Topology, Molecular Simulation, and Machine Learning as Routes to Exploring Structure and Phase Behavior in Molecular and Atomic Crystals

Crystallization conditions can influence polymorph selection, making an experimentally driven hunt for polymorphs difficult. Such efforts are further complicated when polymorphs initially obtained under a particular experimental protocol “disappear” in favor of another polymorph in subsequent repetitions of the experiment. Consequently, theory and computation can potentially play a vital role in mapping the landscape of crystal polymorphism. Traditional crystal structure prediction methods face their own challenges, and therefore, new approaches are needed. In this talk, I will show, by leveraging concepts from mathematics, specifically geometry and topology, and statistical mechanics in combination with techniques of molecular simulation, traditional methods, and machine learning, that a new paradigm in crystal structure prediction may be emerging. Examples demonstrating prediction of structures of crystals, co-crystals, and phase transitions will be presented.