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

A crystal structure prediction enigma solved: the gallic acid monohydrate system - surprises at 10 K

The seemingly unpredictable structure of gallic acid monohydrate form IV has been investigated using accurate X-ray diffraction measurements at temperatures of 10 and 123 K. The measurements demonstrate that the structure is commensurately modulated at 10 K and disordered at higher temperatures. Aided by charge-density modeling and periodic DFT calculations we show that the disorder gives a substantial stabilization of the structure.

Knowledge-Based Conformer Generation Using the Cambridge Structural Database

Fast generation of plausible molecular conformations is central to molecular modeling. This paper presents an approach to conformer generation that makes extensive use of the information available in the Cambridge Structural Database. By using geometric distributions derived from the Cambridge Structural Database, it is possible to create biologically relevant conformations in the majority of cases analyzed. The paper compares the performance of the approach with previously published evaluations, and presents some cases where the method fails. The method appears to show significantly improved performance in reproduction of the conformations of structures observed in the Cambridge Structural Database and the Protein Data Bank as compared to other published methods of a similar speed.

Supramolecular Organization of Nonstoichiometric Drug Hydrates: Dapsone

The observed moisture- and temperature dependent transformations of the dapsone (4,4'-diaminodiphenyl sulfone, DDS) 0. 33-hydrate were correlated to its structure and the number and strength of the water-DDS intermolecular interactions. A combination of characterization techniques was used, including thermal analysis (hot-stage microscopy, differential scanning calorimetry and thermogravimetric analysis), gravimetric moisture sorption/desorption studies and variable humidity powder X-ray diffraction, along with computational modeling (crystal structure prediction and pair-wise intermolecular energy calculations). Depending on the relative humidity the hydrate contains between 0 and 0.33 molecules of water per molecule DDS. The crystal structure is retained upon dehydration indicating that DDS hydrate shows a non-stoichiometric (de)hydration behavior. Unexpectedly, the water molecules are not located in structural channels but at isolated-sites of the host framework, which is counterintuitively for a hydrate with non-stoichiometric behavior. The water-DDS interactions were estimated to be weaker than water-host interactions that are commonly observed in stoichiometric hydrates and the lattice energies of the isomorphic dehydration product (hydrate structure without water molecules) and (form III) differ only by ~1 kJ mol-1. The computational generation of hypothetical monohydrates confirms that the hydrate with the unusual DDS:water ratio of 3:1 is more stable than a feasible monohydrate structure. Overall, this study highlights that a deeper understanding of the formation of hydrates with non-stoichiometric behavior requires a multidisciplinary approach including suitable experimental and computational methods providing a firm basis for the development and manufacturing of high quality drug products.

Machine learning for the structure-energy-property landscapes of molecular crystals

Molecular crystals play an important role in several fields of science and technology. They frequently crystallize in different polymorphs with substantially different physical properties. To help guide the synthesis of candidate materials, atomic-scale modelling can be used to enumerate the stable polymorphs and to predict their properties, as well as to propose heuristic rules to rationalize the correlations between crystal structure and materials properties. Here we show how a recently-developed machine-learning (ML) framework can be used to achieve inexpensive and accurate predictions of the stability and properties of polymorphs, and a data-driven classification that is less biased and more flexible than typical heuristic rules. We discuss, as examples, the lattice energy and property landscapes of pentacene and two azapentacene isomers that are of interest as organic semiconductor materials. We show that we can estimate force field or DFT lattice energies with sub-kJ mol-1 accuracy, using only a few hundred reference configurations, and reduce by a factor of ten the computational effort needed to predict charge mobility in the crystal structures. The automatic structural classification of the polymorphs reveals a more detailed picture of molecular packing than that provided by conventional heuristics, and helps disentangle the role of hydrogen bonded and π-stacking interactions in determining molecular self-assembly. This observation demonstrates that ML is not just a black-box scheme to interpolate between reference calculations, but can also be used as a tool to gain intuitive insights into structure-property relations in molecular crystal engineering.

Evaluating the Energetic Driving Force for Cocrystal Formation

We present a periodic density functional theory study of the stability of 350 organic cocrystals relative to their pure single-component structures, the largest study of cocrystals yet performed with high-level computational methods. Our calculations demonstrate that cocrystals are on average 8 kJ mol^-1 more stable than their constituent single-component structures and are very rarely (<5% of cases) less stable; cocrystallization is almost always a thermodynamically favorable process. We consider the variation in stability between different categories of systems-hydrogen-bonded, halogen-bonded, and weakly bound cocrystals-finding that, contrary to chemical intuition, the presence of hydrogen or halogen bond interactions is not necessarily a good predictor of stability. Finally, we investigate the correlation of the relative stability with simple chemical descriptors: changes in packing efficiency and hydrogen bond strength. We find some broad qualitative agreement with chemical intuition-more densely packed cocrystals with stronger hydrogen bonding tend to be more stable-but the relationship is weak, suggesting that such simple descriptors do not capture the complex balance of interactions driving cocrystallization. Our conclusions suggest that while cocrystallization is often a thermodynamically favorable process, it remains difficult to formulate general rules to guide synthesis, highlighting the continued importance of high-level computation in predicting and rationalizing such systems.

Fast and accurate quantum Monte Carlo for molecular crystals

Computational approaches based on the fundamental laws of quantum mechanics are now integral to almost all materials design initiatives in academia and industry. If computational materials science is genuinely going to deliver on its promises, then an electronic structure method with consistently high accuracy is urgently needed. We show that, thanks to recent algorithmic advances and the strategy developed in our manuscript, quantum Monte Carlo yields extremely accurate predictions for the lattice energies of materials at a surprisingly modest computational cost. It is thus no longer a technique that requires a world-leading computational facility to obtain meaningful results. While we focus on molecular crystals, the significance of our findings extends to all classes of materials.

Computer simulation plays a central role in modern-day materials science. The utility of a given computational approach depends largely on the balance it provides between accuracy and computational cost. Molecular crystals are a class of materials of great technological importance which are challenging for even the most sophisticated ab initio electronic structure theories to accurately describe. This is partly because they are held together by a balance of weak intermolecular forces but also because the primitive cells of molecular crystals are often substantially larger than those of atomic solids. Here, we demonstrate that diffusion quantum Monte Carlo (DMC) delivers subchemical accuracy for a diverse set of molecular crystals at a surprisingly moderate computational cost. As such, we anticipate that DMC can play an important role in understanding and predicting the properties of a large number of molecular crystals, including those built from relatively large molecules which are far beyond reach of other high-accuracy methods.

Predicting phase behavior of grain boundaries with evolutionary search and machine learning

The study of grain boundary phase transitions is an emerging field until recently dominated by experiments. The major bottleneck in the exploration of this phenomenon with atomistic modeling has been the lack of a robust computational tool that can predict interface structure. Here we develop a computational tool based on evolutionary algorithms that performs efficient grand-canonical grain boundary structure search and we design a clustering analysis that automatically identifies different grain boundary phases. Its application to a model system of symmetric tilt boundaries in Cu uncovers an unexpected rich polymorphism in the grain boundary structures. We find new ground and metastable states by exploring structures with different atomic densities. Our results demonstrate that the grain boundaries within the entire misorientation range have multiple phases and exhibit structural transitions, suggesting that phase behavior of interfaces is likely a general phenomenon.

The atomic structure of grain boundary phases remains unknown and is difficult to investigate experimentally. Here, the authors use an evolutionary algorithm to computationally explore interface structures in higher dimensions and predict low-energy configurations, showing interface phases may be ubiquitous.

A computational exploration of the crystal energy and charge-carrier mobility landscapes of the chiral [6]helicene molecule

The potential of a given π-conjugated organic molecule in an organic semiconductor device is highly dependent on molecular packing, as it strongly influences the charge-carrier mobility of the material. Such solid-state packing is sensitive to subtle differences in their intermolecular interactions and is challenging to predict. Chirality of the organic molecule adds an additional element of complexity to intuitive packing prediction. Here we use crystal structure prediction to explore the lattice-energy landscape of a potential chiral organic semiconductor, [6]helicene. We reproduce the experimentally observed enantiopure crystal structure and explain the absence of an experimentally observed racemate structure. By exploring how the hole and electron-mobility varies across the energy-structure-function landscape for [6]helicene, we find that an energetically favourable and frequently occurring packing motif is particularly promising for electron-mobility, with a highest calculated mobility of 2.9 cm² V^-1 s^-1 (assuming a reorganization energy of 0.46 eV). We also calculate relatively high hole-mobility in some structures, with a highest calculated mobility of 2.0 cm² V^-1 s^-1 found for chains of helicenes packed in a herringbone fashion. Neither the energetically favourable nor high charge-carrier mobility packing motifs are intuitively obvious, and this demonstrates the utility of our approach to computationally explore the energy-structure-function landscape for organic semiconductors. Our work demonstrates a route for the use of computational simulations to aid in the design of new molecules for organic electronics, through the a priori prediction of their likely solid-state form and properties.

Structure and Stability of Molecular Crystals with Many-Body Dispersion-Inclusive Density Functional Tight Binding

Accurate prediction of structure and stability of molecular crystals is crucial in materials science and requires reliable modeling of long-range dispersion interactions. Semiempirical electronic structure methods are computationally more efficient than their ab initio counterparts, allowing structure sampling with significant speedups. We combine the Tkatchenko-Scheffler van der Waals method (TS) and the many-body dispersion method (MBD) with third-order density functional tight-binding (DFTB3) via a charge population-based method. We find an overall good performance for the X23 benchmark database of molecular crystals, despite an underestimation of crystal volume that can be traced to the DFTB parametrization. We achieve accurate lattice energy predictions with DFT+MBD energetics on top of vdW-inclusive DFTB3 structures, resulting in a speedup of up to 3000 times compared with a full DFT treatment. This suggests that vdW-inclusive DFTB3 can serve as a viable structural prescreening tool in crystal structure prediction.

The effect of amino acid backbone length on molecular packing: crystalline tartrates of glycine, β-alanine, γ-aminobutyric acid (GABA) and DL-α-aminobutyric acid (AABA)

We report a novel 1:1 cocrystal of β-alanine with DL-tartaric acid, C₃H₇NO₂·C₄H₆O₆, (II), and three new molecular salts of DL-tartaric acid with β-alanine {3-azaniumylpropanoic acid-3-azaniumylpropanoate DL-tartaric acid-DL-tartrate, [H(C₃H₇NO₂)₂]⁺·[H(C₄H₅O₆)₂]^-, (III)}, γ-aminobutyric acid [3-carboxypropanaminium DL-tartrate, C₄H₁₀NO₂⁺·C₄H₅O₆^-, (IV)] and DL-α-aminobutyric acid {DL-2-azaniumylbutanoic acid-DL-2-azaniumylbutanoate DL-tartaric acid-DL-tartrate, [H(C₄H₉NO₂)₂]⁺·[H(C₄H₅O₆)₂]^-, (V)}. The crystal structures of binary crystals of DL-tartaric acid with glycine, (I), β-alanine, (II) and (III), GABA, (IV), and DL-AABA, (V), have similar molecular packing and crystallographic motifs. The shortest amino acid (i.e. glycine) forms a cocrystal, (I), with DL-tartaric acid, whereas the larger amino acids form molecular salts, viz. (IV) and (V). β-Alanine is the only amino acid capable of forming both a cocrystal [i.e. (II)] and a molecular salt [i.e. (III)] with DL-tartaric acid. The cocrystals of glycine and β-alanine with DL-tartaric acid, i.e. (I) and (II), respectively, contain chains of amino acid zwitterions, similar to the structure of pure glycine. In the structures of the molecular salts of amino acids, the amino acid cations form isolated dimers [of β-alanine in (III), GABA in (IV) and DL-AABA in (V)], which are linked by strong O-H...O hydrogen bonds. Moreover, the three crystal structures comprise different types of dimeric cations, i.e. (A...A)⁺ in (III) and (V), and A⁺...A⁺ in (IV). Molecular salts (IV) and (V) are the first examples of molecular salts of GABA and DL-AABA that contain dimers of amino acid cations. The geometry of each investigated amino acid (except DL-AABA) correlates with the melting point of its mixed crystal.

On-the-Fly Machine Learning of Atomic Potential in Density Functional Theory Structure Optimization

Machine learning (ML) is used to derive local stability information for density functional theory calculations of systems in relation to the recently discovered SnO_{2}(110)-(4×1) reconstruction. The ML model is trained on (structure, total energy) relations collected during global minimum energy search runs with an evolutionary algorithm (EA). While being built, the ML model is used to guide the EA, thereby speeding up the overall rate by which the EA succeeds. Inspection of the local atomic potentials emerging from the model further shows chemically intuitive patterns.

Development of Embedded and Performance of Density Functional Methods for Molecular Crystals

We report an alternative quantum mechanical:quantum mechanical (QM:QM) method to the currently used periodic density functional calculations including dispersion and investigate its performance with respect to main structural and energetic properties of the X23 set of molecular crystals. By setting the goal of reproducing reference periodic BLYP+D3 values and by embedding BLYP+D3 into DFTB, we obtain results similar to those of periodic BLYP+D3-typically within 1-2% in lattice energies and ∼0.4% in cell volumes. The accuracy of this QM:QM method in comparison to DFTB+D and DFT+D for the X23 set of molecular crystals is discussed.

Crystal structure prediction is changing from basic science to applied technology

Prediction of true polymorphs as dynamic ensembles in contrast to hypothetical static crystal structures.

Crystal structure prediction of flexible pharmaceutical-like molecules: density functional tight-binding as an intermediate optimisation method and for free energy estimation

Successful methodologies for theoretical crystal structure prediction (CSP) on flexible pharmaceutical-like organic molecules explore the lattice energy surface to find a set of plausible crystal structures. The initial search stages of CSP studies use relatively simple lattice energy approximations as hundreds of thousands of minima have to be considered. These generated crystal structures often have poor molecular geometries, as well as inaccurate lattice energy rankings, and performing reasonably accurate but computationally affordable optimisations of the crystal structures generated in a search would be highly desirable. Here, we seek to explore whether semi-empirical quantum-mechanical methods can perform this task. We employed the dispersion-corrected tight-binding Hamiltonian (DFTB3-D3) to relax all the inter- and intra-molecular degrees of freedom of several thousands of generated crystal structures of five pharmaceutical-like molecules, saving a large amount of computational effort compared to earlier studies. The computational cost scales better with molecular size and flexibility than other CSP methods, suggesting that it could be extended to even larger and more flexible molecules. On average, this optimisation improved the average reproduction of the eight experimental crystal structures (RMSD15) and experimental conformers (RMSD1) by 4% and 23%, respectively. The intermolecular interactions were then further optimised using distributed multipoles, derived from the molecular wave-functions, to accurately describe the electrostatic components of the intermolecular energies. In all cases, the experimental crystal structures are close to the top of the lattice energy ranking. Phonon calculations on some of the lowest energy structures were also performed with DFTB3-D3 methods to calculate the vibrational component of the Helmholtz free energy, providing further insights into the solid-state behaviour of the target molecules. We conclude that DFTB3-D3 is a cost-effective method for optimising flexible molecules, bridging the gap between the approximate methods used in CSP searches for generating crystal structures and more accurate methods required in the final energy ranking.

A variable-temperature X-ray diffraction and theoretical study of conformational polymorphism in a complex organic molecule (DTC)

Two conformational crystal polymorphs of 3-diethylamino-4-(4-methoxyphenyl)-1,1-dioxo-4H-1λ⁶,2-thiazete-4-carbonitrile (DTC) have been analyzed in the 100 K-room temperature range by single crystal X-ray diffraction and high quality DFT calculations. DTC has strongly polar as well as aliphatic substituents but no hydrogen bonding groups, and thus qualifies as a test molecule for the relative importance of electrostatic vs. dispersion–repulsion terms. The two polymorphs have the same P2₁/n space group and differ by a flipping of the –OCH₃ group, the two conformations being almost equi-energetic and separated by a low barrier. The system is monotropic in the observed temperature range with nearly identical thermal expansion coefficients and energy–temperature slopes, one phase consistently predicted to be more stable in agreement with the relative ease of appearance. Energy decompositions show that the electrostatic term is dominant and stabilizes with decreasing temperature. Dispersion and repulsion show the expected behavior, the former becoming more stabilizing at lower temperature in contrast with increasing repulsion at higher density. Absolute values and trends are very similar in the two phases, explaining the small total energy difference. Geometrical analyses of intermolecular contacts using fingerprint plots, as well as the study of molecular dipole moments as a function of T in the framework of the Quantum Theory of Atoms in Molecules, reveal more details of phase stability.

A small conformational change in the asymmetric unit has a significant effect on how non-covalent interactions determine (i) the crystal packing and (ii) the effect of T on the relative balance of electrostatics and dispersion–repulsions.

Is zeroth order crystal structure prediction (CSP_0) coming to maturity? What should we aim for in an ideal crystal structure prediction code?

Crystal structure prediction based on searching for the global minimum in the lattice energy (CSP_0) is growing in use for guiding the discovery of new materials, for example, new functional materials, new phases of interest to planetary scientists and new polymorphs relevant to pharmaceutical development. This Faraday Discussion can assess the progress of CSP_0 over the range of types of materials to which CSP is currently and could be applied, which depends on our ability to model the variety of interatomic forces in crystals. The basic hypothesis, that the outcome of crystallisation is determined by thermodynamics, needs examining by considering methods of modelling relative thermodynamic stability not only as a function of pressure and temperature, but also of size, solvent and the presence of heterogeneous templates or impurities (CSP_thd). Given that many important materials persist, and indeed may be formed, when they are not the most thermodynamically stable structure, we need to define what would be required of an ideal CSP code (CSP_aim).

Data-driven learning and prediction of inorganic crystal structures

Machine learning-based interatomic potentials, fitting energy landscapes “on the fly”, are emerging and promising tools for crystal structure prediction.

21st century developments in the understanding and control of molecular solids

This highlight article surveys some of the key recent advances in crystallization techniques, polymorphism, co-crystals, amorphous materials and crystal engineering.

Computational and analytical approaches for investigating hydrates: the neat and hydrated solid-state forms of 3-(3-methylimidazolium-1-yl)propanoate

The interconversion pathways and stability ranges of OOCEMIM solid-state forms have been elucidated.

Evolutionary niching in the GAtor genetic algorithm for molecular crystal structure prediction

The effects of evolutionary niching are investigated for the crystal structure prediction of 1,3-dibromo-2-chloro-5-fluorobenzene.

How many ritonavir cases are there still out there?

The number of dormant ritonavir cases is estimated based on 41 commercial pharmaceutical crystal structure prediction studies.

Identifying pragmatic quasi-harmonic electronic structure approaches for modeling molecular crystal thermal expansion

Quasi-harmonic approaches provide an economical route to modeling the temperature dependence of molecular crystal structures and properties. Several studies have demonstrated good performance of these models, at least for rigid molecules, when using fragment-based approaches with correlated wavefunction techniques. Many others have found success employing dispersion-corrected density functional theory (DFT). Here, a hierarchy of models in which the energies, geometries, and phonons are computed either with correlated methods or DFT are examined to identify which combinations produce useful predictions for properties such as the molar volume, enthalpy, and entropy as a function of temperature. The results demonstrate that refining DFT geometries and phonons with single-point energies based on dispersion-corrected second-order Møller-Plesset perturbation theory can provide clear improvements in the molar volumes and enthalpies compared to those obtained from DFT alone. Predicted entropies, which are governed by vibrational contributions, benefit less clearly from the hybrid schemes. Using these hybrid techniques, the room-temperature thermochemistry of acetaminophen (paracetamol) is predicted to address the discrepancy between two experimental sublimation enthalpy measurements.

ROY revisited, again: the eighth solved structure

X-ray powder diffraction and crystal structure prediction algorithms are used in synergy to establish the crystal structure of the eighth polymorph of ROY, form R05.

From serendipity to supramolecular design: assessing the utility of computed crystal form landscapes in inferring the risks of crystal hydration in carboxylic acids

Calculated structural descriptors for predicted anhydrate polymorphs are used to assess the risks of crystal hydration in carboxylic acids.

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

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

First-principles stability ranking of molecular crystal polymorphs with the DFT+MBD approach

The ability to accurately calculate the relative stabilities of numerous polymorphs of a given molecular crystal is crucial for the success of any molecular crystal structure prediction (CSP) approach. We have recently presented a hierarchical CSP procedure based on van-der-Waals-inclusive density functional theory [Hoja et al., 2018, arXiv:1803.07503], which yields excellent stability rankings for molecular crystals involving rigid molecules, salts, co-crystals, and highly polymorphic drug-like molecules. This approach includes many-body dispersion effects, exact exchange, as well as vibrational free energies. Here, we discuss in detail the impact of these effects on the obtained stability rankings. In addition, we assess the impact of the approximations used in our hierarchical procedure. We show that our procedure is generally robust to 1-2 kJ mol-1 for the systems in the latest CSP blind test but vibrational free energies for crystals involving flexible molecules would benefit from directly including many-body dispersion interactions. In addition, we also discuss the effect of temperature on the structure of molecular crystals and a simple but effective method for estimating anharmonic effects.

Crystal structure prediction: reflections on present status and challenges

In these Concluding Remarks, I try to summarize my personal view of the enormous progress made in the field of CSP and the open questions and challenges that keep this field more exciting than ever.

Computational Chemistry: The Fate of Current Methods and Future Challenges

"Where do we go from here?" is the underlying question regarding the future (perhaps foreseeable) developments in computational chemistry. Although this young discipline has already permeated practically all of chemistry, it is likely to become even more powerful with the rapid development of computational hard- and software.

Stochastic Neural Network Approach for Learning High-Dimensional Free Energy Surfaces

The generation of free energy landscapes corresponding to conformational equilibria in complex molecular systems remains a significant computational challenge. Adding to this challenge is the need to represent, store, and manipulate the often high-dimensional surfaces that result from rare-event sampling approaches employed to compute them. In this Letter, we propose the use of artificial neural networks as a solution to these issues. Using specific examples, we discuss network training using enhanced-sampling methods and the use of the networks in the calculation of ensemble averages.

Ab initio random structure searching of organic molecular solids: assessment and validation against experimental data

This paper explores the capability of using the DFT-D ab initio random structure searching (AIRSS) method to generate crystal structures of organic molecular materials, focusing on a system (m-aminobenzoic acid; m-ABA) that is known from experimental studies to exhibit abundant polymorphism. Within the structural constraints selected for the AIRSS calculations (specifically, centrosymmetric structures with Z = 4 for zwitterionic m-ABA molecules), the method is shown to successfully generate the two known polymorphs of m-ABA (form III and form IV) that have these structural features. We highlight various issues that are encountered in comparing crystal structures generated by AIRSS to experimental powder X-ray diffraction (XRD) data and solid-state magic-angle spinning (MAS) NMR data, demonstrating successful fitting for some of the lowest energy structures from the AIRSS calculations against experimental low-temperature powder XRD data for known polymorphs of m-ABA, and showing that comparison of computed and experimental solid-state NMR parameters allows different hydrogen-bonding motifs to be discriminated.

Unraveling Complexity in the Solid Form Screening of a Pharmaceutical Salt: Why so Many Forms? Why so Few?

The solid form landscape of 5-HT2a antagonist 3-(4-(benzo[d]isoxazole-3-yl)piperazin-1-yl)-2,2-dimethylpropanoic acid hydrochloride (B5HCl) proved difficult to establish. Many crystalline materials were produced by solid form screening, but few forms readily grew high quality crystals to afford a clear picture or understanding of the solid form landscape. Careful control of crystallization conditions, a range of experimental methods, computational modeling of solvate structures, and crystal structure prediction were required to see potential arrangements of the salt in its crystal forms. Structural diversity in the solid form landscape of B5HCl was apparent in the layer structures for the anhydrate polymorphs (Forms I and II), dihydrate and a family of solvates with alcohols. The alcohol solvates, which provided a distinct packing from the neat forms and the dihydrate, form layers with conserved hydrogen bonding between B5HCl and the solvent, as well as stacking of the aromatic rings. The ability of the alcohol hydrocarbon moieties to efficiently pack between the layers accounted for the difficulty in growing some solvate crystals and the inability of other solvates to crystallize altogether. Through a combination of experiment and computation, the crystallization problems, form stability, and desolvation pathways of B5HCl have been rationalized at a molecular level.

Exchange-Hole Dipole Dispersion Model for Accurate Energy Ranking in Molecular Crystal Structure Prediction II: Nonplanar Molecules

The crystal structure prediction (CSP) of a given compound from its molecular diagram is a fundamental challenge in computational chemistry with implications in relevant technological fields. A key component of CSP is the method to calculate the lattice energy of a crystal, which allows the ranking of candidate structures. This work is the second part of our investigation to assess the potential of the exchange-hole dipole moment (XDM) dispersion model for crystal structure prediction. In this article, we study the relatively large, nonplanar, mostly flexible molecules in the first five blind tests held by the Cambridge Crystallographic Data Centre. Four of the seven experimental structures are predicted as the energy minimum, and thermal effects are demonstrated to have a large impact on the ranking of at least another compound. As in the first part of this series, delocalization error affects the results for a single crystal (compound X), in this case by detrimentally overstabilizing the π-conjugated conformation of the monomer. Overall, B86bPBE-XDM correctly predicts 16 of the 21 compounds in the five blind tests, a result similar to the one obtained using the best CSP method available to date (dispersion-corrected PW91 by Neumann et al.). Perhaps more importantly, the systems for which B86bPBE-XDM fails to predict the experimental structure as the energy minimum are mostly the same as with Neumann's method, which suggests that similar difficulties (absence of vibrational free energy corrections, delocalization error,...) are not limited to B86bPBE-XDM but affect GGA-based DFT-methods in general. Our work confirms B86bPBE-XDM as an excellent option for crystal energy ranking in CSP and offers a guide to identify crystals (organic salts, conjugated flexible systems) where difficulties may appear.

Use of Crystal Structure Informatics for Defining the Conformational Space Needed for Predicting Crystal Structures of Pharmaceutical Molecules

Determining the range of conformations that a flexible pharmaceutical-like molecule could plausibly adopt in a crystal structure is a key to successful crystal structure prediction (CSP) studies. We aim to use conformational information from the crystal structures in the Cambridge Structural Database (CSD) to facilitate this task. The conformations produced by the CSD Conformer Generator are reduced in number by considering the underlying rotamer distributions, an analysis of changes in molecular shape, and a minimal number of molecular ab initio calculations. This method is tested for five pharmaceutical-like molecules where an extensive CSP study has already been performed. The CSD informatics-derived set of crystal structure searches generates almost all the low-energy crystal structures previously found, including all experimental structures. The workflow effectively combines information on individual torsion angles and then eliminates the combinations that are too high in energy to be found in the solid state, reducing the resources needed to cover the solid-state conformational space of a molecule. This provides insights into how the low-energy solid-state and isolated-molecule conformations are related to the properties of the individual flexible torsion angles.

Theoretical predictions suggest carbon dioxide phases III and VII are identical

Accurate electronic structure calculations for the structures and simulated Raman spectra of high-pressure carbon dioxide suggest phases III and VII are identical, and the phase diagram should be revised.

Solid carbon dioxide exhibits a rich phase diagram at high pressures. Metastable phase III is formed by compressing dry ice above ∼10–12 GPa. Phase VII occurs at similar pressures but higher temperatures, and its stability region is disconnected from III on the phase diagram. Comparison of large-basis-set quasi-harmonic second-order Møller–Plesset perturbation theory calculations and experiment suggests that the long-accepted structure of phase III is problematic. The experimental phase III and VII structures both relax to the same phase VII structure. Furthermore, Raman spectra predicted for phase VII are in good agreement with those observed experimentally for both phase III and VII, while those for the purported phase III structure agree poorly with experimental observations. Crystal structure prediction is employed to search for other potential structures which might account for phase III, but none are found. Together, these results suggest that phases III and VII are likely identical.

Benchmarking Quantum Chemical Methods: Are We Heading in the Right Direction?

Theoreticians and experimentalists should work together more closely to establish reliable rankings and benchmarks for quantum chemical methods. Comparison to carefully designed experimental benchmark data should be a priority. Guidelines to improve the situation for experiments and calculations are proposed.

ζ-Glycine: insight into the mechanism of a polymorphic phase transition

Glycine is the simplest and most polymorphic amino acid, with five phases having been structurally characterized at atmospheric or high pressure. A sixth form, the elusive ζ phase, was discovered over a decade ago as a short-lived intermediate which formed as the high-pressure ∊ phase transformed to the γ form on decompression. However, its structure has remained unsolved. We now report the structure of the ζ phase, which was trapped at 100 K enabling neutron powder diffraction data to be obtained. The structure was solved using the results of a crystal structure prediction procedure based on fully ab initio energy calculations combined with a genetic algorithm for searching phase space. We show that the fate of ζ-glycine depends on its thermal history: although at room temperature it transforms back to the γ phase, warming the sample from 100 K to room temperature yielded β-glycine, the least stable of the known ambient-pressure polymorphs.

Experimental and Computational Hydrate Screening: Cytosine, 5-Flucytosine and Their Solid Solution

The structural, temperature- and moisture dependent stability features of cytosine and 5-flucytosine monohydrates, two pharmaceutically important compounds, were rationalized using complementary experimental and computational approaches. Moisture sorption/desorption, water activity, thermal analysis and calorimetry were applied to determine the stability ranges of hydrate ↔ anhydrate systems, while X-ray diffraction, IR spectroscopy and crystal structure prediction provided the molecular level understanding. At 25 °C, the critical water activity for the cytosine hydrate ↔ anhydrate system is ~0.43 and for 5-flucytosine ~0.41. In 5-flucytosine the water molecules are arranged in open channels, therefore the kinetic desorption data, dehydration < 40% relative humidity (RH), conform with the thermodynamic data, whereas for the cytosine isolated site hydrate dehydration was observed at RH < 15%. Peritectic dissociation temperatures of the hydrates were measured to be 97 °C and 84.2 °C for cytosine and 5-flucytosine, respectively, and the monohydrate to anhydrate transition enthalpies to be around 10 kJ mol-1. Computed crystal energy landscapes not only revealed that the substitution of C5 (H or F) controls the packing and properties of cytosine/5-flucytosine solid forms, but also have enabled the finding of a monohydrate solid solution of the two substances which shows increased thermal- and moisture-dependent stability compared to 5-flucytosine monohydrate.

Pharmaceutical cocrystals, salts and multicomponent systems; intermolecular interactions and property based design

As small molecule drugs become harder to develop and less cost effective for patient use, efficient strategies for their property improvement become increasingly important to global health initiatives. Improvements in the physical properties of Active Pharmaceutical Ingredients (APIs), without changes in the covalent chemistry, have long been possible through the application of binary component solids. This was first achieved through the use of pharmaceutical salts, within the last 10-15years with cocrystals and more recently coamorphous systems have also been consciously applied to this problem. In order to rationally discover the best multicomponent phase for drug development, intermolecular interactions need to be considered at all stages of the process. This review highlights the current thinking in this area and the state of the art in: pharmaceutical multicomponent phase design, the intermolecular interactions in these phases, the implications of these interactions on the material properties and the pharmacokinetics in a patient.

Polymorphic phase transitions: Macroscopic theory and molecular simulation

Transformations in the solid state are of considerable interest, both for fundamental reasons and because they underpin important technological applications. The interest spans a wide spectrum of disciplines and application domains. For pharmaceuticals, a common issue is unexpected polymorphic transformation of the drug or excipient during processing or on storage, which can result in product failure. A more ambitious goal is that of exploiting the advantages of metastable polymorphs (e.g. higher solubility and dissolution rate) while ensuring their stability with respect to solid state transformation. To address these issues and to advance technology, there is an urgent need for significant insights that can only come from a detailed molecular level understanding of the involved processes. Whilst experimental approaches at best yield time- and space-averaged structural information, molecular simulation offers unprecedented, time-resolved molecular-level resolution of the processes taking place. This review aims to provide a comprehensive and critical account of state-of-the-art methods for modelling polymorph stability and transitions between solid phases. This is flanked by revisiting the associated macroscopic theoretical framework for phase transitions, including their classification, proposed molecular mechanisms, and kinetics. The simulation methods are presented in tutorial form, focusing on their application to phase transition phenomena. We describe molecular simulation studies for crystal structure prediction and polymorph screening, phase coexistence and phase diagrams, simulations of crystal-crystal transitions of various types (displacive/martensitic, reconstructive and diffusive), effects of defects, and phase stability and transitions at the nanoscale. Our selection of literature is intended to illustrate significant insights, concepts and understanding, as well as the current scope of using molecular simulations for understanding polymorphic transitions in an accessible way, rather than claiming completeness. With exciting prospects in both simulation methods development and enhancements in computer hardware, we are on the verge of accessing an unprecedented capability for designing and developing dosage forms and drug delivery systems in silico, including tackling challenges in polymorph control on a rational basis.

Structure Prediction for Surface-Induced Phases of Organic Monolayers: Overcoming the Combinatorial Bottleneck

Structure determination and prediction pose a major challenge to computational material science, demanding efficient global structure search techniques tailored to identify promising and relevant candidates. A major bottleneck is the fact that due to the many combinatorial possibilities, there are too many possible geometries to be sampled exhaustively. Here, an innovative computational approach to overcome this problem is presented that explores the potential energy landscape of commensurate organic/inorganic interfaces where the orientation and conformation of the molecules in the tightly packed layer is close to a favorable geometry adopted by isolated molecules on the surface. It is specifically designed to sample the energetically lowest lying structures, including the thermodynamic minimum, in order to survey the particularly rich and intricate polymorphism in such systems. The approach combines a systematic discretization of the configuration space, which leads to a huge reduction of the combinatorial possibilities with an efficient exploration of the potential energy surface inspired by the Basin-Hopping method. Interfacing the algorithm with first-principles calculations, the power and efficiency of this approach is demonstrated for the example of the organic molecule TCNE (tetracyanoethylene) on Au(111). For the pristine metal surface, the global minimum structure is found to be at variance with the geometry found by scanning tunneling microscopy. Rather, our results suggest the presence of surface adatoms or vacancies that are not imaged in the experiment.

Powder diffraction and crystal structure prediction identify four new coumarin polymorphs

Coumarin, a simple, commodity chemical isolated from beans in 1820, has, to date, only yielded one solid state structure. Here, we report a rich polymorphism of coumarin grown from the melt. Four new metastable forms were identified and their crystal structures were solved using a combination of computational crystal structure prediction algorithms and X-ray powder diffraction. With five crystal structures, coumarin has become one of the few rigid molecules showing extensive polymorphism at ambient conditions. We demonstrate the crucial role of advanced electronic structure calculations including many-body dispersion effects for accurate ranking of the stability of coumarin polymorphs and the need to account for anharmonic vibrational contributions to their free energy. As such, coumarin is a model system for studying weak intermolecular interactions, crystallization mechanisms, and kinetic effects.

Charge Transport in Molecular Materials: An Assessment of Computational Methods

The booming field of molecular electronics has fostered a surge of computational research on electronic properties of organic molecular solids. In particular, with respect to a microscopic understanding of transport and loss mechanisms, theoretical studies assume an ever-increasing role. Owing to the tremendous diversity of organic molecular materials, a great number of computational methods have been put forward to suit every possible charge transport regime, material, and need for accuracy. With this review article we aim at providing a compendium of the available methods, their theoretical foundations, and their ranges of validity. We illustrate these through applications found in the literature. The focus is on methods available for organic molecular crystals, but mention is made wherever techniques are suitable for use in other related materials such as disordered or polymeric systems.

31P-dephased, 13C-detected REDOR for NMR crystallography at natural isotopic abundance

Typically, the process of NMR-based structure determination relies on accurately measuring a large number of internuclear distances to serve as restraints for simulated annealing calculations. In solids, the rotational-echo double-resonance (REDOR) experiment is a widely used approach to determine heteronuclear dipolar couplings corresponding to distances usually in the range of 1.5-8Å. A challenge in the interpretation of REDOR data is the degeneracy of symmetric subunits in an oligomer or equivalent molecules in a crystal lattice, which produce REDOR trajectories that depend explicitly on two or more distances instead of one. This degeneracy cannot be overcome by either spin dilution (for molecules containing 31P, 19F and other highly abundant nuclei) or selective pulses (in the case where there is chemical shift degeneracy). For small, crystalline molecules, such as phosphoserine, we demonstrate that as many as five inter-molecular distances must be considered to model 31P-dephased REDOR data accurately. We report excellent agreement between simulation and experiment once lattice couplings, 31P chemical shift anisotropy, and radio-frequency field inhomogeneity are all taken into account. We also discuss the systematic inaccuracies that may result from approximations that consider only the initial slope of the REDOR trajectory and/or that utilize a two- or three-spin system. Furthermore, we demonstrate the applicability of 31P-dephased REDOR for validation or refinement of candidate crystal structures and show that this approach is especially informative for NMR crystallography of 31P-containing molecules.