Predicting polymorphism in molecular crystals using orientational entropy

Abstract

We introduce a computational method to discover polymorphs in molecular crystals at finite temperature. The method is based on reproducing the crystallization process starting from the liquid and letting the system discover the relevant polymorphs. This idea, however, conflicts with the fact that crystallization has a time scale much longer than that of molecular simulations. In order to bring the process within affordable simulation time, we enhance the fluctuations of a collective variable by constructing a bias potential with well tempered metadynamics. We use as collective variable an entropy surrogate based on an extended pair correlation function that includes the correlation between the orientation of pairs of molecules. We also propose a similarity metric between configurations based on the extended pair correlation function and a generalized Kullback-Leibler divergence. In this way, we automatically classify the configurations as belonging to a given polymorph using our metric and a hierarchical clustering algorithm. We find all relevant polymorphs for both substances and we predict new polymorphs. One of them is stabilized at finite temperature by entropic effects.Polymorphism is the ability that substances have to crystallize into different structures. A paradigmatic example is carbon that in its two main polymorphs, graphite and diamond, exhibits amazingly different properties. Polymorphism is also important from a practical point of view since controlling which crystal structure forms is of the utmost importance in many manufacturing processes. The pharmaceutical industry suffers in particular the consequences of polymorphism 1,2 . Active pharmaceutical ingredients are usually small, organic molecules that frequently exist in a plethora of crystalline forms. Different polymorphs can be patented separately and usually lead to different drug performances. Therefore a comprehensive screening of polymorphs is crucial to avoid a rival company from releasing to the market the same molecule in a different polymorph 3 , and to anticipate the transformation of one polymorph into another during the manufacturing process or the shelf life 4 .The screening of polymorphs was traditionally performed experimentally in spite of the large costs involved 2 . In the last 15 years the increase in computer power and the development of algorithms able to screen a large number of polymorphs has lead to a very significant successes in polymorph prediction 5-9 . Such methods are based on the search of local minima on the potential energy surface. The minima are ordered by energy and typically corrected for thermal effects using the harmonic approximation. However no method can claim to be able to scan exhaustively all the relevant low-lying minima. In addition, entropic effects beyond the harmonic approximation can be significant. Not only they a) Electronic mail: parrinello@phys.chem.ethz.ch can alter the delicate energetic balance between the different polymorphs but even stabilize structures that are not local minima of t...

Systematic Finite-Temperature Reduction of Crystal Energy Landscapes

“…Several examples of CVs used for this scope can be found in the enhanced sampling literature. 17,19,20,37,38,41,42 In typical WT-metaD performed in this work, the bias potential is updated every 1 ps with Gaussians characterized by an initial height of 2 kJ mol −1 and a width of 20 kg m −3 for the density and 2 kJ mol −1 for the lattice energy. These simulations are performed using GROMACS patched with PLUMED 2.…”

Dynamic simulation of liquid molecular nanoclusters: structure, stability and quantification of internal (pseudo)symmetries

“…The distribution of angles between molecular C-H vectors in chloroform clusters is on the contrary perfectly uniform in distance (ESI, Figure S2). Quantitative treatment of orientation probability densities in bulk systems [22][23][24] could be given for a more detailed discussion of the matter; this would be however outside the scope of the present work. We merely point out that the distribution of inter ring angles in liquid benzene clusters is identical to that of the bulk liquid (ESI, Figure S3).…”

Calculation of phase diagrams in the multithermal-multibaric ensemble

“…During the first stage the possible polymorphs of a system are explored using a crystal structure prediction algorithm (see for instance refs. 11,22,23). Once the polymorphs are known, in a second stage one can tailor the order parameter presented here to target each structure.…”