Extending methods for relative stability of polymorphs: A diabat approach
Polymorphs are different crystal structures for the same molecule or compound. Many molecules can crystallize into several different polymorphs, each with different solubility and growth/dissolution kinetics. Polymorphism is especially important in pharmaceuticals
as many drugs are administered as crystalline solids. Relative stability of polymorphs affects solubility which consecutively affects the bioavailability of the solid form. Ab initio calculations typically infer stability from static energy calculations or harmonically
approximate the entropy. Polymorphs of organic molecular crystals may be separated by small free energy differences and hence it is important to account for the entropy exactly. Classical force field based approaches enable complete free energy calculations
with advanced sampling methods. These methods, however, typically use thermodynamic integration and are expensive multi-stage simulations.
We discuss a method to directly yield the polymorph free energy difference in this thesis. The framework combines ideas from the well-established lattice-switch Monte Carlo procedure and relationships that have been previously used in the electron transfer
literature. We demonstrate the applicability of the method by computing Helmholtz free energy differences for the Gaussian core solid using just two unbiased simulations. We generalize the framework to accurately calculate Gibbs free energy differences of arbitrary
triclinic polymorphs. Finally, we extend the method to yield relative stability of organic molecular crystals. We demonstrate the method for benzene polymorphs and all five experimentally reported polymorphs of pharmaceutically relevant carbamazepine.