Topology, Molecular Simulation, and Machine Learning as Routes to Predicting Structure and Phase Behavior in Molecular Crystals*

The different solid structures or polymorphs of atomic and molecular crystals often possess different physical and chemical properties.  Structural differences between organic molecular crystal polymorphs can affect, for example, bioavailability of active pharmaceutical formulations, the lethality of contact insecticides, and diffusive behavior in host-guest systems.  In metallic crystals, structural differences may determine how different phases may be used in electronic device applications.  Crystallization conditions can influence polymorph selection, making an experimentally driven hunt for polymorphs difficult.  These 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.  Theory and computation can potentially play a vital role in mapping the landscape of crystal polymorphism.  Traditional methods for predicting crystal structures and investigating solid-solid phase transformation behavior 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 classical and quantum statistical mechanics in combination with techniques of molecular simulation, and machine learning, that new paradigms are emerging in our ability to predict molecular crystal structures and determine kinetics of polymorphic phase transformations and guest-molecule diffusion.