Machine learned configurational mappings for free energy estimation between monatomic crystal polymorphs

Predicting the relative stabilities of crystalline polymorphs is crucial to the discovery and design of novel solid phase materials. Modern crystal structure prediction workflows often utilize free energy estimation methods such as the Einstein crystal method to rank crystal stabilities, but such approaches rely on burdensome alchemical transformations. Configurational mappings bypass such transformations, presenting a promising approach for efficiently and rigorously calculating free energy differences among polymorphs. In this work, we propose several data driven mappings between monatomic polymorph ensembles, including a Boltzmann generator inspired normalizing flow and a principal component analysis of harmonic crystal motions. We then apply these mappings to the face centered cubic and hexagonal close packed lattices of Lennard-Jones spheres as a test system, quantifying mapping quality via the statistical uncertainty in free energy estimation. We describe how machine learning mapping approaches to free energy estimation can enable high-throughput in silico characterization of solid-solid phase coexistence.