Collective Variables for Conformational Polymorphism in Molecular Crystals

Abstract

Controlling polymorphism in molecular crystals is crucial in the pharmaceutical, dye, and pesticide industries. However, its theoretical description is extremely challenging, due to the associated long time scales (>1 μs). We present an efficient procedure for identifying collective variables that promote transitions between conformational polymorphs in molecular dynamics simulations. It involves applying a simple dimensionality reduction algorithm to data from short (∼ps) simulations of the isolated conformers that correspond to each polymorph. We demonstrate the utility of our method in the challenging case of the important energetic material, CL-20, which has three anhydrous conformational polymorphs at ambient pressure. Using these collective variables in Metadynamics simulations, we observe transitions between all solid polymorphs in the biased trajectories. We reconstruct the free energy surface and identify previously unknown defect and intermediate forms in the transition from one known polymorph to another. Our method provides insights into complex conformational polymorphic transitions of flexible molecular crystals.

Finite temperature string by K-means clustering sampling with order parameters as collective variables for molecular crystals: application to polymorphic transformation between β-CL-20 and ε-CL-20

“…Therefore, a smaller free energy barrier was observed in the Markovian milestoning process than that in the PMF, and as mentioned by Ovchinnikov, 92 Santiso, 23 and He et al , 53 the former was a more accurate representation of the free energy involved in the homogeneous nucleation process. Recently, Elishav et al 96 identified two effective collective variables, the linear combinations of the improper angles between the nitro group and the central molecular cage, by performing a harmonic linear discriminant analysis (HLDA) and MC-HLDA 104,105 on a set of labeled molecular descriptors from well-tempered Metadynamics 106 simulations, and constructed the free energy surface of the conformational polymorphism between β-CL-20 and ε-CL-20. 96 They found that the difference in free energy between β-CL-20 and ε-CL-20 was 4.0 kcal mol −1 , close to our results in this work (∼6.0 kcal mol −1 ).…”

“…Today, in addition to the path-based FTS, many rare event methods have been established to perform the calculations of polymorphic transformation, such as metadynamics, adiabatic free energy dynamics, etc. 96,[107][108][109][110][111][112][113][114][115][116] This will further reveal the essence of polymorphic transformation from various aspects. (1) By using the general average-based sampling, the simulation of the replica in one sampling space covers the adjacent regions along the transition path, and connecting the adjacent points forms an unsmoothed initial string.…”

“…Elishav et al have also found the obvious degree of overlap for the polymorphs of CL-20. 96 The degree of overlap for the distance OPs (y d C ) is more pronounced than that for the bond or relative orientation OPs (y b C or y r C ), and it is the lowest for y b C . Nevertheless, in order to highlight the influence of the distance distribution on the free energy and intermolecular interaction, in this work we mainly chose the distance and bond orientation OPs for the calculations of the free energy and cooperativity effect described below.…”

Application of the method for visualization of noncovalent interactions in conformational polymorphs of four organic acids

“…The phenomenon of polymorphism (Bernstein, 2020;Cruz-Cabeza & Bernstein, 2014;Nangia, 2008;Elishav et al, 2023) is extremely relevant for the development of science and the pharmaceutical industry. On the one hand, the presence of various crystal structures of the same compound allows one to study trends between the crystal structures and their physicochemical properties.…”

Theoretical and computational approaches to study crystal nucleation from solution

“…In two-step processes, a two-dimensional CV space representing the extent of the largest cluster and of the largest ordered domain in the nucleating phase have also emerged as good descriptors of the reaction coordinate [43,46,89,90], which also lend themselves to a theoretical description of two-step nucleation [45]. More recently, the application of Machine Learning methods and the data-driven identification of low-dimensional reaction coordinates for nucleation has emerged as a viable strategy to identify combinations of CVs that enable an effective, low-dimensional description of nucleation processes [43,148,180,181,182], that allows for the application of biased enhanced sampling by driving the polymorph-specific crystal nucleation. [167] The definition of effective CVs for describing and enhancing the sampling of complex nucleation processes in solution also hinges on our ability to define order parameters that can resolve well the atomic environments that are characteristic of specific crystalline structures.…”