Static and lattice vibrational energy differences between polymorphs

A computational study of 1061 experimentally determined crystal structures of 508 polymorphic organic molecules has been performed with state-of-the-art lattice energy minimisation methods, using a hybrid method that combines density functional theory intramolecular energies with an anisotropic atom–atom intermolecular model. Rigid molecule lattice dynamical calculations have also been performed to estimate the vibrational contributions to lattice free energies. Distributions of the differences in lattice energy, free energy, zero point energy, entropy and heat capacity between polymorphs are presented. Polymorphic lattice energy differences are typically very small: over half of polymorph pairs are separated by less than 2 kJ mol?1 and lattice energy differences exceed 7.2 kJ mol?1 in only 5% of cases. Unsurprisingly, vibrational contributions to polymorph free energy differences at ambient conditions are dominated by entropy differences. The distribution of vibrational energy differences is narrower than lattice energy differences, rarely exceeding 2 kJ mol?1. However, these relatively small vibrational free energy contributions are large enough to cause a re-ranking of polymorph stability below, or at, room temperature in 9% of the polymorph pair

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

The ability to anticipate the shape adopted by flexible molecules in the solid state is crucial for engineering and predicting crystal packing and, hence, properties. In this study, the conformations adopted by flexible molecules in their crystal structures are assessed in terms of their relationship to the calculated global conformational landscape. The study quantifies the limits on molecular strain that can be induced by intermolecular interactions in single-component crystal structures of molecules with no intramolecular hydrogen bonding, demonstrating that some molecules are distorted by up to 20 kJ/mol by crystal packing forces. Furthermore, we find that crystallisation often selects high energy conformers, but only when the high energy conformer is more extended than the lower energy options, allowing for greater intermolecular stabilisation. Based on these observations, we propose that the crystallisability of conformers is assessed in terms of their energies and surface areas. We formulate this as a parameterised pseudo-energy related to molecular surface area, which leads to a dramatic improvement in our ability to predict the conformations adopted by molecules in their crystal structure

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

This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by the International Union of Crystallography.We present a re-parameterization of the 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 to 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 parameterisation, are systematically underestimated when compared to measured sublimation enthalpies, with mean absolute errors of between 7.4 and 9.0%.Engineering and Physical Sciences Research Council (Doctoral Training Account studentship

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

We present a re-parameterization of the 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 to 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 parameterisation, are systematically underestimated when compared to measured sublimation enthalpies, with mean absolute errors of between 7.4 and 9.0%

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

Attempts to co-crystallise the nucleobases adenine, thymine, guanine, and cytosine with 1,10-phenanthroline by ball milling and solvent evaporation methods are described. A 1:1 co-crystal of cytosine and 1,10-phenanthroline can be obtained by grinding or by solvent evaporation. The structure contains two crystallographically independent cytosine and two independent 1,10-phenanthroline molecules (Z′ = 2). The cytosine molecules form two similar but crystallographically independent hydrogen-bonded chains, while the 1,10-phenanthroline molecules are arranged in π-stacks. Between the chains of cytosine and the π-stacks exist N-H⋯N and C-H⋯N interactions. Crystal structure prediction (CSP) calculations were applied to all four systems to assess their potential for co-crystallisation as well as the likely structures and intermolecular interactions that could result from co-crystallisation. Calculations on the cytosine system demonstrate that co-crystallisation results in a lower energy than the crystalline forms of the two starting materials, in line with the co-crystal formation observed. For the systems which did not form a co-crystal, CSP was used to explore potential packing arrangements, but found none which were lower in energy than that of the pure crystalline forms. In these cases there is significant disruption to the nucleobase hydrogen bonding between the pure compound and the hypothetical co-crystal. For pure adenine and guanine, the hydrogen-bonded ribbons form sheets which must be broken, whereas for thymine, the lack of hydrogen bond donors does not allow the hydrogen bonding present for pure thymine to be maintained while forming thymine-1,10-phenanthroline hydrogen bonds

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

Attempts to co-crystallise the nucleobases adenine, thymine, guanine, and cytosine with 1,10-phenanthroline by ball milling and solvent evaporation methods are described. A 1 : 1 co-crystal of cytosine and 1,10-phenanthroline can be obtained by grinding or by solvent evaporation. The structure contains two crystallographically independent cytosine and two independent 1,10-phenanthroline molecules (Z? = 2). The cytosine molecules form two similar but crystallographically independent hydrogen-bonded chains, while the 1,10-phenanthroline molecules are arranged in ?-stacks. Between the chains of cytosine and the ?-stacks exist N–H?N and C–H?N interactions. Crystal structure prediction (CSP) calculations were applied to all four systems to assess their potential for co-crystallisation as well as the likely structures and intermolecular interactions that could result from co-crystallisation. Calculations on the cytosine system demonstrate that co-crystallisation results in a lower energy than the crystalline forms of the two starting materials, in line with the co-crystal formation observed. For the systems which did not form a co-crystal, CSP was used to explore potential packing arrangements, but found none which were lower in energy than that of the pure crystalline forms. In these cases there is significant disruption to the nucleobase hydrogen bonding between the pure compound and the hypothetical co-crystal. For pure adenine and guanine, the hydrogen-bonded ribbons form sheets which must be broken, whereas for thymine, the lack of hydrogen bond donors does not allow the hydrogen bonding present for pure thymine to be maintained while forming thymine-1,10-phenanthroline hydrogen bonds

Structure prediction of crystals, surfaces and nanoparticles

We review the current techniques used in the prediction of crystal structures and their surfaces and of the structures of nanoparticles. The main classes of search algorithm and energy function are summarized, and we discuss the growing role of methods based on machine learning. We illustrate the current status of the field with examples taken from metallic, inorganic and organic systems. This article is part of a discussion meeting issue ‘Dynamic in situ microscopy relating structure and function’

Highly unusual triangular crystals of theophylline: The influence of solvent on the growth rates of polar crystal faces

A noteworthy feature of the compound theophylline is that it forms crystals with a triangular habit, an extremely rare phenomenon for an organic molecule. Here, we investigate the formation of these crystals, comprised of the polymorph Form II (Pna21), and demonstrate that the triangles are obtained from solvents which are highly hydrophobic, or which have a hydrogen bond acceptor group and no hydrogen bond donor group. The formation of the triangular crystal habit is rationalized on the basis of the way such solvents interact with the inequivalent (001) and (00-1) polar crystal faces of Form II. Interactions are significantly stronger at one face than the other, inhibiting growth in one direction and limiting crystal growth to a single, triangle shaped, growth sector. This rationalization also enabled interesting surface features observed by atomic force microscopy to be interpreted. Furthermore, we report a second, previously unreported, type of triangular crystal of theophylline for which the angle at the tip of the triangle is obtuse rather than acute. These crystals are proposed, with the aid of transmission electron microscopy and crystal structure prediction, to be a new polymorphic form of theophyllin

Mining predicted crystal structure landscapes with high throughput crystallisation: old molecules, new insights

Organic molecules tend to close pack to form dense structures when they are crystallized from organic solvents. Porous molecular crystals defy this rule: they typically crystallize with lattice solvent in the interconnected pores. However, the design and discovery of such structures is often challenging and time consuming, in part because it is difficult to predict solvent effects on crystallization. Here, we combine crystal structure prediction (CSP) with a high-throughput crystallization screening method to accelerate the discovery of stable hydrogen-bonded frameworks. We exemplify this strategy by finding new phases of two well-studied molecules in a computationally targeted way. Specifically, we find a new porous polymorph of trimesic acid, δ-TMA, that has a guest free hexagonal pore structure, as well as three new solvent-stabilized diamondoid frameworks of adamantane-1,3,5,7-tetracarboxylic acid (ADTA)

Computational modelling of solvent effects in a prolific solvatomorphic porous organic cage

Crystal structure prediction methods can enable the in silico design of functional molecular crystals, but solvent effects can have a major influence on relative lattice energies sometimes thwarting predictions. This is particularly true for porous solids, where solvent included in the pores can have an important energetic contribution. Here we present a Monte Carlo solvent insertion procedure for predicting the solvent filling of porous structures from crystal structure prediction landscapes, tested using a highly solvatomorphic porous organic cage molecule, CC1. We use this method to rationalise the fact that the predicted global energy minimum structure for CC1 is never observed from solvent crystallisation. We also explain the formation of three different solvatomorphs of CC1 from three structurally-similar chlorinated solvents. Calculated solvent stabilisation energies are found to correlate with experimental results from thermogravimetric analysis, suggesting a future computational framework for a priori materials design that includes solvation effects