Frank J. J. Leusen

Significant progress in predicting the crystal structures of small organic molecules – a report on the fourth blind test

We report on the organization and outcome of the fourth blind test of crystal structure prediction, an international collaborative project organized to evaluate the present state in computational methods of predicting the crystal structures of small organic molecules. There were 14 research groups which took part, using a variety of methods to generate and rank the most likely crystal structures for four target systems: three single-component crystal structures and a 1:1 cocrystal. Participants were challenged to predict the crystal structures of the four systems, given only their molecular diagrams, while the recently determined but as-yet unpublished crystal structures were withheld by an independent referee. Three predictions were allowed for each system. The results demonstrate a dramatic improvement in rates of success over previous blind tests; in total, there were 13 successful predictions and, for each of the four targets, at least two groups correctly predicted the observed crystal structure. The successes include one participating group who correctly predicted all four crystal structures as their first ranked choice, albeit at a considerable computational expense. The results reflect important improvements in modelling methods and suggest that, at least for the small and fairly rigid types of molecules included in this blind test, such calculations can be constructively applied to help understand crystallization and polymorphism of organic molecules.

Towards crystal structure prediction of complex organic compounds – a report on the fifth blind test

The results of the fifth blind test of crystal structure prediction, which show important success with more challenging large and flexible molecules, are presented and discussed.

A Major Advance in Crystal Structure Prediction

The goal of predicting the crystal structure of an organic molecule from its molecular structure alone is of considerable industrial importance. The task is complicated, owing to the number of degrees of freedom to be explored, the complexities of intermolecular and intramolecular forces, and the difficulty in choosing a suitable computational criterion for identifying those crystal structures favored by nature. The difficulty of the task is clearly demonstrated by the regular “Crystal Structure Prediction Blind Test”, which is organized by the Cambridge Crystallographic Data Centre. A Blind Test has taken place in 1999, 2001, 2004, and recently in 2007. Participants are provided with three or four molecular structures and invited to predict, within six months, up to three crystal structures which they think each compound will adopt. The experimental crystal structures have been determined but are not available until after the participants have supplied their predictions. The limited number of successful predictions reported in the previous Blind Tests reveals just how difficult crystal structure prediction (CSP) can be. “Success” in this context means that the observed, experimental crystal structure is found among the three submitted predictions of a participant. All of the previous successful predictions were based on force-field methods, in which the intermolecular and intramolecular forces are represented by analytical functions. Herein, the successful application of a new CSP approach to all four compounds of the 2007 Blind Test is presented. The four compounds chosen for the 2007 Blind Test are shown in Scheme 1. In essence, two problems need to be addressed in CSP. First, there is the physical problem of accurately describing the relative stabilities of all possible crystal packing alternatives. Second, there is the mathematical problem of finding all low-lying minima on the lattice energy hypersurface, a function with many variables, including the unit cell dimensions, the space group, the number of molecules in the asymmetric unit, their conformation(s), and their packing in the crystal lattice. The high number of degrees of freedom results in a complex global optimization problem, for which several solution strategies have been put forward. The central part of the approach used herein is a hybrid method, developed by one of the authors (M.A.N.), for the calculation of lattice energies that combines density functional theory (DFT) simulations using the Vienna Ab initio Simulation Package (VASP) program with an empirical van der Waals (vdW) correction expressed in terms of a sum over isotropic atom–atom pair potentials. As solid-state DFT calculations are time-consuming and cannot be used directly for crystal structure generation, the hybrid method is used for the generation of reference data, from which a tailormade force field (TMFF) is derived for every molecule under consideration. The force field involves atomic point charges calculated from bond increments, isotropic vdW potentials, and covalent bond stretch, angle bend, torsion, and inversion terms. Non-equivalent atoms are attributed different forcefield atom types to allow for maximum customizability. The reference data include the electrostatic potential around the molecule, as well as energies and forces at, and around, local energy minima of densely packed crystal structures and isolated molecules in large simulation boxes. All force-field parameters, in particular bond increments and vdW constants, can be fitted to the reference data simultaneously. It is important that the TMFF provides a sufficiently faithful representation of the hybrid potential-energy surface, both in terms of structure and energetics. Consistency checks that enable this to be verified during the CSP will be described below. The TMFF provides lattice energies and forces to a crystal structure generation engine. The version used for the 2007 Blind Test combines a random structure generation mechanism with an efficient lattice-energy minimizer. Molecular flexibility is treated as an integral part of the crystal structure generation process, and all 230 space groups are considered. Scheme 1. Molecular structures of the 2007 Blind Test compounds. The Roman numerals refer to the numbering scheme used in the Blind Tests. Compound XV is a cocrystal.

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

The results of the sixth blind test of organic crystal structure prediction methods are presented and discussed, highlighting progress for salts, hydrates and bulky flexible molecules, as well as on-going challenges.

Crystal structures of quinacridones

The crystal structure of the αI-phase of quinacridone was determined from non-indexed X-ray powder data by means of crystal structure prediction and subsequent Rietveld refinement. This αI-phase is another polymorph than the α-phase reported by Lincke [G. Lincke and H.-U. Finzel, Cryst. Res. Technol. 1996, 31, 441–452.]. The crystal structures of the β and γ polymorphs were determined from single crystal data. The knowledge of the crystal structures can be used for crystal engineering, i.e., for targeted syntheses of pigments having desired properties, especially for the syntheses of new red pigments.

Modeling the interplay of inter- and intramolecular hydrogen bonding in conformational polymorphs

The predicted stability differences of the conformational polymorphs of oxalyl dihydrazide and ortho-acetamidobenzamide are unrealistically large when the modeling of intermolecular energies is solely based on the isolated-molecule charge density, neglecting charge density polarization. Ab initio calculated crystal electron densities showed qualitative differences depending on the spatial arrangement of molecules in the lattice with the greatest variations observed for polymorphs that differ in the extent of inter- and intramolecular hydrogen bonding. We show that accounting for induction dramatically alters the calculated stability order of the polymorphs and reduces their predicted stability differences to be in better agreement with experiment. Given the challenges in modeling conformational polymorphs with marked differences in hydrogen bonding geometries, we performed an extensive periodic density functional study with a range of exchange-correlation functionals using both atomic and plane wave basis sets. Although such electronic structure methods model the electrostatic and polarization contributions well, the underestimation of dispersion interactions by current exchange-correlation functionals limits their applicability. The use of an empirical dispersion-corrected density functional method consistently reduces the structural deviations between the experimental and energy minimized crystal structures and achieves plausible stability differences. Thus, we have established which types of models may give worthwhile relative energies for crystal structures and other condensed phases of flexible molecules with intra- and intermolecular hydrogen bonding capabilities, advancing the possibility of simulation studies on polymorphic pharmaceuticals.

Revisiting the blind tests in crystal structure prediction: accurate energy ranking of molecular crystals.

In the 2007 blind test of crystal structure prediction hosted by the Cambridge Crystallographic Data Centre (CCDC), a hybrid DFT/MM method correctly ranked each of the four experimental structures as having the lowest lattice energy of all the crystal structures predicted for each molecule. The work presented here further validates this hybrid method by optimizing the crystal structures (experimental and submitted) of the first three CCDC blind tests held in 1999, 2001, and 2004. Except for the crystal structures of compound IX, all structures were reminimized and ranked according to their lattice energies. The hybrid method computes the lattice energy of a crystal structure as the sum of the DFT total energy and a van der Waals (dispersion) energy correction. Considering all four blind tests, the crystal structure with the lowest lattice energy corresponds to the experimentally observed structure for 12 out of 14 molecules. Moreover, good geometrical agreement is observed between the structures determined by the hybrid method and those measured experimentally. In comparison with the correct submissions made by the blind test participants, all hybrid optimized crystal structures (apart from compound II) have the smallest calculated root mean squared deviations from the experimentally observed structures. It is predicted that a new polymorph of compound V exists under pressure.

Towards ab initio screening of co-crystal formation through lattice energy calculations and crystal structure prediction of nicotinamide, isonicotinamide, picolinamide and paracetamol multi-component crystals

Co-crystallisation of a drug with another molecule to form a new crystalline material is an appealing route to enhance physical properties. Despite mounting research effort, there is still considerable uncertainty whether a given co-crystal will form. Previous attempts to use lattice energy calculations to investigate whether a potential co-crystal is thermodynamically more stable than its pure co-former crystals have been inconclusive. In the present study, dispersion-corrected density functional theory is used to minimise the lattice energies of all known co-crystals and salts of nicotinamide, isonicotinamide and picolinamide, and their corresponding neutral co-formers (excluding any organometallic compounds). Out of the resulting 102 co-crystals and salts, 99 (97%) are found to be more stable than their corresponding co-formers. In addition, full crystal structure prediction studies show that two paracetamol co-crystals are very unstable in comparison to their co-formers, thus explaining why these co-crystals have not been observed experimentally. These results demonstrate that a simple yet accurate thermodynamic approach can predict reliably whether a co-crystal can be formed.

Prediction of the mechanical behaviour of crystalline solids.

ABSTRACTPurposeTo explore the use of crystal inter-planar d-spacings and slip-plane interaction energies for predicting and characterising mechanical properties of crystalline solids.MethodsPotential relationships were evaluated between mechanical properties and inter-planar d-spacing, inter-planar interaction energy, and dispersive surface energy as determined using inverse gas chromatography (IGC) for a set of pharmaceutical materials. Inter-planar interaction energies were determined by molecular modelling.ResultsGeneral trends were observed between mechanical properties and the largest inter-planar d-spacing, inter-planar interaction energies, and IGC dispersive surface energy. A number of materials showed significant deviations from general trends. Weak correlations and outliers were rationalised.ConclusionsResults suggest that the highest d-spacing of a material could serve as a first-order indicator for ranking mechanical behaviour of pharmaceutical powders, but with some reservation. Inter-planar interaction energy normalised for surface area shows only a weak link with mechanical properties and does not appear to capture essential physics of deformation. A novel framework linking mechanical properties of crystals to the distinct quantities, slip-plane energy barrier and inter-planar interaction (detachment) energy is proposed.

Influence of Solvent on the Morphology and Subsequent Comminution of Ibuprofen Crystals by Air Jet Milling

Crystal morphology plays an important role in drug processing and delivery, which may be controlled during crystallisation. In this study, ibuprofen particles with different size and morphology were produced by controlled crystallisation in order to evaluate their impact on particle size reduction. Results suggest that the micronisation behaviour of ibuprofen was markedly influenced by the morphology and size of starting materials. It was possible to reduce the size of ibuprofen particles to sizes less than 5 µm during dry milling, which is markedly below the reported brittle-ductile transition size. Results also indicate that the particle size reduction mechanism is influenced by the size and morphology of the starting ibuprofen crystals. Dissolution behaviour of ibuprofen was shown to be influenced by the solid surface chemistry of micronised drug particles. The molecular modelling study provided deeper understanding of the experimental findings observed in this study.