Panagiotis G. Karamertzanis

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crystal structures of the four systems, given only their molecular diagrams, while the recently determined but as-yet unpublished crystal structures were withheld by an independent referee.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

Successful prediction of a model pharmaceutical in the fifth blind test of crystal structure prediction

The range of target structures in the fifth international blind test of crystal structure prediction was extended to include a highly flexible molecule, (benzyl-(4-(4-methyl-5-(p-tolylsulfonyl)-1,3-thiazol-2-yl)phenyl)carbamate, as a challenge representative of modern pharmaceuticals. Two of the groups participating in the blind test independently predicted the correct structure. The methods they used are described and contrasted, and the implications of the capability to tackle molecules of this complexity are discussed.

Ab initio crystal structure prediction—I. Rigid molecules

A new methodology for the prediction of molecular crystal structures using only the atomic connectivity of the molecule under consideration is presented. The approach is based on the global minimization of the lattice enthalpy of the crystal. The modeling of the electrostatic interactions is accomplished through a set of distributed charges that are optimally and automatically selected and positioned based on results of quantum mechanical calculations. A four‐step global optimization algorithm is used for the identification of the local minima of the lattice enthalpy surface. A parallelized implementation of the algorithm permits a much more extensive search of the solution space than has hitherto been possible, allowing the identification of crystal structures in less frequently occurring space groups and with more than one molecule in the asymmetric unit. The algorithm has been applied successfully to the prediction of the crystal structures of 3‐aza‐bicyclo(3.3.1)nonane‐2,4‐dione (P21/a, Z′ = 1), allopurinol (P21/c, Z′ = 1), 1,3,4,6,7,9‐hexa‐azacycl(3.3.3)azine (Pbca, Z′ = 2), and triethylenediamine (P63/m, Z′ = 1). In all cases, the experimentally known structure is among the most stable predicted structures, but not necessarily the global minimum.

Efficient Handling of Molecular Flexibility in Lattice Energy Minimization of Organic Crystals

This paper presents a novel algorithm, CrystalOptimizer, for the minimization of the lattice energy of crystals formed by flexible molecules. The algorithm employs isolated-molecule quantum mechanical (QM) calculations of the intramolecular energy and conformation-dependent atomic multipoles in the course of the lattice energy minimization. The algorithm eliminates the need to perform QM calculations at each iteration of the minimization by using Local Approximate Models (LAMs), with a minimal impact on accuracy. Additional computational efficiencies are achieved by storing QM-derived components of the lattice energy model in a database and reusing them in subsequent calculations whenever possible. This makes the approach particularly well suited to applications that involve a sequence of lattice energy evaluations, such as crystal structure prediction. The algorithm is capable of handling efficiently complex systems with considerable conformational flexibility. The paper presents examples of the algorithms application ranging from single-component crystals to cocrystals and salts of flexible molecules with tens of intramolecular degrees of freedom whose optimal values are determined by the interplay of conformational strain and packing forces. For any given molecule, the degree of flexibility to be considered can vary from a few torsional angles to relaxation of the entire set of torsion angles, bond angles, and bond lengths present in the molecule.

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.

Which, if any, hydrates will crystallise? Predicting hydrate formation of two dihydroxybenzoic acids

A study of two dihydroxybenzoic acid isomers shows that computational methods can be used to predict hydrate formation, the compound:water ratio and hydrate crystal structures. The calculations also help identify a novel hydrate found in the solid form screening that validates this study.

Computer-aided molecular design of solvents for accelerated reaction kinetics.

Solvents can significantly alter the rates and selectivity of liquid-phase organic reactions, often hindering the development of new synthetic routes or, if chosen wisely, facilitating routes by improving rates and selectivities. To address this challenge, a systematic methodology is proposed that quickly identifies improved reaction solvents by combining quantum mechanical computations of the reaction rate constant in a few solvents with a computer-aided molecular design (CAMD) procedure. The approach allows the identification of a high-performance solvent within a very large set of possible molecules. The validity of our CAMD approach is demonstrated through application to a classical nucleophilic substitution reaction for the study of solvent effects, the Menschutkin reaction. The results were validated successfully by in situ kinetic experiments. A space of 1,341 solvents was explored in silico, but required quantum-mechanical calculations of the rate constant in only nine solvents, and uncovered a solvent that increases the rate constant by 40%.

The thermal stability of lattice-energy minima of 5-fluorouracil: Metadynamics as an aid to polymorph prediction

This paper reports a novel methodology for the free-energy minimization of crystal structures exhibiting strong, anisotropic interactions due to hydrogen bonding. The geometry of the thermally expanded cell was calculated by exploiting the dependence of the free-energy derivatives with respect to cell lengths and angles on the average pressure tensor computed in short molecular dynamics simulations. All dynamic simulations were performed with an elaborate anisotropic potential based on a distributed multipole analysis of the isolated molecule charge density. Changes in structure were monitored via simulated X-ray diffraction patterns. The methodology was used to minimize the free energy at ambient conditions of a set of experimental and hypothetical 5-fluorouracil crystal structures, generated in a search for lattice-energy minima with the same model potential. Our results demonstrate that the majority ( approximately 75%) of lattice-energy minima are thermally stable at ambient conditions, and hence, the free-energy (like the lattice-energy) surface is complex and highly undulating. Metadynamics trajectories (Laio, A.; Parrinello, M. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 12562) started from the free-energy minima only produced transitions that preserved the hydrogen-bonding motif, and thus, further developments are needed for this method to efficiently explore such free-energy surfaces. The existence of so many free-energy minima, with large barriers for the alteration of the hydrogen-bonding motif, is consistent with the range of motifs observed in crystal structures of 5-fluorouracil and other 5-substituted uracils.

Is the Induction Energy Important for Modeling Organic Crystals

We compare two methods for estimating the induction energy in organic molecular crystals by approximating the charge density polarization in the crystalline state. The first is a distributed atomic polarizability model combined with distributed multipole moments, derived from ab initio monomer properties. The second uses an ab initio calculation of the molecular charge density in a point-charge field. Various parameters of the models, such as the rank of polarizability model, effect of self-consistent iterations, and damping, are investigated. The methods are applied to a range of observed and predicted crystal structures of three particularly challenging molecules, namely oxalyl dihydrazide, 3-azabicyclo[3,3,1]nonane-2,4-dione, and carbamazepine, as well as demonstrating the importance of induction in the naphthalene crystal. The two models agree well considering the different approximations made, and it is shown that the induction energy can be an important discriminator in the relative lattice energies of structures with substantially different hydrogen-bonding motifs.