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Materials design requires systematic and broadly applicable methods to extract structureproperty relationships. In the context of molecules, physics-based representations are key ingredients for the subsequent machine learning of various properties. We focus here on thermodynamic properties of (complex) molecular liquids: establishing links between condensed-phase intermolecular structures and thermodynamic properties. Compared to electronic properties, they pose two challenges: (i) a Boltzmann-ensemble representation and (ii) the relevance of the environment. We address these aspects by adapting the Spectrum of London and Axilrod-Teller-Muto representation (SLATM). Atomic representations describe both covalent and non-covalent interactions, which we sum over all constituents of a molecule. We further ensemble-average the representation to relate it to thermodynamic properties. As an application, we focus here on a challenging biomolecular system: lipid selectivity of small molecules in mitochondrial membranes. We rely on coarse-grained molecular dynamics simulations. Dimensionality reduction of the ensemble SLATM using principal components reveals simple, interpretable relationships between structure and free energy. Our methodology offers a systematic route to connect higher-order intermolecular interactions with thermodynamics.

Molecular design requires systematic and broadly applicable methods to extract structure–property relationships. The focus of this study is on learning thermodynamic properties from molecular-liquid simulations. The methodology relies on an atomic representation originally developed for electronic properties: the Spectrum of London and Axilrod–Teller–Muto representation (SLATM). SLATM’s expansion in one-, two-, and three-body interactions makes it amenable to probing structural ordering in molecular liquids. We show that such representation encodes enough critical information to permit the learning of thermodynamic properties via linear methods. We demonstrate our approach on the preferential insertion of small solute molecules toward cardiolipin membranes and monitor selectivity against a similar lipid. Our analysis reveals simple, interpretable relationships between two- and three-body interactions and selectivity, identifies key interactions to build optimal prototypical solutes, and charts a two-dimensional projection that displays clearly separated basins. The methodology is generally applicable to a variety of thermodynamic properties.

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