  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.
