A Seven-Facet Polyhedron Captures the Composition-Only Formation-Energy Landscape of Inorganic Solids

In this talk, we show that the convex hull of formation energies for solid compounds involving elements from hydrogen to uranium admits a remarkably simple description over the 92-dimensional space of chemical compositions, despite the enormous combinatorial complexity of possible atomic structures. By training an interpretable max-affine model directly on near-hull formation energies from the Materials Project density-functional theory database, we find that the hull can be reconstructed to DFT accuracy using a polyhedron with only seven facets.
These facets define seven chemically coherent materials classes, with just seven coefficients per element sufficing to capture the dominant energetic trends across composition space. Remarkably, this compact, composition-only representation generalizes far beyond bulk formation energies. Without retraining or structural input, the same model reproduces trends in DFT-calculated defect formation energies, captures experimentally observed elemental mixing correlations in high-entropy materials, and enables the construction and optimization of Pourbaix diagrams for electrochemical stability.
Together, these results show that many chemical properties governed by energy differences can be expressed as simple linear combinations of a small set of interpretable, element-specific parameters. The result is a bonding-geometry-free thermodynamic framework that unifies stability, defects, mixing, and electrochemistry, and enables rapid, interpretable screening across vast chemical spaces.