Data-Driven Approach to Derive Polymorph-Specific Order Parameters for Crystal Nucleation

Abstract

The formation of stable crystals from a metastable solution, known as crystal nucleation, which plays a vital role in the pharmaceutical, chemical, and food processing industries. The outcome of the nucleation process is influenced by factors such as temperature, solute concentration, additives, and solvent. Different molecular arrangements lead to the formation of crystal polymorphs with distinct properties. Producing the correct polymorph is essential for use in the pharmaceutical industry. Since nucleation is an activated process, overcoming free-energy barriers in brute-force molecular dynamics (MD) simulations is infeasible except at very high supersaturations. Several methods were developed to address the time-scale issue, such as enhanced and path-sampling methods. However, these methods heavily rely on the choice of order parameters (OPs). Classical OPs, such as Steinhardt’s, work well for atomic systems and simple molecules.[1] However, they fail to distinguish the crystal polymorphs comprised of flexible molecules.[2] Modified bond-orientational OPs and quaternions have been used for systems like glycine[3] and urea [4], but they remain system-specific. In this regard, we propose to use a machine learning approach to develop OPs that can not only distinguish the crystal from the solution phase but also distinguish among competing polymorphs. Initially, we worked with simple systems such as LJ and water to validate our approach. Then we extended our approach to complex molecules like orcinol, which exhibit the full range of polymorphic behavior one can expect in molecular crystals, making it ideal for such an investigation. We have considered two anhydrous forms of orcinol crystals along with the melt for our analysis. In this regard, we worked with both supervised and unsupervised learning to derive OPs for crystal polymorphs. This data-driven approach to predict accurate OPs will certainly help the crystal nucleation community to gain better insights into the nucleation process.