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.

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.

A pressure-induced superhard SiCN4 compound uncovered by first-principles calculations

Silicon-carbon-nitride (Si-C-N) compounds are a family of potential superhard materials with many excellent chemical and physical properties; however, only SiCN, Si2CN4 and SiC2N4 were synthesized. Here, we theoretically report a new SiCN4 compound with P41212, Fdd2 and R3̄ structures by first-principles structural predictions based on the particle swarm optimization algorithm. Pressure-induced structural phase transitions from P41212 to Fdd2, and then to the R3̄ phase were determined at 2 GPa and 249 GPa. By comparing enthalpy differences with 1/3Si3N4 + C + 4/3N2, it was found that these structures tend to decompose at ambient pressure. However, with the increase of pressure, the enthalpy differences of Fdd2 and R3̄ structures turn to be negative and they can be stabilized at a pressure of more than 41 GPa. They are also dynamically stable as no imaginary frequencies were found in their stabilized pressure ranges. The calculated band gap is 4.37 eV for P41212, 3.72 eV for Fdd2 and 3.81 eV for the R3̄ phase by using the Heyd-Scuseria-Ernzerhof (HSE06) method and the estimated Vickers hardness values are higher than 40 GPa by adopting the elastic modulus based hardness formula, which confirmed their superhard characteristics. These results provide significant insights into Si-C-N systems and will inevitably promote the future experimental works.

Tailoring the dimensionality of metal complexes via ligand modifications

A series of CuII complexes obtained under the same reaction conditions has been analyzed to gain insight into the effect of the ligand composition on the final reaction product. Dipodal ligands containing N-donor imidazole rings and a benzene ring as a spacer with different numbers of methyl substituents on the aromatic rings were selected for the study such as 1,3-bis(imidazol-1-ylmethyl)benzene (L1), 1,3-bis(imidazol-1-ylmethyl)-5-methylbenzene (L2), 1,3-bis(imidazol-1-ylmethyl)-2,4,6-trimethylbenzene (L3), 1,3-bis(2-methylimidazol-1-ylmethyl)-2,4,6-trimethylbenzene (L4). L4 has not been reported previously and was synthesized for this study. The formed metal complexes show the presence of polymeric (ligand with no or one methyl substituent; 1-4), or discrete motifs (3- or 5-methyl substituents; 5-7). The new metal complexes 3, 5 and 6 were analyzed using single-crystal X-ray diffraction and powder diffraction. In addition, the structural analyses were supported by computational methods.

Improved Description of Intra- and Intermolecular Interactions through Dispersion-Corrected Second-Order Møller-Plesset Perturbation Theory

ConspectusThe quantum chemical modeling of organic crystals and other molecular condensed-phase problems requires computationally affordable electronic structure methods which can simultaneously describe intramolecular conformational energies and intermolecular interactions accurately. To achieve this, we have developed a spin-component-scaled, dispersion-corrected second-order Møller-Plesset perturbation theory (SCS-MP2D) model. SCS-MP2D augments canonical MP2 with a dispersion correction which removes the uncoupled Hartree-Fock dispersion energy present in canonical MP2 and replaces it with a more reliable coupled Kohn-Sham treatment, all evaluated within the framework of Grimme's D3 dispersion model. The spin-component scaling is then used to improve the description of the residual (nondispersion) portion of the correlation energy.The SCS-MP2D model improves upon earlier corrected MP2 models in a few ways. Compared to the highly successful dispersion-corrected MP2C model, which is based solely on intermolecular perturbation theory, the SCS-MP2D dispersion correction improves the description of both inter- and intramolecular interactions. The dispersion correction can also be evaluated with trivial computational cost, and nuclear analytic gradients are computed readily to enable geometry optimizations. In contrast to earlier spin-component scaling MP2 models, the optimal spin-component scaling coefficients are only mildly sensitive to the choice of training data, and a single global parametrization of the model can describe both thermochemistry and noncovalent interactions.The resulting dispersion-corrected, spin-component-scaled MP2 (SCS-MP2D) model predicts conformational energies and intermolecular interactions with accuracy comparable to or better than those of many range-separated and double-hybrid density functionals, as is demonstrated on a variety of benchmark tests. Among the functionals considered here, only the revDSD-PBEP86-D3(BJ) functional gives consistently smaller errors in benchmark tests. The results presented also hint that further improvements of SCS-MP2D may be possible through a more robust fitting procedure for the seven empirical parameters.To demonstrate the performance of SCS-MP2D further, several applications to molecular crystal problems are presented. The three chosen examples all represent cases where density-driven delocalization error causes GGA or hybrid density functionals to artificially stabilize crystals exhibiting more extended π-conjugation. Our pragmatic strategy addresses the delocalization error by combining a periodic density functional theory (DFT) treatment of the infinite lattice with intramolecular/conformational energy corrections computed with SCS-MP2D. For the anticancer drug axitinib, applying the SCS-MP2D conformational energy correction produces crystal polymorph stabilities that are consistent with experiment, in contrast to earlier studies. For the crystal structure prediction of the ROY molecule, so named for its colorful red, orange, and yellow crystals, this approach leads to the first plausible crystal energy landscape, and it reveals that the lowest-energy polymorphs have already been found experimentally. Finally, in the context of photomechanical crystals, which transform light into mechanical work, these techniques are used to predict the structural transformations and extract design principles for maximizing the work performed.

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.

Polymorphs of Substituted p-Toluenesulfonanilide: Synthesis, Single-Crystal Analysis, Hirshfeld Surface Exploration, and Theoretical Investigation

Polymorphism is an exciting feature of chemical systems where a compound can exist in different crystal forms. The present investigation is focused on the two polymorphic forms, triclinic (MSBT) and monoclinic (MSBM), of ethyl 3-iodo-4-((4-methylphenyl)sulfonamido)benzoate prepared from ethyl 4-amino-3-iodobenzoate. The prepared polymorphs were unambiguously confirmed by single-crystal X-ray diffraction (SC-XRD) analysis. According to the SC-XRD results, the molecular configurations of both structures are stabilized by intramolecular N-H···I and C-H···O bonding. The crystal packing of MSBT is different as compared to the crystal packing of MSBM because MSBT is crystallized in the triclinic crystal system with the space group P1̅, whereas MSBM is crystallized in the monoclinic crystal system with the space group P21/c. The molecules of MSBT are interlinked in the form of dimers through N-H···O bonding to form R22(8) loops, while the MSBM molecules are connected with each other in the form of an infinite chain through C-H···O bonding. The crystal packing of both compounds is further stabilized by off-set π···π stacking interactions between phenyl rings, which is found stronger in MSBM as compared to in MSBT. Moreover, Hirshfeld surface exploration of the polymorphs was carried out, and the results were compared with the closely related literature structure. Accordingly, the supramolecular assembly of these polymorphs is mainly stabilized by noncovalent interactions or intermolecular interactions. Furthermore, a density functional theory (DFT) study was also carried out, which provided good support for the SC-XRD and Hirshfeld studies, suggesting the formation of both intramolecular and intermolecular interactions for both compounds.

Advanced crystallisation methods for small organic molecules

Molecular materials based on small organic molecules often require advanced structural analysis, beyond the capability of spectroscopic techniques, to fully characterise them. In such cases, diffraction methods such as single crystal X-ray diffraction (SCXRD), are one of the most powerful tools available to researchers, providing molecular and structural elucidation at atomic level resolution, including absolute stereochemistry. However SCXRD, and related diffraction methods, are heavily dependent on the availability of suitable, high-quality crystals, thus crystallisation often becomes the major bottleneck in preparing samples. Following a summary of classical methods for the crystallisation of small organic molecules, this review will focus on a number of recently developed advanced methods for crystalline material sample preparation for SCXRD. This review will cover two main areas of modern small organic molecule crystallisation, namely the inclusion of molecules within host complexes (e.g., "crystalline sponge" and tetraaryladamantane based inclusion chaperones) and the use of high-throughput crystallisation, employing "under-oil" approaches (e.g., microbatch under-oil and ENaCt). Representative examples have been included for each technique, together with a discussion of their relative advantages and limitations to aid the reader in selecting the most appropriate technique to overcome a specific analytical challenge.

Metalating 5-Methyl-2-[(2-nitrophenyl)amino]-3-thiophenecarbonitrile (ROY): Understanding the Denticity and Speciation of Complexes of the ROY Anion

5-Methyl-2-[(2-nitrophenyl)amino]-3-thiophenecarbonitrile (ROY) is considered to be the most crystalline polymorphic organic molecule discovered to date with 12 fully characterized crystal structures present in the Cambridge Structural Database (CSD). However, metal complexes of ROY have not previously been described. Here, we explore the synthetic chemistry of ROY (denoted as H-ROY hereafter for the purpose of our study) and demonstrate that it can be deprotonated using either NaH or KH and that the resulting sodium and potassium salts of H-ROY can be cleanly isolated. Furthermore, we introduce two new metal complexes of the ROY anion (ROY^-) with Co(II) and Ni(II) cations, formed by the reaction of the sodium salt of ROY, Na(ROY), with the respective transition-metal chloride salts. Solid-state X-ray diffraction studies confirm the presence of Co(II) or Ni(II) centers, with the ROY^- ligand in a 1:2 ratio forming neutral trinuclear clusters of the forms [Co₃ROY₆] (Co-ROY) and [Ni₃ROY₆] (Ni-ROY) in both cases. Here, the ROY^- moiety interacts with the metal center through the anionic N atom, an O atom of the -NO₂ group, and the N atom of the -CN group. IR and electronic absorption spectroscopies reveal the influence of the Co(II) and Ni(II) centers on the properties of the complexes. Taken together, our results show that the metal complexes of the H-ROY proligand can be prepared with late 3d transition metals. The results of these structural chemistry studies may contribute to resolving polymorphism in H-ROY and related compounds.

Range-dependence of two-body intermolecular interactions and their energy components in molecular crystals

Routinely assessing the stability of molecular crystals with high accuracy remains an open challenge in the computational sciences. The many-body expansion decomposes computation of the crystal lattice energy into an embarrassingly parallel collection of computations over molecular dimers, trimers, and so forth, making quantum chemistry techniques tractable for many crystals of small organic molecules. By examining the range-dependence of different types of energetic contributions to the crystal lattice energy, we can glean qualitative understanding of solid-state intermolecular interactions as well as practical, exploitable reductions in the number of computations required for accurate energies. Here, we assess the range-dependent character of two-body interactions of 24 small organic molecular crystals using the physically interpretable components from symmetry-adapted perturbation theory (electrostatics, exchange repulsion, induction/polarization, and London dispersion). We also examine correlations between the convergence rates of electrostatics and London dispersion terms with molecular dipole moments and polarizabilities, to provide guidance for estimating convergence rates in other molecular crystals.

Polymorphic selectivity in crystal nucleation

Crystal nucleation rates have been measured in the supercooled melts of two richly polymorphic glass-forming liquids: ROY and nifedipine (NIF). ROY or 5-methyl-2-[(2-nitrophenyl)amino]-3-thiophenecarbonitrile is known for its crystals of red, orange, and yellow colors and many polymorphs of solved structures (12). Of the many polymorphs, ON (orange needles) nucleates the fastest with the runner up (Y04) trailing by a factor of 103 when compared under the same mobility-limited condition, while the other unobserved polymorphs are slower yet by at least 5 orders of magnitude. Similarly, of the six polymorphs of NIF, [Formula: see text]′ nucleates the fastest, [Formula: see text]′ is slower by a factor of 10, and the rest are slower yet by at least 5 decades. In both systems, the faster-nucleating polymorphs are not built from the lowest-energy conformers, while they tend to have higher energies and lower densities and thus greater similarity to the liquid phase by these measures. The temperature ranges of this study covered the glass transition temperature Tg of each system, and we find no evidence that the nucleation rate is sensitive to the passage of Tg. At the lowest temperatures investigated, the rates of nucleation and growth are proportional to each other, indicating that a similar kinetic barrier controls both processes. The classical nucleation theory provides an accurate description of the observed nucleation rates if the crystal growth rate is used to describe the kinetic barrier for nucleation. The quantitative rates of both nucleation and growth for the competing polymorphs enable prediction of the overall rate of crystallization and its polymorphic outcome.

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.

Packing Preferences of Chalcones: A Model Conjugated Pharmaceutical Scaffold

We sought the crystal packing preferences of the chalcone scaffold by analyzing 232 single-component crystal structures of chalcones with a small (six or fewer non-hydrogen atoms) substituent on either or both rings, including the unsubstituted molecule. This covers 216 molecules, as some are polymorphic, and 277 independent molecular conformations, as 16% of the crystal structures have more than one symmetry independent molecule. Quantum mechanical conformational profiles of the unsubstituted molecule and the almost 5000 crystal structures within 20 kJ mol^-1 of the global minimum generated in a crystal structure prediction (CSP) study have been used to complement this analysis. Although π conjugation would be expected to favor a planar molecule, there are a significant number of crystal structures containing nonplanar molecules with an approximately 50° angle between the aromatic rings. The relative orientations of the molecules in the inversion-related dimers and translation-related dimers in the experimental crystal structures show the same trends as in the CSP-generated structures for the unsubstituted molecule, allowing for the substituent making the side-to-side distances larger. There is no type of dimer geometry associated with particularly favorable lattice energies for the chalcone core. Less than a third of the experimental structures show a face-to-face contact associated with π···π stacking. Analysis of the experimental crystal structures with XPac and Mercury finds various pairs of isostructural crystals, but the largest isostructural set had only 15 structures, with all substituents (mainly halogens) in the para position. The most common one-dimensional motif, found in half of the experimental crystal structures, is a translation-related side-to-side packing, which can be adopted by all the observed conformations. This close-packed motif can be adopted by chalcones with a particularly wide variety of substituents as the substituents are at the periphery. Thus, although the crystal structures of the substituted chalcones show thermodynamically plausible packings of the chalcone scaffold, there is little evidence for any crystal engineering principle of preferred chalcone scaffold packing beyond close packing of the specific molecule.

Portrayal of the color polymorphism in the 5-acetyl-derivative of ROY

A novel derivative of ROY, AcROY, was synthesized and studied in this work, where 3 different colored polymorphs were identified. The observed polymorphism of AcROY is an interesting case of packing-determined color polymorphism.

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.

Spin-component-scaled and dispersion-corrected second-order Møller-Plesset perturbation theory: A path toward chemical accuracy

Second-order Moller-Plesset perturbation theory (MP2) provides a valuable alternative to density functional theory for modeing problems in organic and biological chemistry. However, MP2 suffers from known limitations in the description...

Direct evidence for distinct colour origins in ROY polymorphs

ROY is one of the most well-studied families of crystal structures owing to it being the most polymorphic organic material on record. The various red, orange, and yellow colours of its crystal structures are widely-believed to originate from molecular conformation, though the orange needle (ON) polymorph is thought to be an exception. We report high-pressure, single-crystal X-ray measurements which provide direct experimental evidence that the colour origin in ON is intermolecular, revealing that the molecule undergoes minimal deformation but still exhibits a pronounced, reversible, pale orange → dark red colour change between ambient pressure and 4.18 GPa. Our experimental data are rationalised with band structures, calculated using an accurate hybrid DFT approach, where we are able to account for the variation in colour for five polymorphs of ROY. We highlight the outlier behaviour of ON which shows marked π⋯π stacking interactions that are directly modified through application of pressure. Band structure calculations confirm these intermolecular interactions as the origin of the colour change.

Prolific Polymorph Generator ROY in Its Liquid and Glass: Two Conformational Populations Mirroring the Crystalline-State Distribution

5-Methyl-2-[(2-nitrophenyl)amino]-3-thiophenecarbonitrile, dubbed ROY for its numerous crystal polymorphs of red, orange, and yellow colors, has been studied in its liquid and glassy state by infrared spectroscopy. Two populations of conformers are observed, whose equilibrium is characterized by ΔH = 2.4 kJ/mol and ΔS = 8.0 J/K/mol. The two populations correspond to the global and local minima of the torsional energy surface and to the conformational preference of the 13 crystal polymorphs. The local minimum features a more coplanar arrangement of the two aromatic rings, greater π conjugation, and lower CN stretch frequency. In the gas phase, the lowest-energy path between the two minima has an energy barrier 3.9 kJ/mol above the global minimum, consistent with the rapid equilibration between the two populations. The relevance of our result for understanding the prolific polymorphism of ROY is discussed.

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.

Crystal Structure Prediction Methods for Organic Molecules: State of the Art

The prediction of the crystal structures that a given organic molecule is likely to form is an important theoretical problem of significant interest for the pharmaceutical and agrochemical industries, among others. As evidenced by a series of six blind tests organized over the past 2 decades, methodologies for crystal structure prediction (CSP) have witnessed substantial progress and have now reached a stage of development where they can begin to be applied to systems of practical significance. This article reviews the state of the art in general-purpose methodologies for CSP, placing them within a common framework that highlights both their similarities and their differences. The review discusses specific areas that constitute the main focus of current research efforts toward improving the reliability and widening applicability of these methodologies, and offers some perspectives for the evolution of this technology over the next decade.

Data-efficient machine learning for molecular crystal structure prediction

The combination of modern machine learning (ML) approaches with high-quality data from quantum mechanical (QM) calculations can yield models with an unrivalled accuracy/cost ratio. However, such methods are ultimately limited by the computational effort required to produce the reference data. In particular, reference calculations for periodic systems with many atoms can become prohibitively expensive for higher levels of theory. This trade-off is critical in the context of organic crystal structure prediction (CSP). Here, a data-efficient ML approach would be highly desirable, since screening a huge space of possible polymorphs in a narrow energy range requires the assessment of a large number of trial structures with high accuracy. In this contribution, we present tailored Δ-ML models that allow screening a wide range of crystal candidates while adequately describing the subtle interplay between intermolecular interactions such as H-bonding and many-body dispersion effects. This is achieved by enhancing a physics-based description of long-range interactions at the density functional tight binding (DFTB) level-for which an efficient implementation is available-with a short-range ML model trained on high-quality first-principles reference data. The presented workflow is broadly applicable to different molecular materials, without the need for a single periodic calculation at the reference level of theory. We show that this even allows the use of wavefunction methods in CSP.

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.

Statistical Mechanical Approximations to More Efficiently Determine Polymorph Free Energy Differences for Small Organic Molecules

Methods to efficiently determine the relative stability of polymorphs of organic crystals are highly desired in crystal structure predictions (CSPs). Current methodologies include calculating the free energy of static lattice phonons, quasi-harmonic approximations (QHA), and computing the full thermodynamic cycle using replica exchange molecular dynamics (REMD). We found that 13 out of the 29 systems minimized from experimental crystal structures restructured to a lower energy minimum when heated and annealed using REMD, a phenomenon that QHA alone cannot capture. Here, we present a series of methods that are intermediate in accuracy and expense between QHA and computing the full thermodynamic cycle, which can save 42-80% of the computational cost and introduces, on this benchmark, a relatively small (0.16 ± 0.04 kcal/mol) error relative to the full thermodynamic cycle. In particular, a method that Boltzmann weights harmonic free energies from along the trajectory of REMD replica exchange appears to be an appropriate intermediate between QHA and the full thermodynamic cycle using MD when screening crystal polymorph stability.

Minimizing Polymorphic Risk through Cooperative Computational and Experimental Exploration

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

Multifidelity Statistical Machine Learning for Molecular Crystal Structure Prediction

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

Encapsulated Nanodroplet Crystallization of Organic-Soluble Small Molecules

Single-crystal X-ray diffraction analysis (SCXRD) constitutes a universal approach for the elucidation of molecular structure and the study of crystalline forms. However, the discovery of viable crystallization conditions remains both experimentally challenging and resource intensive in both time and the quantity of analyte(s). We report a robot-assisted, high-throughput method for the crystallization of organic-soluble small molecules in which we employ only micrograms of analyte per experiment. This allows hundreds of crystallization conditions to be screened in parallel with minimal overall sample requirements. Crystals suitable for SCXRD are grown from nanoliter droplets of a solution of analyte in organic solvent(s), each of which is encapsulated within an inert oil to control the rate of solvent loss. This encapsulated nanodroplet crystallization methodology can also be used to search for new crystal forms, as exemplified through both our discovery of a new (13^th) polymorph of the olanzapine precursor ROY and SCXRD analysis of the “uncrystallizable” agrochemical dithianon.

•

Single crystals of small molecules are grown from nanoscale droplets of organic solvent

•

Discovery of the 13^th polymorph (R18) of olanzapine precursor ROY

•

X-ray diffraction analysis of “uncrystallizable” agrochemical dithianon

Small molecules can form crystalline solids, in which individual molecules pack together into ordered three-dimensional arrays. Once a suitable crystal is grown, the packing and atomic connectivity of the constituent molecules can be studied by X-ray diffraction. However, the discovery of experimental conditions for successful crystal growth is often challenging. We have developed a nanoscale crystallization technique for organic-soluble small molecules by using high-throughput liquid-handling robotics to undertake multiple crystallization experiments simultaneously with minimal sample requirements and high success rates. We showcase our methodology through the crystallization of a diverse set of small molecules, including “uncrystallizables,” combined with structural analysis by X-ray diffraction. We anticipate that this rapid and reliable method for small-molecule crystallization will have far-reaching impact, facilitating academic and industrial research in the molecular sciences.

ROY Reclaims Its Crown: New Ways To Increase Polymorphic Diversity

Chemical compounds that exist in multiple crystalline forms are said to exhibit polymorphism. Polymorphs have the same composition, but their structures and properties can vary markedly. In many fields, conditions for crystallizing compounds of interest are screened exhaustively to generate as many polymorphs as possible, from which the most advantageous form can be selected. We report new ways to search for polymorphs and increase polymorphic diversity, based on crystallization induced by suitably designed mixed-crystal seeds. The potential of the strategy has been demonstrated by using it to produce new polymorphs of the benchmark compound ROY as single crystals structurally characterized by X-ray diffraction. This allows ROY to reclaim its crown as the most polymorphic compound in the Cambridge Structural Database. More generally, the methods promise to become valuable tools for polymorphic screening in all fields where crystalline solids are used.

Overcoming the difficulties of predicting conformational polymorph energetics in molecular crystals via correlated wavefunction methods

Molecular crystal structure prediction is increasingly being applied to study the solid form landscapes of larger, more flexible pharmaceutical molecules. Despite many successes in crystal structure prediction, van der Waals-inclusive density functional theory (DFT) methods exhibit serious failures predicting the polymorph stabilities for a number of systems exhibiting conformational polymorphism, where changes in intramolecular conformation lead to different intermolecular crystal packings. Here, the stabilities of the conformational polymorphs of o-acetamidobenzamide, ROY, and oxalyl dihydrazide are examined in detail. DFT functionals that have previously been very successful in crystal structure prediction perform poorly in all three systems, due primarily to the poor intramolecular conformational energies, but also due to the intermolecular description in oxalyl dihydrazide. In all three cases, a fragment-based dispersion-corrected second-order Møller-Plesset perturbation theory (MP2D) treatment of the crystals overcomes these difficulties and predicts conformational polymorph stabilities in good agreement with experiment. These results highlight the need for methods which go beyond current-generation DFT functionals to make crystal polymorph stability predictions truly reliable.

Charge mobility calculation of organic semiconductors without use of experimental single-crystal data

Prediction of material properties of newly designed molecules is a long-term goal in organic electronics. In general, it is a difficult problem, because the material properties are dominated by the unknown packing structure. We present a practical method to obtain charge transport properties of organic single crystals, without use of experimental single-crystal data. As a demonstration, we employ the promising molecule C10-DNBDT. We succeeded in quantitative evaluation of charge mobility of the single crystal using our quantum wave-packet dynamical simulation method. Here, the single-crystal data is computationally obtained by searching possible packing structures from structural formula of the molecule. We increase accuracy in identifying the actual crystal structure from suggested ones by using not only crystal energy but also similarity between calculated and experimental powder X-ray diffraction patterns. The proposed methodology can be a theoretical design technique for efficiently developing new high-performance organic semiconductors, since it can estimate the charge transport properties at early stage in the process of material development.

Disappearing disorder

Disorder in crystal structures can disappear, depending on the circumstances, as shown by multi-temperature measurements, aspherical-atom refinement and computational analyses.

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

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

Machine-Learned Fragment-Based Energies for Crystal Structure Prediction

Crystal structure prediction involves a search of a complex configurational space for local minima corresponding to stable crystal structures, which can be performed efficiently using atom-atom force fields for the assessment of intermolecular interactions. However, for challenging systems, the limitations in the accuracy of force fields prevent a reliable assessment of the relative thermodynamic stability of potential structures, while the cost of fully quantum mechanical approaches can limit applications of the methods. We present a method to rapidly improve force field lattice energies by correcting two-body interactions with a higher level of theory in a fragment-based approach and predicting these corrections with machine learning. Corrected lattice energies with commonly used density functionals and second order perturbation theory (MP2) all significantly improve the ranking of experimentally known polymorphs where the rigid molecule model is applicable. The relative lattice energies of known polymorphs are also found to systematically improve with the fragment corrections. Predicting two-body interactions with atom-centered symmetry functions in a Gaussian process is found to give highly accurate results using as little as 10-20% of the data for training, reducing the cost of the energy correction by up to an order of magnitude. The machine learning approach opens up the possibility of more widespread use of fragment-based methods in crystal structure prediction, whose increased accuracy at a low computational cost will benefit applications in areas such as polymorph screening and computer-guided materials discovery.