, Tunable Properties

This Review aims to summarize advances over the last 15 years in the development of active pharmaceutical ingredient ionic liquids (API-ILs), which make up a prospective game-changing strategy to overcome multiple problems with conventional solid-state drugs, for example, polymorphism. A critical part of the present Review is the collection of API-ILs and deep eutectic solvents (DESs) prepared to date. The Review covers rules for rational design of API-ILs and tools for API-IL formation, syntheses, and characterization. Nomenclature and ionic speciation, and the confusion that these may cause, are highlighted, particularly for speciation in both ILs and DESs of intermediate ionicity. We also highlight in vivo and in vitro pharmaceutical activity studies, with differences in pharmacokinetic/pharmacodynamic depending on ionicity of API-ILs. A brief overview is provided for the ILs used to deliver drugs, and the Review concludes with key prospects and roadblocks in translating API-ILs into pharmaceutical manufacturing.

Discriminating and understanding molecular crystal polymorphism

Polymorph discrimination for a molecular crystal has long been a challenging task, which, nonetheless, is a major concern in the pharmaceutical industry. In this work, we have investigated polymorph discrimination on three different molecular crystals, tetrolic acid, oxalic acid, and oxalyl dihydrazide, covering both packing polymorphism and conformational polymorphism. To gain more understanding, we have performed energy decomposition analysis based on many-body expansion, and have compared the results from the XO-PBC method, that is, the eXtended ONIOM method (XO) with the periodic boundary condition (PBC), with those from some commonly used dispersion corrected density functional theory (DFT-D) methods. It is shown here that, with the XYG3 doubly hybrid functional chosen as the target high level to capture the intra- and short-range intermolecular interactions, and the periodic PBE as the basic low level to take long range interactions into account, the XO-PBC(XYG3:PBE) method not only obtains the correct experimental stability orderings, but also predicts reasonable polymorph energy ranges for all three cases. Our results have demonstrated the usefulness of the present theoretical methods, in particular XO-PBC, while highlighted the importance of a better treatment of different kinds of interactions to be beneficial to polymorph control.

A theoretical framework for the design of molecular crystal engines

Photomechanical molecular crystals have garnered attention for their ability to transform light into mechanical work, but difficulties in characterizing the structural changes and mechanical responses experimentally have hindered the development of practical organic crystal engines. This study proposes a new computational framework for predicting the solid-state crystal-to-crystal photochemical transformations entirely from first principles, and it establishes a photomechanical engine cycle that quantifies the anisotropic mechanical performance resulting from the transformation. The approach relies on crystal structure prediction, solid-state topochemical principles, and high-quality electronic structure methods. After validating the framework on the well-studied [4 + 4] cycloadditions in 9-methyl anthracene and 9-tert-butyl anthracene ester, the experimentally-unknown solid-state transformation of 9-carboxylic acid anthracene is predicted for the first time. The results illustrate how the mechanical work is done by relaxation of the crystal lattice to accommodate the photoproduct, rather than by the photochemistry itself. The large ∼10⁷ J m^-3 work densities computed for all three systems highlight the promise of photomechanical crystal engines. This study demonstrates the importance of crystal packing in determining molecular crystal engine performance and provides tools and insights to design improved materials in silico.

Efficient Crystal Structure Prediction for Structurally Related Molecules with Accurate and Transferable Tailor-Made Force Fields

Crystal structure prediction (CSP) his generally used to complement experimental solid form screening and applied to individual molecules in drug development. The fast development of algorithms and computing resources offers the opportunity to use CSP earlier and for a broader range of applications in the drug design cycle. This study presents a novel paradigm of CSP specifically designed for structurally related molecules, referred to as Quick-CSP. The approach prioritizes more accurate physics through robust and transferable tailor-made force fields (TMFFs), such that significant efficiency gains are achieved through the reduction of expensive ab initio calculations. The accuracy of the TMFF is increased by the introduction of electrostatic multipoles, and the fragment-based force field parameterization scheme is demonstrated to be transferable for a family of chemically related molecules. The protocol is benchmarked with structurally related compounds from the Bromodomain and Extraterminal (BET) domain inhibitors series. A new convergence criterion is introduced that aims at performing only as many ab initio optimizations of crystal structures as required to locate the bottom of the crystal energy landscape within a user-defined accuracy. The overall approach provides significant cost savings ranging from three- to eight-fold less than the full-CSP workflow. The reported advancements expand the scope and utility of the underlying CSP building blocks as well as their novel reassembly to other applications earlier in the drug design cycle to guide molecule design and selection.

From Powders to Single Crystals: A Crystallographer's Toolbox for Small-Molecule Structure Determination

Although the crystal structures of small-molecule compounds are often determined from single-crystal X-ray diffraction (scXRD), recent advances in three-dimensional electron diffraction (3DED) and crystal structure prediction (CSP) methods promise to expand the structure elucidation toolbox available to the crystallographer. Herein, a comparative assessment of scXRD, 3DED, and CSP in combination with powder X-ray diffraction is carried out on two former drug candidate compounds and a multicomponent crystal of a key building block in the synthesis of gefapixant citrate.

Reliable crystal structure predictions from first principles

An inexpensive and reliable method for molecular crystal structure predictions (CSPs) has been developed. The new CSP protocol starts from a two-dimensional graph of crystal’s monomer(s) and utilizes no experimental information. Using results of quantum mechanical calculations for molecular dimers, an accurate two-body, rigid-monomer ab initio-based force field (aiFF) for the crystal is developed. Since CSPs with aiFFs are essentially as expensive as with empirical FFs, tens of thousands of plausible polymorphs generated by the crystal packing procedures can be optimized. Here we show the robustness of this protocol which found the experimental crystal within the 20 most stable predicted polymorphs for each of the 15 investigated molecules. The ranking was further refined by performing periodic density-functional theory (DFT) plus dispersion correction (pDFT+D) calculations for these 20 top-ranked polymorphs, resulting in the experimental crystal ranked as number one for all the systems studied (and the second polymorph, if known, ranked in the top few). Alternatively, the polymorphs generated can be used to improve aiFFs, which also leads to rank one predictions. The proposed CSP protocol should result in aiFFs replacing empirical FFs in CSP research.

Developing theoretical frameworks to predict new polymorphs is highly desirable. Here the authors present an ab initio based force-field approach for crystal structure prediction offering a dramatic computational speed-up over fully ab initio schemes.

A density-functional benchmark of vibrational free-energy corrections for molecular crystal polymorphism

Many crystal structure prediction protocols only concern themselves with the electronic energy of molecular crystals. However, vibrational contributions to the free energy ( Fvib) can be significant in determining accurate stability rankings for crystal candidates. While force-field studies have been conducted to gauge the magnitude of these free-energy corrections, highly accurate results from quantum mechanical methods, such as density-functional theory (DFT), are desirable. Here, we introduce the PV17 set of 17 polymorphic pairs of organic molecular crystals, for which plane wave DFT is used to calculate the vibrational free energies and free-energy differences (Δ Fvib) between each pair. Our DFT results confirm that the vibrational free-energy corrections are small, having a mean value of 1.0 kJ/mol and a maximum value of 2.3 kJ/mol for the PV17 set. Furthermore, we assess the accuracy of a series of lower-cost DFT, semi-empirical, and force-field models for computing Δ Fvib that have been proposed in the literature. It is found that calculating Fvib using the Γ-point frequencies does not provide Δ Fvib values of sufficiently high quality. In addition, Δ Fvib values calculated using various approximate methods have mean absolute errors relative to our converged DFT results of equivalent or larger magnitude than the vibrational free-energy corrections themselves. Thus, we conclude that, in a crystal structure prediction protocol, it is preferable to forego the inclusion of vibrational free-energy corrections than to estimate them with any of the approximate methods considered here.

The interplay of intra- and intermolecular errors in modeling conformational polymorphs

Conformational polymorphs of organic molecular crystals represent a challenging test for quantum chemistry because they require careful balancing of the intra- and intermolecular interactions. This study examines 54 molecular conformations from 20 sets of conformational polymorphs, along with the relative lattice energies and 173 dimer interactions taken from six of the polymorph sets. These systems are studied with a variety of van der Waals-inclusive density functionals theory models; dispersion-corrected spin-component-scaled second-order Møller–Plesset perturbation theory (SCS-MP2D); and domain local pair natural orbital coupled cluster singles, doubles, and perturbative triples [DLPNO-CCSD(T)]. We investigate how delocalization error in conventional density functionals impacts monomer conformational energies, systematic errors in the intermolecular interactions, and the nature of error cancellation that occurs in the overall crystal. The density functionals B86bPBE-XDM, PBE-D4, PBE-MBD, PBE0-D4, and PBE0-MBD are found to exhibit sizable one-body and two-body errors vs DLPNO-CCSD(T) benchmarks, and the level of success in predicting the relative polymorph energies relies heavily on error cancellation between different types of intermolecular interactions or between intra- and intermolecular interactions. The SCS-MP2D and, to a lesser extent, ωB97M-V models exhibit smaller errors and rely less on error cancellation. Implications for crystal structure prediction of flexible compounds are discussed. Finally, the one-body and two-body DLPNO-CCSD(T) energies taken from these conformational polymorphs establish the CP1b and CP2b benchmark datasets that could be useful for testing quantum chemistry models in challenging real-world systems with complex interplay between intra- and intermolecular interactions, a number of which are significantly impacted by delocalization error.

Emerging Landscape of Computational Modeling in Pharmaceutical Development

Computational chemistry applications have become an integral part of the drug discovery workflow over the past 35 years. However, computational modeling in support of drug development has remained a relatively uncharted territory for a significant part of both academic and industrial communities. This review considers the computational modeling workflows for three key components of drug preclinical and clinical development, namely, process chemistry, analytical research and development, as well as drug product and formulation development. An overview of the computational support for each step of the respective workflows is presented. Additionally, in context of solid form design, special consideration is given to modern physics-based virtual screening methods. This covers rational approaches to polymorph, coformer, counterion, and solvent virtual screening in support of solid form selection and design.

Progress in understanding crystallisation: a personal perspective

After this discussion meeting, most participants felt that we do not understand crystallisation. However, in the 1980s I believe that most scientists would have considered that crystallisation was adequately understood....

Along the road to Crystal Structure Prediction (CSP) of pharmaceutical-like molecules

Computational methods used for predicting crystal structures of organic compounds are mature enough to be routinely used with many rigid and semi-rigid organic molecules. The usefulness of Crystal Structure Prediction...

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.

Modeling the α- and β-resorcinol phase boundary via combination of density functional theory and density functional tight-binding

The ability to predict not only what organic crystal structures might occur but also the thermodynamic conditions under which they are the most stable would be extremely useful for discovering and designing new organic materials. The present study takes a step in that direction by predicting the temperature- and pressure-dependent phase boundary between the α and β polymorphs of resorcinol using density functional theory (DFT) and the quasi-harmonic approximation. To circumvent the major computational bottleneck associated with computing a well-converged phonon density of states via the supercell approach, a recently developed approximation is employed, which combines a supercell phonon density of states from dispersion-corrected third-order density functional tight binding [DFTB3-D3(BJ)] with frequency corrections derived from a smaller B86bPBE-XDM functional DFT phonon calculation on the crystallographic unit cell. This mixed DFT/DFTB quasi-harmonic approach predicts the lattice constants and unit cell volumes to within 1%-2% at lower pressures. It predicts the thermodynamic phase boundary in almost perfect agreement with the experiment, although this excellent agreement does reflect fortuitous cancellation of errors between the enthalpy and entropy of transition.

Novel Physics-Based Ensemble Modeling Approach That Utilizes 3D Molecular Conformation and Packing to Access Aqueous Thermodynamic Solubility: A Case Study of Orally Available Bromodomain and Extraterminal Domain Inhibitor Lead Optimization Series

Drug design with patient centricity for ease of administration and pill burden requires robust understanding of the impact of chemical modifications on relevant physicochemical properties early in lead optimization. To this end, we have developed a physics-based ensemble approach to predict aqueous thermodynamic crystalline solubility, with a 2D chemical structure as the input. Predictions for the bromodomain and extraterminal domain (BET) inhibitor series show very close match (0.5 log unit) with measured thermodynamic solubility for cases with low crystal anisotropy and good match (1 log unit) for high anisotropy structures. The importance of thermodynamic solubility is clearly demonstrated by up to a 4 log unit drop in solubility compared to kinetic (amorphous) solubility in some cases and implications thereof, for instance on human dose. We have also demonstrated that incorporating predicted crystal structures in thermodynamic solubility prediction is necessary to differentiate (up to 4 log unit) between solubility of molecules within the series. Finally, our physics-based ensemble approach provides valuable structural insights into the origins of 3-D conformational landscapes, crystal polymorphism, and anisotropy that can be leveraged for both drug design and development.

Improved quantitative crystal-structure comparison using powder diffractograms via anisotropic volume correction

A new anisotropic volume correction improves quantitative crystal structure comparison. Benchmarking against the 6th crystal structure prediction blind test data results in identification of two previously uncredited matching structures.

Transforming Computed Energy Landscapes into Experimental Realities: The Role of Structural Rugosity

We exploit the possible link between structural surface roughness and difficulty of crystallisation. Polymorphs with smooth surfaces may nucleate and crystallise more readily than polymorphs with rough surfaces. The concept is applied to crystal structure prediction landscapes and reveals a promising complementary way of ranking putative crystal structures.

Crystal forms in pharmaceutical applications: olanzapine, a gift to crystal chemistry that keeps on giving

This contribution reviews the efforts of many scientists around the world to discover and structurally characterize olanzapine crystal forms, clearing up inconsistencies in the scientific and patent literature and highlighting the challenges in identifying new forms amidst 60+ known polymorphs and solvates. Owing to its remarkable solid-state chemistry, olanzapine has emerged over the last three decades as a popular tool compound for developing new experimental and computational methods for enhanced molecular level understanding of solid-state structure, form diversity and crystallization outcomes. This article highlights the role of olanzapine in advancing the fundamental understanding of crystal forms, interactions within crystal structures, and growth units in molecular crystallization, as well as influencing the way in which drugs are developed today.

Virtual Coformer Screening by Crystal Structure Predictions: Crucial Role of Crystallinity in Pharmaceutical Cocrystallization

One of the most popular strategies of the optimization of drug properties in the pharmaceutical industry appears to be a solid form changing into a cocrystalline form. A number of virtual screening approaches have been previously developed to allow a selection of the most promising cocrystal formers (coformers) for an experimental follow-up. A significant drawback of those methods is related to the lack of accounting for the crystallinity contribution to cocrystal formation. To address this issue, we propose in this study two virtual coformer screening approaches based on a modern cloud-computing crystal structure prediction (CSP) technology at a dispersion-corrected density functional theory (DFT-D) level. The CSP-based methods were for the first time validated on challenging cases of indomethacin and paracetamol cocrystallization, for which the previously developed approaches provided poor predictions. The calculations demonstrated a dramatic improvement of the virtual coformer screening performance relative to the other methods. It is demonstrated that the crystallinity contribution to the formation of paracetamol and indomethacin cocrystals is a dominant one and, therefore, should not be ignored in the virtual screening calculations. Our results encourage a broad utilization of the proposed CSP-based technology in the pharmaceutical industry as the only virtual coformer screening method that directly accounts for the crystallinity contribution.

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.

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.