Marcus A. Neumann

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crystal structures of the four systems, given only their molecular diagrams, while the recently determined but as-yet unpublished crystal structures were withheld by an independent referee.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.

X-Cell: a novel indexing algorithm for routine tasks and difficult cases

X-Cell is a novel indexing algorithm that makes explicit use of systematic absences to search for possible indexing solutions from cells with low numbers of calculated reflections to cells with high numbers of reflections. Space groups with the same pattern of systematic absences are grouped together in powder extinction classes, and for a given peak number range an independent search is carried out in each powder extinction class. The method has the advantage that the correct cell is likely to be found before the rapid increase of possible solutions slows down the search significantly. A successive dichotomy approach is used to establish a complete list of all possible indexing solutions. The dichotomy procedure is combined with a search for the zero-point shift of the diffraction pattern, and impurity peaks can be dealt with by allowing for a user-defined portion of unindexed reflections. To rank indexing solutions with varying numbers of unindexed reflections, a new figure of merit is introduced that takes into account the highest level of agreement typically obtained for completely incorrect unit cells. The indexing of long and flat unit cells is facilitated by the possibility to search for rows or zones in reciprocal space first and then to use the lattice parameters of the dominant row or zone in the unit-cell search. The main advantages of X-Cell are robustness and completeness, as demonstrated by a validation study on a variety of compounds. The dominant phase of phase mixtures can be indexed in the presence of up to 50% of impurity peaks if high-quality synchrotron data are available.

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.

Validation of experimental molecular crystal structures with dispersion-corrected density functional theory calculations

The accuracy of a dispersion-corrected density functional theory method is validated against 241 experimental organic crystal structures from Acta Cryst. Section E.

Tailor-made force fields for crystal-structure prediction.

A general procedure is presented to derive a complete set of force-field parameters for flexible molecules in the crystalline state on a case-by-case basis. The force-field parameters are fitted to the electrostatic potential as well as to accurate energies and forces generated by means of a hybrid method that combines solid-state density functional theory (DFT) calculations with an empirical van der Waals correction. All DFT calculations are carried out with the VASP program. The mathematical structure of the force field, the generation of reference data, the choice of the figure of merit, the optimization algorithm, and the parameter-refinement strategy are discussed in detail. The approach is applied to cyclohexane-1,4-dione, a small flexible ring. The tailor-made force field obtained for cyclohexane-1,4-dione is used to search for low-energy crystal packings in all 230 space groups with one molecule per asymmetric unit, and the most stable crystal structures are reoptimized in a second step with the hybrid method. The experimental crystal structure is found as the most stable predicted crystal structure both with the tailor-made force field and the hybrid method. The same methodology has also been applied successfully to the four compounds of the fourth CCDC blind test on crystal-structure prediction. For the five aforementioned compounds, the root-mean-square deviations between lattice energies calculated with the tailor-made force fields and the hybrid method range from 0.024 to 0.053 kcal/mol per atom around an average value of 0.034 kcal/mol per atom.

Combined crystal structure prediction and high-pressure crystallization in rational pharmaceutical polymorph screening

Organic molecules, such as pharmaceuticals, agro-chemicals and pigments, frequently form several crystal polymorphs with different physicochemical properties. Finding polymorphs has long been a purely experimental game of trial-and-error. Here we utilize in silico polymorph screening in combination with rationally planned crystallization experiments to study the polymorphism of the pharmaceutical compound Dalcetrapib, with 10 torsional degrees of freedom one of the most flexible molecules ever studied computationally. The experimental crystal polymorphs are found at the bottom of the calculated lattice energy landscape, and two predicted structures are identified as candidates for a missing, thermodynamically more stable polymorph. Pressure-dependent stability calculations suggested high pressure as a means to bring these polymorphs into existence. Subsequently, one of them could indeed be crystallized in the 0.02 to 0.50 GPa pressure range and was found to be metastable at ambient pressure, effectively derisking the appearance of a more stable polymorph during late-stage development of Dalcetrapib.

Validation of molecular crystal structures from powder diffraction data with dispersion-corrected density functional theory (DFT-D)

The accuracy of 215 experimental organic crystal structures from powder diffraction data is validated against a dispersion-corrected density functional theory method.

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.