Report on the sixth blind test of organic crystal structure prediction methods

Accurate Lattice Free Energies of Packing Polymorphs from Probabilistic Generative Models

Finite-temperature lattice free energy differences between polymorphs of molecular crystals are fundamental to understanding and predicting the relative stability relationships underpinning polymorphism, yet are computationally expensive to obtain. Here, we implement and critically assess machine-learning-enabled targeted free energy calculations derived from flow-based generative models to compute the free energy difference between two ice crystal polymorphs (Ice XI and Ic), modeled with a fully flexible empirical classical force field. We demonstrate that even when remapping from an analytical reference distribution, such methods enable a cost-effective and accurate calculation of free energy differences between disconnected metastable ensembles when trained on locally ergodic data sampled exclusively from the ensembles of interest. Unlike classical free energy perturbation methods, such as the Einstein crystal method, the targeted approach analyzed in this work requires no additional sampling of intermediate perturbed Hamiltonians, offering significant computational savings. To systematically assess the accuracy of the method, we monitored the convergence of free energy estimates during training by implementing an overfitting-aware weighted averaging strategy. By comparing our results with ground-truth free energy differences computed with the Einstein crystal method, we assess the accuracy and efficiency of two different model architectures, employing two different representations of the supercell degrees of freedom (Cartesian vs quaternion-based). We conduct our assessment by comparing free energy differences between crystal supercells of different sizes and temperatures and assessing the accuracy in extrapolating lattice free energies to the thermodynamic limit. While at low temperatures and in small system sizes, the models perform with similar accuracy. We note that for larger systems and high temperatures, the choice of representation is key to obtaining generalizable results of quality comparable to that obtained from the Einstein crystal method. We believe this work to be a stepping stone toward efficient free energy calculations in larger, more complex molecular crystals.

A robust crystal structure prediction method to support small molecule drug development with large scale validation and blind study

Crystal polymorphism is an important and fascinating aspect of solid state chemistry with far reaching implications in the pharmaceuticals, agrisciences, nutraceuticals, battery and aviation industries. Late appearing more stable polymorphs have caused numerous issues in the pharmaceutical industry. Experimental polymorph screening can be very expensive and time consuming, and sometimes may miss important low energy polymorphs due to an inability to exhaust all crystallization conditions. In this paper, we report a crystal structure prediction (CSP) method with state of the art accuracy and efficiency, validated on a large and diverse dataset including 66 molecules with 137 experimentally known polymorphic forms. The method combines a novel systematic crystal packing search algorithm and the use of machine learning force fields in a hierarchical crystal energy ranking. Our method not only reproduces all the experimentally known polymorphs, but also suggests new low energy polymorphs yet to be discovered by experiment that might pose potential risks to development of the currently known forms of these compounds. In addition, we report the prediction results of a blinded study, results for Target XXXI from the seventh CSP blind test, and demonstrate how the method can be used to accelerate clinical formulation design and derisk downstream processing.

Accelerating structure prediction of molecular crystals using actively trained moment tensor potential

Inspired by the recent success of machine-learned interatomic potentials for crystal structure prediction of inorganic crystals, we present a methodology that exploits moment tensor potentials (MTP) and active learning (based on maxvol algorithm) to accelerate structure prediction of molecular crystals. Benzene and glycine are used as test systems. The obtained potentials are able to rank different benzene and glycine polymorphs in good agreement with density-functional theory. Hence, we argue that MTP can be used to accelerate the computationally guided polymorph search.

Dispersionless Nonhybrid Density Functional

A dispersion-corrected density functional theory (DFT+D) method has been developed. It includes a nonhybrid dispersionless generalized gradient approximation (GGA) functional paired with a literature-parametrized dispersion function. The functional's 9 adjustable parameters were optimized using a training set of 589 benchmark interaction energies. The resulting method performs better than other GGA-based DFT+D methods, giving a mean unsigned error of 0.33 kcal/mol. It even performs better than some more expensive meta-GGA or hybrid dispersion-corrected functionals. An important advantage of using the new functional is that its dispersion energy given by the D component is very close to the true dispersion energy at all intermolecular separations, whereas in other similarly accurate DFT+D approaches, such a dispersion contribution in the van der Waals minimum region is only a small fraction of the true value.

Data-efficient fine-tuning of foundational models for first-principles quality sublimation enthalpies

Calculating sublimation enthalpies of molecular crystal polymorphs is relevant to a wide range of technological applications. However, predicting these quantities at first-principles accuracy - even with the aid of machine learning potentials - is a challenge that requires sub-kJ mol-1 accuracy in the potential energy surface and finite-temperature sampling. We present an accurate and data-efficient protocol for training machine learning interatomic potentials by fine-tuning the foundational MACE-MP-0 model and showcase its capabilities on sublimation enthalpies and physical properties of ice polymorphs. Our approach requires only a few tens of training structures to achieve sub-kJ mol-1 accuracy in the sublimation enthalpies and sub-1% error in densities at finite temperature and pressure. Exploiting this data efficiency, we perform preliminary NPT simulations of hexagonal ice at the random phase approximation level and demonstrate a good agreement with experiments. Our results show promise for finite-temperature modelling of molecular crystals with the accuracy of correlated electronic structure theory methods.

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.

Spiers Memorial Lecture: NMR crystallography

Chemical function is directly related to the spatial arrangement of atoms. Consequently, the determination of atomic-level three-dimensional structures has transformed molecular and materials science over the past 60 years. In this context, solid-state NMR has emerged to become the method of choice for atomic-level characterization of complex materials in powder form. In the following we present an overview of current methods for chemical shift driven NMR crystallography, illustrated with applications to complex materials.

Characterization of ephedrine HCl and pseudoephedrine HCl using quadrupolar NMR crystallography guided crystal structure prediction

Quadrupolar NMR crystallography guided crystal structure prediction (QNMRX-CSP) is a nascent protocol for predicting, solving, and refining crystal structures. QNMRX-CSP employs a combination of solid-state NMR data from quadrupolar nuclides (i.e., nuclear spin >1/2), static lattice energies and electric field gradient (EFG) tensors from dispersion-corrected density functional theory (DFT-D2*) calculations, and powder X-ray diffraction (PXRD) data; however, it has so far been applied only to organic HCl salts with small and rigid organic components, using 35Cl EFG tensor data for both structural refinement and validation. Herein, QNMRX-CSP is extended to ephedrine HCl (Eph) and pseudoephedrine HCl (Pse), which are diastereomeric compounds that feature distinct space groups and organic components that are larger and more flexible. A series of benchmarking calculations are used to generate structural models that are validated against experimental data, and to explore the impacts of the: (i) starting structural models (i.e., geometry-optimized fragments based on either a known crystal structure or an isolated gas-phase molecule) and (ii) selection of unit cell parameters and space groups. Finally, we use QNMRX-CSP to predict the structure of Pse in the dosage form Sudafed® using only 35Cl SSNMR data as experimental input. This proof-of-concept work suggests the possibility of employing QNMRX-CSP to solve the structures of organic HCl salts in dosage forms - something which is often beyond the capabilities of conventional, diffraction-based characterization methods.

A computationally efficient quasi-harmonic study of ice polymorphs using the FFLUX force field

FFLUX is a multipolar machine-learned force field that uses Gaussian process regression models trained on data from quantum chemical topology calculations. It offers an efficient way of predicting both lattice and free energies of polymorphs, allowing their stability to be assessed at finite temperatures. Here the Ih, II and XV phases of ice are studied, building on previous work on formamide crystals and liquid water. A Gaussian process regression model of the water monomer was trained, achieving sub-kJ mol-1 accuracy. The model was then employed in simulations with a Lennard-Jones potential to represent intermolecular repulsion and dispersion. Lattice constants of the FFLUX-optimized crystal structures were comparable with those calculated by PBE+D3, with FFLUX calculations estimated to be 103-105 times faster. Lattice dynamics calculations were performed on each phase, with ices Ih and XV found to be dynamically stable through phonon dispersion curves. However, ice II was incorrectly identified as unstable due to the non-bonded potential used, with a new phase (labelled here as II' and to our knowledge not found experimentally) identified as more stable. This new phase was also found to be dynamically stable using density functional theory but, unlike in FFLUX calculations, II remained the more stable phase. Finally, Gibbs free energies were accessed through the quasi-harmonic approximation for the first time using FFLUX, allowing thermodynamic stability to be assessed at different temperatures and pressures through the construction of a phase diagram.

Advancing dynamic quantum crystallography: enhanced models for accurate structures and thermodynamic properties

X-ray diffraction (XRD) has evolved significantly since its inception, becoming a crucial tool for material structure characterization. Advancements in theory, experimental techniques, diffractometers and detection technology have led to the acquisition of highly accurate diffraction patterns, surpassing previous expectations. Extracting comprehensive information from these patterns necessitates different models due to the influence of both electron density and thermal motion on diffracted beam intensity. While electron-density modelling has seen considerable progress [e.g. the Hansen-Coppens multipole model and Hirshfeld Atom Refinement (HAR)], the treatment of thermal motion has remained largely unchanged. We have developed a novel method that combines the strengths of the advanced charge-density models [Aspherical Atom Models (AAMs), such as HAR or the Transferable Aspherical Atom Model (TAAM)] and the thermal motion model (normal modes refinement, NoMoRe). We denote this approach AAM_NoMoRe, wherein instead of refining routine anisotropic displacement parameters (ADPs) against single-crystal X-ray diffraction data, we refine the frequencies obtained from periodic density functional theory (DFT) calculations. In this work, we demonstrate the effectiveness of this model by presenting its application to model compounds, such as alanine, xylitol, naphthalene and glycine polymorphs, highlighting the influence of our method on the H-atom positions and shape of their ADPs, which are comparable with neutron data. We observe a significant decrease in the similarity index for H-atom ADPs after AAM_NoMoRe in comparison to only AAM, aligning more closely with neutron data. Due to the use of aspherical form factors (AAM), our approach demonstrates better fitting performance, as indicated by consistently lower wR2 values compared to the Independent Atom Model (IAM) refinement and a significant decrease compared to the traditional NoMoRe model. Furthermore, we present the estimation of a key thermodynamic property, namely, heat capacity, and demonstrate its alignment with experimental calorimetric data.

The seventh blind test of crystal structure prediction: structure ranking methods

A seventh blind test of crystal structure prediction has been organized by the Cambridge Crystallographic Data Centre. The results are presented in two parts, with this second part focusing on methods for ranking crystal structures in order of stability. The exercise involved standardized sets of structures seeded from a range of structure generation methods. Participants from 22 groups applied several periodic DFT-D methods, machine learned potentials, force fields derived from empirical data or quantum chemical calculations, and various combinations of the above. In addition, one non-energy-based scoring function was used. Results showed that periodic DFT-D methods overall agreed with experimental data within expected error margins, while one machine learned model, applying system-specific AIMnet potentials, agreed with experiment in many cases demonstrating promise as an efficient alternative to DFT-based methods. For target XXXII, a consensus was reached across periodic DFT methods, with consistently high predicted energies of experimental forms relative to the global minimum (above 4 kJ mol-1 at both low and ambient temperatures) suggesting a more stable polymorph is likely not yet observed. The calculation of free energies at ambient temperatures offered improvement of predictions only in some cases (for targets XXVII and XXXI). Several avenues for future research have been suggested, highlighting the need for greater efficiency considering the vast amounts of resources utilized in many cases.

Polymorph sampling with coupling to extended variables: enhanced sampling of polymorph energy landscapes and free energy perturbation of polymorph ensembles

A novel approach to computationally enhance the sampling of molecular crystal structures is proposed and tested. This method is based on the use of extended variables coupled to a Monte Carlo based crystal polymorph generator. Inspired by the established technique of quasi-random sampling of polymorphs using the rigid molecule constraint, this approach represents molecular clusters as extended variables within a thermal reservoir. Polymorph unit-cell variables are generated using pseudo-random sampling. Within this framework, a harmonic coupling between the extended variables and polymorph configurations is established. The extended variables remain fixed during the inner loop dedicated to polymorph sampling, enforcing a stepwise propagation of the extended variables to maintain system exploration. The final processing step results in a polymorph energy landscape, where the raw structures sampled to create the extended variable trajectory are re-optimized without the thermal coupling term. The foundational principles of this approach are described and its effectiveness using both a Metropolis Monte Carlo type algorithm and modifications that incorporate replica exchange is demonstrated. A comparison is provided with pseudo-random sampling of polymorphs for the molecule coumarin. The choice to test a design of this algorithm as relevant for enhanced sampling of crystal structures was due to the obvious relation between molecular structure variables and corresponding crystal polymorphs as representative of the inherent vapor to crystal transitions that exist in nature. Additionally, it is shown that the trajectories of extended variables can be harnessed to extract fluctuation properties that can lead to valuable insights. A novel thermodynamic variable is introduced: the free energy difference between ensembles of Z' = 1 and Z' = 2 crystal polymorphs.

Contrasting conformational behaviors of molecules XXXI and XXXII in the seventh blind test of crystal structure prediction

Accurate modeling of conformational energies is key to the crystal structure prediction of conformational polymorphs. Focusing on molecules XXXI and XXXII from the seventh blind test of crystal structure prediction, this study employs various electronic structure methods up to the level of domain-local pair natural orbital coupled cluster singles and doubles with perturbative triples [DLPNO-CCSD(T1)] to benchmark the conformational energies and to assess their impact on the crystal energy landscapes. Molecule XXXI proves to be a relatively straightforward case, with the conformational energies from generalized gradient approximation (GGA) functional B86bPBE-XDM changing only modestly when using more advanced density functionals such as PBE0-D4, ωB97M-V, and revDSD-PBEP86-D4, dispersion-corrected second-order Møller-Plesset perturbation theory (SCS-MP2D), or DLPNO-CCSD(T1). In contrast, the conformational energies of molecule XXXII prove difficult to determine reliably, and variations in the computed conformational energies appreciably impact the crystal energy landscape. Even high-level methods such as revDSD-PBEP86-D4 and SCS-MP2D exhibit significant disagreements with the DLPNO-CCSD(T1) benchmarks for molecule XXXII, highlighting the difficulty of predicting conformational energies for complex, drug-like molecules. The best-converged predicted crystal energy landscape obtained here for molecule XXXII disagrees significantly with what has been inferred about the solid-form landscape experimentally. The identified limitations of the calculations are probably insufficient to account for the discrepancies between theory and experiment on molecule XXXII, and further investigation of the experimental solid-form landscape would be valuable. Finally, assessment of several semi-empirical methods finds r2SCAN-3c to be the most promising, with conformational energy accuracy intermediate between the GGA and hybrid functionals and a low computational cost.

Assessment of the exchange-hole dipole moment dispersion correction for the energy ranking stage of the seventh crystal structure prediction blind test

The seventh blind test of crystal structure prediction (CSP) methods substantially increased the level of complexity of the target compounds relative to the previous tests organized by the Cambridge Crystallographic Data Centre. In this work, the performance of density-functional methods is assessed using numerical atomic orbitals and the exchange-hole dipole moment dispersion correction (XDM) for the energy-ranking phase of the seventh blind test. Overall, excellent performance was seen for the two rigid molecules (XXVII, XXVIII) and for the organic salt (XXXIII). However, for the agrochemical (XXXI) and pharmaceutical (XXXII) targets, the experimental polymorphs were ranked fairly high in energy amongst the provided candidate structures and inclusion of thermal free-energy corrections from the lattice vibrations was found to be essential for compound XXXI. Based on these results, it is proposed that the importance of vibrational free-energy corrections increases with the number of rotatable bonds.

The seventh blind test of crystal structure prediction: structure generation methods

A seventh blind test of crystal structure prediction was organized by the Cambridge Crystallographic Data Centre featuring seven target systems of varying complexity: a silicon and iodine-containing molecule, a copper coordination complex, a near-rigid molecule, a cocrystal, a polymorphic small agrochemical, a highly flexible polymorphic drug candidate, and a polymorphic morpholine salt. In this first of two parts focusing on structure generation methods, many crystal structure prediction (CSP) methods performed well for the small but flexible agrochemical compound, successfully reproducing the experimentally observed crystal structures, while few groups were successful for the systems of higher complexity. A powder X-ray diffraction (PXRD) assisted exercise demonstrated the use of CSP in successfully determining a crystal structure from a low-quality PXRD pattern. The use of CSP in the prediction of likely cocrystal stoichiometry was also explored, demonstrating multiple possible approaches. Crystallographic disorder emerged as an important theme throughout the test as both a challenge for analysis and a major achievement where two groups blindly predicted the existence of disorder for the first time. Additionally, large-scale comparisons of the sets of predicted crystal structures also showed that some methods yield sets that largely contain the same crystal structures.

Large-Scale Parameter Estimation for Crystal Structure Prediction. Part 1: Dataset, Methodology, and Implementation

Crystal structure prediction (CSP) seeks to identify all thermodynamically accessible solid forms of a given compound and, crucially, to establish the relative thermodynamic stability between different polymorphs. The conventional hierarchical CSP workflow suggests that no single energy model can fulfill the needs of all stages in the workflow, and energy models across a spectrum of fidelities and computational costs are required. Hybrid ab initio/empirical force-field (HAIEFF) models have demonstrated a good balance of these two factors, but the force-field component presents a major bottleneck for model accuracy. Existing parameter estimation tools for fitting this empirical component are inefficient and have severe limitations on the manageable problem size. This, combined with a lack of reliable reference data for parameter fitting, has resulted in development in the force-field component of HAIEFF models having mostly stagnated. In this work, we address these barriers to progress. First, we introduce a curated database of 755 organic crystal structures, obtained using high quality, solid-state DFT-D calculations, which provide a complete set of geometry and energy data. Comparisons to various theoretical and experimental data sources indicate that this database provides suitable diversity for parameter fitting. In tandem, we also put forward a new parameter estimation algorithm implemented as the CrystalEstimator program. Our tests demonstrate that CrystalEstimator is capable of efficiently handling large-scale parameter estimation problems, simultaneously fitting as many as 62 model parameters based on data from 445 structures. This problem size far exceeds any previously reported works related to CSP force-field parametrization. These developments form a strong foundation for all future work involving parameter estimation of transferable or tailor-made force-fields for HAIEFF models. This ultimately opens the way for significant improvements in the accuracy achieved by the HAIEFF models.

Equivariant Neural Networks Utilizing Molecular Clusters for Accurate Molecular Crystal Lattice Energy Predictions

Equivariant neural networks have emerged as prominent models in advancing the construction of interatomic potentials due to their remarkable data efficiency and generalization capabilities for out-of-distribution data. Here, we expand the utility of these networks to the prediction of crystal structures consisting of organic molecules. Traditional methods for computing crystal structure properties, such as plane-wave quantum chemical methods based on density functional theory (DFT), are prohibitively resource-intensive, often necessitating compromises in accuracy and the choice of exchange-correlation functional. We present an approach that leverages the efficiency, and transferability of equivariant neural networks, specifically Allegro, to predict molecular crystal structure energies at a reduced computational cost. Our neural network is trained on molecular clusters using a highly accurate Gaussian-type orbital (GTO)-based method as the target level of theory, eliminating the need for costly periodic DFT calculations, while providing access to all families of exchange-corelation functionals and post-Hartree-Fock methods. The trained model exhibits remarkable accuracy in predicting lattice energies, aligning closely with those computed by plane-wave based DFT methods, thus representing significant cost reductions. Furthermore, the Allegro network was seamlessly integrated with the USPEX framework, accelerating the discovery of low-energy crystal structures during crystal structure prediction.

Introducing chirality in porous organic cages through solid-state interactions

Molecular cages contain an internal cavity designed to encapsulate other molecules, resulting in applications in molecular separation, gas storage, and catalysis. Introducing chirality in cage molecules can improve the selective separation of chiral molecules and add new functionalities due to the realisation of chiral photophysical properties. It has recently been shown that solid-state supramolecular interactions between achiral cages can result in the formation of chiral cavities. Here, we develop a computational technique to predict when achiral cages form chiral cavities in the solid-state through the combination of atomistic calculations and coarse-grained modelling to predict the crystalline phase behaviour. Our focus is on the achiral cage B11, which contains rotatable arene rings on the vertices of the cage that can form propeller-like orientations, inducing a chiral cavity. We show that by using dimer pair calculations, we can inform coarse-grained models to predict the packing of the cage. Our results reveal how the supramolecular interactions drive chirality in the achiral cages without the need for a chiral guest. These findings are a first step towards understanding how we can design chirality through supramolecular interactions by using abstract coarse-grained models to inform design principles for targeted solid-state phase behaviour.

Templated Nucleation of Clotrimazole and Ketoprofen on Polymer Substrates

The use of different template surfaces in crystallization experiments can directly influence the nucleation kinetics, crystal growth, and morphology of active pharmaceutical ingredients (APIs). Consequently, templated nucleation is an attractive approach to enhance crystal nucleation kinetics and preferentially nucleate desired crystal polymorphs for solid-form drug molecules, particularly large and flexible molecules that are difficult to crystallize. Herein, we investigate the effect of polymer templates on the crystal nucleation of clotrimazole and ketoprofen with both experiments and computational methods. Crystallization was carried out in toluene solvent for both APIs with a template library consisting of 12 different polymers. In complement to the experimental studies, we developed a computational workflow based on molecular dynamics (MD) and derived descriptors from the simulations to score and rank API-polymer interactions. The descriptors were used to measure the energy of interaction (EOI), hydrogen bonding, and rugosity (surface roughness) similarity between the APIs and polymer templates. We used a variety of machine learning models (14 in total) along with these descriptors to predict the crystallization outcome of the polymer templates. We found that simply rank-ordering the polymers by their API-polymer interaction energy descriptors yielded 92% accuracy in predicting the experimental outcome for clotrimazole and ketoprofen. The most accurate machine learning model for both APIs was found to be a random forest model. Using these models, we were able to predict the crystallization outcomes for all polymers. Additionally, we have performed a feature importance analysis using the trained models and found that the most predictive features are the energy descriptors. These results demonstrate that API-polymer interaction energies are correlated with heterogeneous crystallization outcomes.

Sublimation of pyridine derivatives: fundamental aspects and application for two-component crystal screening

The saturated vapour pressures of five heterocyclic compounds containing the pyridine fragment, namely, three isomers of aminopyridine (2-aminopyridine (2AmPy), 3-aminopyridine (3AmPy), and 4-aminopyridine (4AmPy)); 3-hydroxypyridine (3OHPy) and 2-(1H-imidazol-2-yl)pyridine (ImPy), were measured at appropriate temperature intervals using a transpiration (inert gas flow) method. The standard molar enthalpies, entropies, and Gibbs energies of sublimation for all the studied substances were determined. Among the compounds studied, the largest value of ΔH298sub was observed for ImPy. The influence of substitution and the effects of hydrogen bonds in the crystal lattices on sublimation parameters are discussed herein. The reliable dependences relating ΔG298sub to Tfus and ΔH298sub to ΔG298sub were plotted. A comparative analysis of several calculation schemes for the estimation of sublimation enthalpy and Gibbs free energy was carried out. Thermodynamic parameters obtained in this study were applied for the evaluation of cocrystallisation thermodynamic functions for two-component crystals (virtual screening) on the basis of the studied substituted pyridines.

A physics-aware neural network for protein-ligand interactions with quantum chemical accuracy

Quantifying intermolecular interactions with quantum chemistry (QC) is useful for many chemical problems, including understanding the nature of protein-ligand interactions. Unfortunately, QC computations on protein-ligand systems are too computationally expensive for most use cases. The flourishing field of machine-learned (ML) potentials is a promising solution, but it is limited by an inability to easily capture long range, non-local interactions. In this work we develop an atomic-pairwise neural network (AP-Net) specialized for modeling intermolecular interactions. This model benefits from a number of physical constraints, including a two-component equivariant message passing neural network architecture that predicts interaction energies via an intermediate prediction of monomer electron densities. The AP-Net model is trained on a comprehensive dataset composed of paired ligand and protein fragments. This model accurately predicts QC-quality interaction energies of protein-ligand systems at a computational cost reduced by orders of magnitude. Applications of the AP-Net model to molecular crystal structure prediction are explored, as well as limitations in modeling highly polarizable systems.

Unprecedented Packing Polymorphism of Oxindole: An Exploration Inspired by Crystal Structure Prediction

Crystal polymorphism, characterized by different packing arrangements of the same compound, strongly ties to the physical properties of a molecule. Determining the polymorphic landscape is complex and time-consuming, with the number of experimentally observed polymorphs varying widely from molecule to molecule. Furthermore, disappearing polymorphs, the phenomenon whereby experimentally observed forms cannot be reproduced, pose a significant challenge for the pharmaceutical industry. Herein, we focused on oxindole (OX), a small rigid molecule with four known polymorphs, including a reported disappearing form. Using crystal structure prediction (CSP), we assessed OX solid-state landscape and thermodynamic stability by comparing predicted structures with experimentally known forms. We then performed melt and solution crystallization in bulk and nanoconfinement to validate our predictions. These experiments successfully reproduced the known forms and led to the discovery of four novel polymorphs. Our approach provided insights into reconstructing disappearing polymorphs and building more comprehensive polymorph landscapes. These results also establish a new record of packing polymorphism for rigid molecules.

Tale of Two Polymorphs: Investigating the Structural Differences and Dynamic Relationship between Nirmatrelvir Solid Forms (Paxlovid)

Two anhydrous polymorphs of the novel antiviral medicine nirmatrelvir were discovered during the development of Paxlovid, Pfizer's oral Covid-19 treatment. A comprehensive experimental and computational approach was necessary to distinguish the two closely related polymorphs, herein identified as Forms 1 and 4. This approach paired experimental methods, including powder X-ray diffraction and single-crystal X-ray diffraction, solid-state experimental methods, thermal analysis, solid-state nuclear magnetic resonance and Raman spectroscopy with computational investigations comprising crystal structure prediction, Gibbs free energy calculations, and molecular dynamics simulations of the polymorphic transition. Forms 1 and 4 were ultimately determined to be enantiotropically related polymorphs with Form 1 being the stable form above the transition temperature of ∼17 °C and designated as the nominated form for drug development. The work described in this paper shows the importance of using highly specialized orthogonal approaches to elucidate the subtle differences in structure and properties of similar solid-state forms. This synergistic approach allowed for unprecedented speed in bringing Paxlovid to patients in record time amidst the pandemic.

Incorporating Noncovalent Interactions in Transfer Learning Gaussian Process Regression Models for Molecular Simulations

FFLUX is a quantum chemical topology-based multipolar force field that uses Gaussian process regression machine learning models to predict atomic energies and multipole moments on the fly for fast and accurate molecular dynamics simulations. These models have previously been trained on monomers, meaning that many-body effects, for example, intermolecular charge transfer, are missed in simulations. Moreover, dispersion and repulsion have been modeled using Lennard-Jones potentials, necessitating careful parametrization. In this work, we take an important step toward addressing these shortcomings and show that models trained on clusters, in this case, a dimer, can be used in FFLUX simulations by preparing and benchmarking a formamide dimer model. To mitigate the computational costs associated with training higher-dimensional models, we rely on the transfer of hyperparameters from a smaller source model to a larger target model, enabling an order of magnitude faster training than with a direct learning approach. The dimer model allows for simulations that account for two-body effects, including intermolecular polarization and charge penetration, and that do not require nonbonded potentials. We show that addressing these limitations allows for simulations that are closer to quantum mechanics than previously possible with the monomeric models.

Force Field X: A computational microscope to study genetic variation and organic crystals using theory and experiment

Force Field X (FFX) is an open-source software package for atomic resolution modeling of genetic variants and organic crystals that leverages advanced potential energy functions and experimental data. FFX currently consists of nine modular packages with novel algorithms that include global optimization via a many-body expansion, acid-base chemistry using polarizable constant-pH molecular dynamics, estimation of free energy differences, generalized Kirkwood implicit solvent models, and many more. Applications of FFX focus on the use and development of a crystal structure prediction pipeline, biomolecular structure refinement against experimental datasets, and estimation of the thermodynamic effects of genetic variants on both proteins and nucleic acids. The use of Parallel Java and OpenMM combines to offer shared memory, message passing, and graphics processing unit parallelization for high performance simulations. Overall, the FFX platform serves as a computational microscope to study systems ranging from organic crystals to solvated biomolecular systems.

Contributions beyond direct random-phase approximation in the binding energy of solid ethane, ethylene, and acetylene

The random-phase approximation (RPA) includes a subset of higher than second-order correlation-energy contributions, but stays in the same complexity class as the second-order Møller-Plesset perturbation theory (MP2) in both Gaussian-orbital and plane-wave codes. This makes RPA a promising ab initio electronic structure approach for the binding energies of molecular crystals. Still, some issues stand out in practical applications of RPA. Notably, compact clusters of nonpolar molecules are poorly described, and the interaction energies strongly depend on the reference single-determinant state. Using the many-body expansion of the binding energy of a crystal, we investigate those issues and the effect of beyond-RPA corrections. We find the beneficial effect of quartic-scaling exchange and non-ring coupled-cluster doubles corrections. The nonadditive interactions in compact trimers of molecules are improved by using the self-consistent Hartree-Fock orbitals instead of the usual Kohn-Sham states, but this kind of orbital input also leads to underestimated dimer energies. Overall, a substantial improvement over the RPA with a renormalized singles approach is possible at a modest quartic-scaling cost, which encourages further research into additional RPA corrections.

The Fe-MAN Challenge: Ferrates-Microkinetic Assessment of Numerical Quantum Chemistry

Organometallic species, such as organoferrate ions, are prototypical nucleophiles prone to reacting with a wide range of electrophiles, including proton donors. In solution, the operation of dynamic equilibria and the simultaneous presence of several organometallic species severely complicate the analysis of these fundamentally important reactions. This can be overcome by gas-phase experiments on mass-selected ions, which allow for the determination of the microscopic reactivity of the target species. In this contribution, we focus on the reactivity of a series of trisarylferrate complexes toward 2,2,2-trifluoroethanol and 2,2-difluoroethanol. By means of mass-spectrometric measurements, we determined the experimental bimolecular rate constants kexp of the gas-phase protolysis reactions of the trisarylferrate anions FePh3- and FeMes3- with the aforementioned acids. Based on these experiments, we carried out a dual blind challenge, inviting theoretical groups to submit their best predictions for the activation barriers and/or theoretical rate constants ktheo. This provides a unique opportunity to evaluate different computational protocols under minimal bias and sets the stage for further benchmarking of quantum chemical methods and data-driven approaches in the future.

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.

Computational Discovery of Intermolecular Singlet Fission Materials Using Many-Body Perturbation Theory

Intermolecular singlet fission (SF) is the conversion of a photogenerated singlet exciton into two triplet excitons residing on different molecules. SF has the potential to enhance the conversion efficiency of solar cells by harvesting two charge carriers from one high-energy photon, whose surplus energy would otherwise be lost to heat. The development of commercial SF-augmented modules is hindered by the limited selection of molecular crystals that exhibit intermolecular SF in the solid state. Computational exploration may accelerate the discovery of new SF materials. The GW approximation and Bethe-Salpeter equation (GW+BSE) within the framework of many-body perturbation theory is the current state-of-the-art method for calculating the excited-state properties of molecular crystals with periodic boundary conditions. In this Review, we discuss the usage of GW+BSE to assess candidate SF materials as well as its combination with low-cost physical or machine learned models in materials discovery workflows. We demonstrate three successful strategies for the discovery of new SF materials: (i) functionalization of known materials to tune their properties, (ii) finding potential polymorphs with improved crystal packing, and (iii) exploring new classes of materials. In addition, three new candidate SF materials are proposed here, which have not been published previously.

Crystal Polymorph Search in the NPT Ensemble via a Deposition/Sublimation Alchemical Path

The formulation of active pharmaceutical ingredients involves discovering stable crystal packing arrangements or polymorphs, each of which has distinct pharmaceutically relevant properties. Traditional experimental screening techniques utilizing various conditions are commonly supplemented with in silico crystal structure prediction (CSP) to inform the crystallization process and mitigate risk. Predictions are often based on advanced classical force fields or quantum mechanical calculations that model the crystal potential energy landscape but do not fully incorporate temperature, pressure, or solution conditions during the search procedure. This study proposes an innovative alchemical path that utilizes an advanced polarizable atomic multipole force field to predict crystal structures based on direct sampling of the NPT ensemble. The use of alchemical (i.e., nonphysical) intermediates, a novel Monte Carlo barostat, and an orthogonal space tempering bias combine to enhance the sampling efficiency of the deposition/sublimation phase transition. The proposed algorithm was applied to 2-((4-(2-(3,4-dichlorophenyl)ethyl)phenyl)amino)benzoic acid (Cambridge Crystallography Database Centre ID: XAFPAY) as a case study to showcase the algorithm. Each experimentally determined polymorph with one molecule in the asymmetric unit was successfully reproduced via approximately 1000 short 1 ns simulations per space group where each simulation was initiated from random rigid body coordinates and unit cell parameters. Utilizing two threads of a recent Intel CPU (a Xeon Gold 6330 CPU at 2.00 GHz), 1 ns of sampling using the polarizable AMOEBA force field can be acquired in 4 h (equating to more than 300 ns/day using all 112 threads/56 cores of a dual CPU node) within the Force Field X software (https://ffx.biochem.uiowa.edu). These results demonstrate a step forward in the rigorous use of the NPT ensemble during the CSP search process and open the door to future algorithms that incorporate solution conditions using continuum solvation methods.

First-Principles Models of Polymorphism of Pharmaceuticals: Maximizing the Accuracy-to-Cost Ratio

Accuracy and sophistication of in silico models of structure, internal dynamics, and cohesion of molecular materials at finite temperatures increase over time. Applicability limits of ab initio polymorph ranking that would be feasible at reasonable costs currently represent crystals of moderately sized molecules (less than 20 nonhydrogen atoms) and simple unit cells (containing rather only one symmetry-irreducible molecule). Extending the applicability range of the underlying first-principles methods to larger systems with a real-life significance, and enabling to perform such computations in a high-throughput regime represent additional challenges to be tackled in computational chemistry. This work presents a novel composite method that combines the computational efficiency of density-functional tight-binding (DFTB) methods with the accuracy of density-functional theory (DFT). Being rooted in the quasi-harmonic approximation, it uses a cheap method to perform all of the costly scans of how static and dynamic characteristics of the crystal vary with respect to its volume. Such data are subsequently corrected to agree with a higher-level model, which must be evaluated only at a single volume of the crystal. It thus enables predictions of structural, cohesive, and thermodynamic properties of complex molecular materials, such as pharmaceuticals or organic semiconductors, at a fraction of the original computational cost. As the composite model retains the solid physical background, it suffers from a minimum accuracy deterioration compared to the full treatment with the costly approach. The novel methodology is demonstrated to provide consistent results for the structural and thermodynamic properties of real-life molecular crystals and their polymorph ranking.

Heterocyclic (pyrazine)carboxamide Ru(ii) complexes: structural, experimental and theoretical studies of interactions with biomolecules and cytotoxicity

Treatments of N-(1H-benzo[d]imidazol-2-yl)pyrazine-2-carboxamide (HL1) and N-(benzo[d]thiazol-2-yl)pyrazine-2-carboxamide carboxamide ligands (HL2) with [Ru(p-cymene)Cl2]2 and [Ru(PPh3)3Cl2] precursors afforded the respective Ru(ii) complexes [Ru(L1)(p-cymene)Cl] (Ru1), [Ru(L2)(p-cymene)Cl] (Ru2), [Ru(L1)(PPh3)2Cl] (Ru3), and [Ru(L2)(PPh3)2Cl] (Ru4). These complexes were characterized by NMR, FT-IR spectroscopies, mass spectrometry, elemental analyses, and crystal X-ray crystallography for Ru2. The molecular structure of complex Ru2 contains one mono-anionic bidentate bound ligand and display pseudo-octahedral piano stool geometry around the Ru(ii) atom. The interactions with calf thymus DNA (CT-DNA) and bovine serum albumin (BSA) were investigated by spectroscopic techniques. The experimental binding studies suggest that complexes Ru1-Ru4 interact with DNA, primarily through minor groove binding, as supported by molecular docking results. Additionally, these complexes exhibit strong quenching of the fluorescence of tryptophan residues in BSA, displaying static quenching. The in vitro cytotoxicity studies of compounds Ru1-Ru4 were assessed in cancer cell lines (A549, PC-3, HT-29, Caco-2, and HeLa), as well as a non-cancer line (KMST-6). Compounds Ru1 and Ru2 exhibited superior cytotoxicity compared to Ru3 and Ru4. The in vitro cytotoxicity and selectivity of compounds Ru1 and Ru2 against A549, PC-3, and Caco-2 cell lines surpassed that of cisplatin.

Organic crystal structure prediction via coupled generative adversarial networks and graph convolutional networks

Organic crystal structures exert a profound impact on the physicochemical properties and biological effects of organic compounds. Quantum mechanics (QM)-based crystal structure predictions (CSPs) have somewhat alleviated the dilemma that experimental crystal structure investigations struggle to conduct complete polymorphism studies, but the high computing cost poses a challenge to its widespread application. The present study aims to construct DeepCSP, a feasible pure machine learning framework for minute-scale rapid organic CSP. Initially, based on 177,746 data entries from the Cambridge Crystal Structure Database, a generative adversarial network was built to conditionally generate trial crystal structures under selected feature constraints for the given molecule. Simultaneously, a graph convolutional attention network was used to predict the density of stable crystal structures for the input molecule. Subsequently, the distances between the predicted density and the definition-based calculated density would be considered to be the crystal structure screening and ranking basis, and finally, the density-based crystal structure ranking would be output. Two such distinct algorithms, performing the generation and ranking functionalities, respectively, collectively constitute the DeepCSP, which has demonstrated compelling performance in marketed drug validations, achieving an accuracy rate exceeding 80% and a hit rate surpassing 85%. Inspiringly, the computing speed of the pure machine learning methodology demonstrates the potential of artificial intelligence in advancing CSP research.

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.

Multimer Embedding Approach for Molecular Crystals up to Harmonic Vibrational Properties

Accurate calculations of molecular crystals are crucial for drug design and crystal engineering. However, periodic high-level density functional calculations using hybrid functionals are often prohibitively expensive for the relevant systems. These expensive periodic calculations can be circumvented by the usage of embedding methods in which, for instance, the periodic calculation is only performed at a lower-cost level and then monomer energies and dimer interactions are replaced by those of the higher-level method. Herein, we extend such a multimer embedding approach to enable energy corrections for trimer interactions and the calculation of harmonic vibrational properties up to the dimer level. We evaluate this approach for the X23 benchmark set of molecular crystals by approximating a periodic hybrid density functional (PBE0+MBD) by embedding multimers into less expensive calculations using a generalized-gradient approximation functional (PBE+MBD). We show that trimer interactions are crucial for accurately approximating lattice energies within 1 kJ/mol and might also be needed for further improvement of lattice constants and hence cell volumes. Finally, the vibrational properties are already very well captured at the monomer and dimer level, making it possible to approximate vibrational free energies at room temperature within 1 kJ/mol.

Accelerated Organic Crystal Structure Prediction with Genetic Algorithms and Machine Learning

We present a high-throughput, end-to-end pipeline for organic crystal structure prediction (CSP)─the problem of identifying the stable crystal structures that will form from a given molecule based only on its molecular composition. Our tool uses neural network potentials to allow for efficient screening and structural relaxation of generated crystal candidates. Our pipeline consists of two distinct stages: random search, whereby crystal candidates are randomly generated and screened, and optimization, where a genetic algorithm (GA) optimizes this screened population. We assess the performance of each stage of our pipeline on 21 molecules taken from the Cambridge Crystallographic Data Centre's CSP blind tests. We show that random search alone yields matches for ≈50% of targets. We then validate the potential of our full pipeline, making use of the GA to optimize the root-mean-square deviation between crystal candidates and the experimentally derived structure. With this approach, we are able to find matches for ≈80% of candidates with 10-100 times smaller initial population sizes than when using random search. Lastly, we run our full pipeline with an ANI model that is trained on a small data set of molecules extracted from crystal structures in the Cambridge Structural Database, generating ≈60% of targets. By leveraging machine learning models trained to predict energies at the density functional theory level, our pipeline has the potential to approach the accuracy of ab initio methods and the efficiency of empirical force fields.

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.

Substituted tetrazoles with N-oxide moiety: critical assessment of thermochemical properties

Modeling of the structure of molecules and simulation of crystal structure followed by the calculation of the enthalpies of formation for 21 salts of three high-energy tetrazole 1N-oxides: 5-nitro-1-hydroxy-1H-tetrazole 1a-1g, 5-trinitromethyl-1-hydroxy-1H-tetrazole 2a-2g and 6-amino-3-(1-hydroxy-1H-tetrazol-5-yl)-1,2,4,5-tetrazine 1,5-dioxide 3a-3g was performed. The methods of quantum chemistry and the method of atom-atom potentials were used. Structural search for optimal crystal packings was carried out in 11 most common space symmetry groups. The enthalpies of formation were obtained and analyzed using two different approaches: VBT and MICCM methods, which allowed to evaluate the quality of these calculation methods. In addition, the results obtained indicate high values of thermochemical characteristics for some of the considered compounds, which have a positive effect on their explosive properties and unveil their future application potential.

Benchmark Data Set of Crystalline Organic Semiconductors

This work reports a Benchmark Data set of Crystalline Organic Semiconductors to test calculations of the structural and electronic properties of these materials in the solid state. The data set contains 67 crystals consisting of mostly rigid molecules with a single dominant conformer, covering the majority of known structural types. The experimental crystal structure is available for the entire data set, whereas zero-temperature unit cell volume can be reliably estimated for a subset of 28 crystals. Using this subset, we benchmark r2SCAN-D3 and PBE-D3 density functionals. Then, for the entire data set, we benchmark approximate density functional theory (DFT) methods, including GFN1-xTB and DFTB3(3ob-3-1), with various dispersion corrections against r2SCAN-D3. Our results show that r2SCAN-D3 geometries are accurate within a few percent, which is comparable to the statistical uncertainty of experimental data at a fixed temperature, but the unit cell volume is systematically underestimated by 2% on average. The several times faster PBE-D3 provides an unbiased estimate of the volume for all systems except for molecules with highly polar bonds, for which the volume is substantially overestimated in correlation with the underestimation of atomic charges. Considered approximate DFT methods are orders of magnitude faster and provide qualitatively correct but overcompressed crystal structures unless the dispersion corrections are fitted by unit cell volume.

Hybrid classical/machine-learning force fields for the accurate description of molecular condensed-phase systems

Electronic structure methods offer in principle accurate predictions of molecular properties, however, their applicability is limited by computational costs. Empirical methods are cheaper, but come with inherent approximations and are dependent on the quality and quantity of training data. The rise of machine learning (ML) force fields (FFs) exacerbates limitations related to training data even further, especially for condensed-phase systems for which the generation of large and high-quality training datasets is difficult. Here, we propose a hybrid ML/classical FF model that is parametrized exclusively on high-quality ab initio data of dimers and monomers in vacuum but is transferable to condensed-phase systems. The proposed hybrid model combines our previous ML-parametrized classical model with ML corrections for situations where classical approximations break down, thus combining the robustness and efficiency of classical FFs with the flexibility of ML. Extensive validation on benchmarking datasets and experimental condensed-phase data, including organic liquids and small-molecule crystal structures, showcases how the proposed approach may promote FF development and unlock the full potential of classical FFs.

Application of the FFLUX Force Field to Molecular Crystals: A Study of Formamide

In this work, we present the first application of the quantum chemical topology force field FFLUX to the solid state. FFLUX utilizes Gaussian process regression machine learning models trained on data from the interacting quantum atom partitioning scheme to predict atomic energies and flexible multipole moments that change with geometry. Here, the ambient (α) and high-pressure (β) polymorphs of formamide are used as test systems and optimized using FFLUX. Optimizing the structures with increasing multipolar ranks indicates that the lattice parameters of the α phase differ by less than 5% to the experimental structure when multipole moments up to the quadrupole are used. These differences are found to be in line with the dispersion-corrected density functional theory. Lattice dynamics calculations are also found to be possible using FFLUX, yielding harmonic phonon spectra comparable to dispersion-corrected DFT while enabling larger supercells to be considered than is typically possible with first-principles calculations. These promising results indicate that FFLUX can be used to accurately determine properties of molecular solids that are difficult to access using DFT, including the structural dynamics, free energies, and properties at finite temperature.

In silico co-crystal design: Assessment of the latest advances

Pharmaceutical co-crystals represent a growing class of crystal forms in the context of pharmaceutical science. They are attractive to pharmaceutical scientists because they significantly expand the number of crystal forms that exist for an active pharmaceutical ingredient and can lead to improvements in physicochemical properties of clinical relevance. At the same time, machine learning is finding its way into all areas of drug discovery and delivers impressive results. In this review, we attempt to provide an overview of machine learning, deep learning and network-based recommendation approaches applied to pharmaceutical co-crystallization. We also present crystal structure prediction as an alternative to machine learning approaches.

A focus on detection of polymorphs by dynamic nuclear polarization solid-state nuclear magnetic resonance spectroscopy

Solid-state nuclear magnetic resonance (ssNMR) spectroscopy has found increasing application as a method for quantification and structure determination of solid forms (polymorphs) of organic solids and active pharmaceutical ingredients (APIs). However, ssNMR spectroscopy suffers from low sensitivity and resolution, making it challenging to detect dilute solid forms that may be present after recrystallization or reaction with co-formers. Cousin et al. (S. F. Cousin et al., Chem. Sci., 2023, https://doi.org/10.1039/D3SC02063K) have demonstrated that dynamic nuclear polarization (DNP) enhanced 13C cross-polarization (CP) saturation recovery experiments can be used to detect dilute polymorphic forms that are present within a mixture of solid forms. Enhancement of the NMR signal by DNP and differences in signal build-up rates for different polymorphs provide the sensitivity and contrast needed to resolve NMR signals from minor polymorphic forms. This method demonstrated by Cousin et al. should aid the discovery of solid drug forms.

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.

Review of Applications of Density Functional Theory (DFT) Quantum Mechanical Calculations to Study the High-Pressure Polymorphs of Organic Crystalline Materials

Since its inception, chemistry has been predominated by the use of temperature to generate or change materials, but applications of pressure of more than a few tens of atmospheres for such purposes have been rarely observed. However, pressure is a very effective thermodynamic variable that is increasingly used to generate new materials or alter the properties of existing ones. As computational approaches designed to simulate the solid state are normally tuned using structural data at ambient pressure, applying them to high-pressure issues is a highly challenging test of their validity from a computational standpoint. However, the use of quantum chemical calculations, typically at the level of density functional theory (DFT), has repeatedly been shown to be a great tool that can be used to both predict properties that can be later confirmed by experimenters and to explain, at the molecular level, the observations of high-pressure experiments. This article's main goal is to compile, analyze, and synthesize the findings of works addressing the use of DFT in the context of molecular crystals subjected to high-pressure conditions in order to give a general overview of the possibilities offered by these state-of-the-art calculations.

Ab Initio Crystal Structure Prediction of the Energetic Materials LLM-105, RDX, and HMX

Crystal structure prediction (CSP) is performed for the energetic materials (EMs) LLM-105 and α-RDX, as well as the α and β conformational polymorphs of 1,3,5,7-tetranitro-1,3,5,7-tetraazacyclooctane (HMX), using the genetic algorithm (GA) code, GAtor, and its associated random structure generator, Genarris. Genarris and GAtor successfully generate the experimental structures of all targets. GAtor's symmetric crossover scheme, where the space group symmetries of parent structures are treated as genes inherited by offspring, is found to be particularly effective. However, conducting several GA runs with different settings is still important for achieving diverse samplings of the potential energy surface. For LLM-105 and α-RDX, the experimental structure is ranked as the most stable, with all of the dispersion-inclusive density functional theory (DFT) methods used here. For HMX, the α form was persistently ranked as more stable than the β form, in contrast to experimental observations, even when correcting for vibrational contributions and thermal expansion. This may be attributed to insufficient accuracy of dispersion-inclusive DFT methods or to kinetic effects not considered here. In general, the ranking of some putative structures is found to be sensitive to the choice of the DFT functional and the dispersion method. For LLM-105, GAtor generates a putative structure with a layered packing motif, which is desirable thanks to its correlation with low sensitivity. Our results demonstrate that CSP is a useful tool for studying the ubiquitous polymorphism of EMs and shows promise of becoming an integral part of the EM development pipeline.

The first HyDRA challenge for computational vibrational spectroscopy

Vibrational spectroscopy in supersonic jet expansions is a powerful tool to assess molecular aggregates in close to ideal conditions for the benchmarking of quantum chemical approaches. The low temperatures achieved as well as the absence of environment effects allow for a direct comparison between computed and experimental spectra. This provides potential benchmarking data which can be revisited to hone different computational techniques, and it allows for the critical analysis of procedures under the setting of a blind challenge. In the latter case, the final result is unknown to modellers, providing an unbiased testing opportunity for quantum chemical models. In this work, we present the spectroscopic and computational results for the first HyDRA blind challenge. The latter deals with the prediction of water donor stretching vibrations in monohydrates of organic molecules. This edition features a test set of 10 systems. Experimental water donor OH vibrational wavenumbers for the vacuum-isolated monohydrates of formaldehyde, tetrahydrofuran, pyridine, tetrahydrothiophene, trifluoroethanol, methyl lactate, dimethylimidazolidinone, cyclooctanone, trifluoroacetophenone and 1-phenylcyclohexane-cis-1,2-diol are provided. The results of the challenge show promising predictive properties in both purely quantum mechanical approaches as well as regression and other machine learning strategies.

Structure prediction in low dimensions: concepts, issues and examples

Structure prediction of stable and metastable polymorphs of chemical systems in low dimensions has become an important field, since materials that are patterned on the nano-scale are of increasing importance in modern technological applications. While many techniques for the prediction of crystalline structures in three dimensions or of small clusters of atoms have been developed over the past three decades, dealing with low-dimensional systems-ideal one-dimensional and two-dimensional systems, quasi-one-dimensional and quasi-two-dimensional systems, as well as low-dimensional composite systems-poses its own challenges that need to be addressed when developing a systematic methodology for the determination of low-dimensional polymorphs that are suitable for practical applications. Quite generally, the search algorithms that had been developed for three-dimensional systems need to be adjusted when being applied to low-dimensional systems with their own specific constraints; in particular, the embedding of the (quasi-)one-dimensional/two-dimensional system in three dimensions and the influence of stabilizing substrates need to be taken into account, both on a technical and a conceptual level. This article is part of a discussion meeting issue 'Supercomputing simulations of advanced materials'.

Exploring the Supramolecular Interactions and Thermal Stability of Dapsone:Bipyridine Cocrystals by Combining Computational Chemistry with Experimentation

The application of computational screening methodologies based on H-bond propensity scores, molecular complementarity, molecular electrostatic potentials, and crystal structure prediction has guided the discovery of novel cocrystals of dapsone and bipyridine (DDS:BIPY). The experimental screen, which included mechanochemical and slurry experiments as well as the contact preparation, resulted in four cocrystals, including the previously known DDS:4,4'-BIPY (2:1, CC₄₄-B) cocrystal. To understand the factors governing the formation of the DDS:2,2'-BIPY polymorphs (1:1, CC₂₂-A and CC₂₂-B) and the two DDS:4,4'-BIPY cocrystal stoichiometries (1:1 and 2:1), different experimental conditions (such as the influence of solvent, grinding/stirring time, etc.) were tested and compared with the virtual screening results. The computationally generated (1:1) crystal energy landscapes had the experimental cocrystals as the lowest energy structures, although distinct cocrystal packings were observed for the similar coformers. H-bonding scores and molecular electrostatic potential maps correctly indicated cocrystallization of DDS and the BIPY isomers, with a higher likelihood for 4,4'-BIPY. The molecular conformation influenced the molecular complementarity results, predicting no cocrystallization for 2,2'-BIPY with DDS. The crystal structures of CC₂₂-A and CC₄₄-A were solved from powder X-ray diffraction data. All four cocrystals were fully characterized by a range of analytical techniques, including powder X-ray diffraction, infrared spectroscopy, hot-stage microscopy, thermogravimetric analysis, and differential scanning calorimetry. The two DDS:2,2'-BIPY polymorphs are enantiotropically related, with form B being the stable polymorph at room temperature (RT) and form A being the higher temperature form. Form B is metastable but kinetically stable at RT. The two DDS:4,4'-BIPY cocrystals are stable at room conditions; however, at higher temperatures, CC₄₄-A transforms to CC₄₄-B. The cocrystal formation enthalpy order, derived from the lattice energies, was calculated as follows: CC₄₄-B > CC₄₄-A > CC₂₂-A.