Systematic Finite-Temperature Reduction of Crystal Energy Landscapes

Crystal structure prediction (CSP) is the calculation of the crystal structures of solids from first principles. Predicting the crystal structure of a compound, based only on its composition, has been a goal of the physical sciences since the early 1950s. Predicting organic crystal structures is important in academic and industrial science, particularly for pharmaceuticals and pigments, where understanding polymorphism is beneficial. Unfortunately, the crystal structures of molecular substances, particularly organic compounds, are very hard to predict and rank in order of stability. Previous studies have shown that current crystal structure prediction methods tend to overestimate the number of potential polymorphs of organic molecules. Therefore there is need for techniques that can coarsen the landscapes of crystal structures generated by CSP into a smaller set of crystal structures that are persistent, distinct at finite temperatures, and more likely to correspond to real polymorphs.

On the bright side, CSP has evolved over the past decade to the point where the identification of local minima in the rugged potential energy surface associated with the packing of irregularly shaped organic molecules has been established as the standard approach in the field. In fact, applications of the CSP methods based on the estimate of relative lattice energies, here identified by the abbreviation CSP_0, are blossoming within both industry and academia, finding applications in pharmaceutical manufacturing and functional materials design. Nevertheless, CSP_0 techniques only partially capture the physics underlying polymorphism. To this end, the need for an accurate technique has been on the rise. In light of this, University College London researchers: Dr. Nicholas Francia, Dr. Louise S. Price, Professor Sarah L. Price and Dr. Matteo Salvalaglio, in collaboration with Dr. Jonas Nyman at the Eli Lilly and Company introduced and tested a new protocol to tackle the issue of overprediction by using molecular dynamics simulations and enhanced sampling methods. Their work is currently published in the research journal, Crystal Growth & Design.

Their aim was to reduce the overprediction by systematically applying molecular dynamics simulations and biased sampling methods to cluster subsets of structures that could easily interconvert at finite temperature and pressure. In this view, they were able to rationally reduce the number of predicted putative polymorphs in crystal structure prediction (CSP)-generated crystal energy landscapes. In particular, their approach employed an unsupervised clustering approach to analyze independent finite-temperature molecular dynamics trajectories and hence identify a representative structure of each cluster of distinct lattice energy minima that were effectively equivalent at finite temperature and pressure.

The authors reported that when their approach was tested in two small organic molecules exhibiting polymorphism: namely, urea and succinic acid, a reduction in the number of candidates required for evaluation as potential polymorphs was seen. Moreover, they noted that finite-temperature sampling of the density/energy collective variable space starting from crystal structures generated from CSP_0 yielded several examples of crystal supercells that had a structure consistent with the most populated clusters, but incorporating defects.

In summary, the study demonstrated the application of a systematic coarsening approach of CSP_0-generated crystal energy landscapes, based on the application of both unbiased and biased molecular dynamics simulation methods, coupled with the clustering of finite-temperature structures based on probabilistic structural fingerprints. Overall, the researchers presented new method for reducing the number of low energy crystal structures from temperature-free CSP, using molecular dynamics and enhanced sampling techniques, which result in a small number of thermally stable putative polymorphs. In a statement to Advances in Engineering, Dr. Matteo Salvalaglio emphasized that the ideas they reported were general and will provide a useful, physics-based strategy for the systematic reduction of crystal energy landscapes.