Modelling temperature-dependent properties of polymorphic organic molecular crystals

We present a large-scale study of the temperature-dependence of structures, free energy differences and properties of polymorphic molecular organic crystals. Lattice-vibrational Gibbs free energy differences between 475 pairs of polymorphs of organic molecular crystals have been calculated at 0 K and at their respective melting points, using a highly accurate anisotropic multipole-based force field and including thermal expansion through the use of a (negative) thermal pressure. Re-ranking of the relative thermodynamic stability of the polymorphs in each pair indicates the possibility of an enantiotropic phase transition between the crystal structures, which occurs in 21% of the studied systems. While vibrational contributions to free energies can have a significant effect on thermodynamic stability, the impact of thermal expansion on polymorph free energy differences is generally very small. We also calculate thermal expansion coefficients for the 864 crystal structures and investigate the temperature-dependence of mechanical properties, and pairwise differences in these properties between polymorphs.

Enhanced NMR Discrimination of Pharmaceutically Relevant Molecular Crystal Forms through Fragment-Based Ab Initio Chemical Shift Predictions

Chemical shift prediction plays an important role in the determination or validation of crystal structures with solid-state nuclear magnetic resonance (NMR) spectroscopy. One of the fundamental theoretical challenges lies in discriminating variations in chemical shifts resulting from different crystallographic environments. Fragment-based electronic structure methods provide an alternative to the widely used plane wave gauge-including projector augmented wave (GIPAW) density functional technique for chemical shift prediction. Fragment methods allow hybrid density functionals to be employed routinely in chemical shift prediction, and we have recently demonstrated appreciable improvements in the accuracy of the predicted shifts when using the hybrid PBE0 functional instead of generalized gradient approximation (GGA) functionals like PBE. Here, we investigate the solid-state ¹³C and ¹⁵N NMR spectra for multiple crystal forms of acetaminophen, phenobarbital, and testosterone. We demonstrate that the use of the hybrid density functional instead of a GGA provides both higher accuracy in the chemical shifts and increased discrimination among the different crystallographic environments. Finally, these results also provide compelling evidence for the transferability of the linear regression parameters mapping predicted chemical shieldings to chemical shifts that were derived in an earlier study.

Pharmaceutical polymorph control in a drug-mimetic supramolecular gel

A supramolecular gel designed to chemically mimic the structure of a pharmaceutical compound controls the polymorphic outcome of the crystallization of the substrate.

We report the synthesis of a bis(urea) gelator designed to specifically mimic the chemical structure of the highly polymorphic drug substance ROY. Crystallization of ROY from toluene gels of this gelator results in the formation of the metastable red form instead of the thermodynamic yellow polymorph. In contrast, all other gels and solution control experiments give the yellow form. Conformational and crystal structure prediction methods have been used to propose the structure of the gel and show that the templation of the red form by the targeted gel results from conformational matching of the gelator to the ROY substrate coupled with overgrowth of ROY onto the local periodic structure of the gel fibres.

An optimized intermolecular force field for hydrogen-bonded organic molecular crystals using atomic multipole electrostatics

We present a re-parameterization of a popular intermolecular force field for describing intermolecular interactions in the organic solid state. Specifically we optimize the performance of the exp-6 force field when used in conjunction with atomic multipole electrostatics. We also parameterize force fields that are optimized for use with multipoles derived from polarized molecular electron densities, to account for induction effects in molecular crystals. Parameterization is performed against a set of 186 experimentally determined, low-temperature crystal structures and 53 measured sublimation enthalpies of hydrogen-bonding organic molecules. The resulting force fields are tested on a validation set of 129 crystal structures and show improved reproduction of the structures and lattice energies of a range of organic molecular crystals compared with the original force field with atomic partial charge electrostatics. Unit-cell dimensions of the validation set are typically reproduced to within 3% with the re-parameterized force fields. Lattice energies, which were all included during parameterization, are systematically underestimated when compared with measured sublimation enthalpies, with mean absolute errors of between 7.4 and 9.0%.

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

The sixth blind test of organic crystal structure prediction (CSP) methods has been held, with five target systems: a small nearly rigid molecule, a polymorphic former drug candidate, a chloride salt hydrate, a co-crystal and a bulky flexible molecule. This blind test has seen substantial growth in the number of participants, with the broad range of prediction methods giving a unique insight into the state of the art in the field. Significant progress has been seen in treating flexible molecules, usage of hierarchical approaches to ranking structures, the application of density-functional approximations, and the establishment of new workflows and `best practices' for performing CSP calculations. All of the targets, apart from a single potentially disordered Z' = 2 polymorph of the drug candidate, were predicted by at least one submission. Despite many remaining challenges, it is clear that CSP methods are becoming more applicable to a wider range of real systems, including salts, hydrates and larger flexible molecules. The results also highlight the potential for CSP calculations to complement and augment experimental studies of organic solid forms.

Benchmark fragment-based (1)H, (13)C, (15)N and (17)O chemical shift predictions in molecular crystals

The performance of fragment-based ab initio(1)H, (13)C, (15)N and (17)O chemical shift predictions is assessed against experimental NMR chemical shift data in four benchmark sets of molecular crystals. Employing a variety of commonly used density functionals (PBE0, B3LYP, TPSSh, OPBE, PBE, TPSS), we explore the relative performance of cluster, two-body fragment, and combined cluster/fragment models. The hybrid density functionals (PBE0, B3LYP and TPSSh) generally out-perform their generalized gradient approximation (GGA)-based counterparts. (1)H, (13)C, (15)N, and (17)O isotropic chemical shifts can be predicted with root-mean-square errors of 0.3, 1.5, 4.2, and 9.8 ppm, respectively, using a computationally inexpensive electrostatically embedded two-body PBE0 fragment model. Oxygen chemical shieldings prove particularly sensitive to local many-body effects, and using a combined cluster/fragment model instead of the simple two-body fragment model decreases the root-mean-square errors to 7.6 ppm. These fragment-based model errors compare favorably with GIPAW PBE ones of 0.4, 2.2, 5.4, and 7.2 ppm for the same (1)H, (13)C, (15)N, and (17)O test sets. Using these benchmark calculations, a set of recommended linear regression parameters for mapping between calculated chemical shieldings and observed chemical shifts are provided and their robustness assessed using statistical cross-validation. We demonstrate the utility of these approaches and the reported scaling parameters on applications to 9-tert-butyl anthracene, several histidine co-crystals, benzoic acid and the C-nitrosoarene SnCl2(CH3)2(NODMA)2.

Rationalization of the Color Properties of Fluorescein in the Solid State: A Combined Computational and Experimental Study

Fluorescein is known to exist in three tautomeric forms defined as quinoid, zwitterionic, and lactoid. In the solid state, the quinoid and zwitterionic forms give rise to red and yellow materials, respectively. The lactoid form has not been crystallized pure, although its cocrystal and solvate forms exhibit colors ranging from yellow to green. An explanation for the observed colors of the crystals is found using a combination of UV/Vis spectroscopy and plane-wave DFT calculations. The role of cocrystal coformers in modifying crystal color is also established. Several new crystal structures are determined using a combination of X-ray and electron diffraction, solid-state NMR spectroscopy, and crystal structure prediction (CSP). The protocol presented herein may be used to predict color properties of materials prior to their synthesis.

Correction: Substituent interference on supramolecular assembly in urea gelators: synthesis, structure prediction and NMR

Correction for 'Substituent interference on supramolecular assembly in urea gelators: synthesis, structure prediction and NMR' by Francesca Piana et al., Soft Matter, 2016, 12, 4034-4043.

Accurate force fields and methods for modelling organic molecular crystals at finite temperatures

We present an assessment of the performance of several force fields for modelling intermolecular interactions in organic molecular crystals using the X23 benchmark set. The performance of the force fields is compared to several popular dispersion corrected density functional methods. In addition, we present our implementation of lattice vibrational free energy calculations in the quasi-harmonic approximation, using several methods to account for phonon dispersion. This allows us to also benchmark the force fields' reproduction of finite temperature crystal structures. The results demonstrate that anisotropic atom-atom multipole-based force fields can be as accurate as several popular DFT-D methods, but have errors 2-3 times larger than the current best DFT-D methods. The largest error in the examined force fields is a systematic underestimation of the (absolute) lattice energy.

Substituent interference on supramolecular assembly in urea gelators: synthesis, structure prediction and NMR

Eighteen N-aryl-N'-alkyl urea gelators were synthesised in order to understand the effect of head substituents on gelation performance. Minimum gelation concentration values obtained from gel formation studies were used to rank the compounds and revealed the remarkable performance of 4-methoxyphenyl urea gelator 15 in comparison to 4-nitrophenyl analogue 14, which could not be simply ascribed to substituent effects on the hydrogen bonding capabilities of the urea protons. Crystal structure prediction calculations indicated alternative low energy hydrogen bonding arrangements between the nitro group and urea protons in gelator 14, which were supported experimentally by NMR spectroscopy. As a consequence, it was possible to relate the observed differences to interference of the head substituents with the urea tape motif, disrupting the order of supramolecular packing. The combination of unbiased structure prediction calculations with NMR is proposed as a powerful approach to investigate the supramolecular arrangement in gel fibres and help understand the relationships between molecular structure and gel formation.

Resorcinol Crystallization from the Melt: A New Ambient Phase and New "Riddles"

Structures of the α and β phases of resorcinol, a major commodity chemical in the pharmaceutical, agrichemical, and polymer industries, were the first polymorphic pair of molecular crystals solved by X-ray analysis. It was recently stated that "no additional phases can be found under atmospheric conditions" (Druzbicki, K. et al. J. Phys. Chem. B 2015, 119, 1681). Herein is described the growth and structure of a new ambient pressure phase, ε, through a combination of optical and X-ray crystallography and by computational crystal structure prediction algorithms. α-Resorcinol has long been a model for mechanistic crystal growth studies from both solution and vapor because prisms extended along the polar axis grow much faster in one direction than in the opposite direction. Research has focused on identifying the absolute sense of the fast direction-the so-called "resorcinol riddle"-with the aim of identifying how solvent controls crystal growth. Here, the growth velocity dissymmetry in the melt is analyzed for the β phase. The ε phase only grows from the melt, concomitant with the β phase, as polycrystalline, radially growing spherulites. If the radii are polar, then the sense of the polar axis is an essential feature of the form. Here, this determination is made for spherulites of β resorcinol (ε, point symmetry 222, does not have a polar axis) with additives that stereoselectively modify growth velocities. Both β and ε have the additional feature that individual radial lamellae may adopt helicoidal morphologies. We correlate the appearance of twisting in β and ε with the symmetry of twist-inducing additives.

Convergence Properties of Crystal Structure Prediction by Quasi-Random Sampling

Generating sets of trial structures that sample the configurational space of crystal packing possibilities is an essential step in the process of ab initio crystal structure prediction (CSP). One effective methodology for performing such a search relies on low-discrepancy, quasi-random sampling, and our implementation of such a search for molecular crystals is described in this paper. Herein we restrict ourselves to rigid organic molecules and, by considering their geometric properties, build trial crystal packings as starting points for local lattice energy minimization. We also describe a method to match instances of the same structure, which we use to measure the convergence of our packing search toward completeness. The use of these tools is demonstrated for a set of molecules with diverse molecular characteristics and as representative of areas of application where CSP has been applied. An important finding is that the lowest energy crystal structures are typically located early and frequently during a quasi-random search of phase space. It is usually the complete sampling of higher energy structures that requires extended sampling. We show how the procedure can first be refined, through targetting the volume of the generated crystal structures, and then extended across a range of space groups to make a full CSP search and locate experimentally observed and lists of hypothetical polymorphs. As the described method has also been created to lie at the base of more involved approaches to CSP, which are being developed within the Global Lattice Energy Explorer (Glee) software, a few of these extensions are briefly discussed.

Modelling of crystal structure of cis-1,2,3,6 and 3,4,5,6-tetrahydrophthalic anhydrides using lattice energy calculations

Lattice energy calculations using a model potential were performed to model the crystal structures of cis-1,2,3,6- and 3,4,5,6-tetrahydrophthalic (THP) anhydrides. The optimized molecular models using the DFT method at the B3LYP/6-31G** level were found consistent with the available experimental evidence and allowed all differences observed in crystal packing between cis-1,2,3,6- and 3,4,5,6-THP anhydrides to be reproduced. Calculations provide evidence for the presence of dipole-dipole C=O⋯C=O intermolecular interactions and support the idea that the molecules distort from their ideal geometries, improving packing in both crystals. The search for minima in the lattice energy of both crystals amongst the more common space groups with Z' = 1, using a simulated annealing crystal structure prediction procedure followed by lattice energy minimization showed that the observed structure of 3,4,5,6-THP anhydride (Z' = 2) is the thermodynamically most stable, and allowed us to justify why 3,4,5,6-THP anhydride crystallizes in such a complex structure with 16 molecules in the unit cell. The computational model was successful in predicting the second observed form at 173 K for cis-1,2,3,6-THP anhydride as a polymorph, and could predict several hypothetical structures with Z' = 1 that appear competitive with the observed structures. The results of phonon estimates of zero point intermolecular vibrational energy and entropy suggest that crystal structures of cis-1,2,3,6-THP anhydride cannot be predicted solely on the basis of lattice energy; factors other than thermodynamics favor the observed structures.

Is the equilibrium composition of mechanochemical reactions predictable using computational chemistry?

The ability of computational methods to predict the structures and energetics that determine the equilibrium of solid state mechanochemical reactions has been assessed. Two previously characterised base-catalysed metathesis reactions between aromatic disulfides are studied using crystal structure prediction methods and lattice energy calculations that combine molecular electronic structure methods with anisotropic atom-atom potentials. We find that lattice energy searches locate three of the six crystal structures as global minima on their respective crystal energy landscapes. The remaining structures are less successfully predicted, due to problems modelling relative conformational energies due to limitations of the density functional theory method for calculating intramolecular energies. Prediction of the overall reaction energies proves challenging for current methods, but the results show promise as a base on which to build more accurate and reliable approaches.

Co-crystallisation of cytosine with 1,10-phenanthroline: computational screening and experimental realisation

Crystal structure prediction calculations applied to co-crystals of 1,10-phenanthroline and nucleobases (A, T, C, G) show that only cytosine is expected to form a 1 : 1 co-crystal. Experiments provide verification for this result although the observed co-crystal crystallises with Z′ = 2, not Z′ = 1.

Static and lattice vibrational energy differences between polymorphs

Lattice energy, entropy and free energy differences for over 500 pairs of known polymorphs are computed and discussed.

Which conformations make stable crystal structures? Mapping crystalline molecular geometries to the conformational energy landscape

Flexible organic molecules often do not adopt their lowest energy conformer in crystal structures. We find that there is a preference for molecules to crystallise with high surface area conformers.

Predicted crystal energy landscapes of porous organic cages

Computational methods predict the crystal packing of porous organic cage molecules, allowing crystal structure and porosity to be predicted starting from the chemical diagram alone.

De novo determination of the crystal structure of a large drug molecule by crystal structure prediction-based powder NMR crystallography

The crystal structure of form 4 of the drug 4-[4-(2-adamantylcarbamoyl)-5-tert-butyl-pyrazol-1-yl]benzoic acid is determined using a protocol for NMR powder crystallography at natural isotopic abundance combining solid-state (1)H NMR spectroscopy, crystal structure prediction, and density functional theory chemical shift calculations. This is the first example of NMR crystal structure determination for a molecular compound of previously unknown structure, and at 422 g/mol this is the largest compound to which this method has been applied so far.