EnGOAT: An Energy–Geometry Analysis Toolkit for Free-Energy Surfaces of Mobile Species in Crystalline Materials

The free-energy surface (FES) of a mobile species in a crystalline host governs its behavior within the material, including properties such as adsorption and transport, but reducing it to quantitative descriptors remains challenging. We present the Energy–GeOmetry Analysis Toolkit (EnGOAT), an open-source framework for the energetic, geometric, and topological analysis of volumetric FES data. Building on the TuTraSt algorithm, EnGOAT partitions the FES into basins and transition states, quantifies their volumes, surface areas, and energy–volume histograms, represents their connectivity as periodic graphs from which minimum-energy pathways and merge trees are obtained, and computes directional self-diffusion coefficients by kinetic Monte Carlo. Because accessibility is defined from energy isosurfaces of the FES rather than from van der Waals radii, the extracted descriptors are probe-specific and reflect the energy landscape actually experienced by the mobile species. Results are stored in a JSON/NumPy data model suited for high-throughput screening and can be explored with a dedicated visualization tool. We demonstrate EnGOAT for CH 4 adsorption in a zeolite and for Li + ion transport in a ceramic electrolyte.