ELF Graphs: Beyond Atoms and Bonds for Molecular Property Prediction

Graph neural networks (GNNs) for molecular property prediction typically represent atoms as nodes and bonds as edges. While this atom-bond representation captures molecular connectivity, it does not explicitly represent the electron density and electron pair topology relevant to electronic structure and reactivity. Two molecular graph representations are introduced that are derived directly from Electron Localization Function (ELF) basins. ELF Attractor Graphs (ELF-AG) augment the molecular graph with core, lone-pair, and bonding basin nodes, whereas Basin Message Passing (BMP) removes atom nodes entirely and represents molecules through the topology of their electron pair basins. On a 43K molecule subset of QM9, both representations improve over conventional atom-bond graphs for predicting HOMO, LUMO, and HOMO-LUMO gap. Notably, BMP achieves performance competitive with a QTAIM enriched molecular graph despite using only electronic and no atomic descriptors. On the much smaller MLtox phototoxicity dataset (493 molecules), ELF topology still outperforms atom-bond graph baselines, but the relative behavior of the two representations changes. ELF-AG outperforms BMP, indicating that retaining atom identity can be beneficial for this biological endpoint. Overall, the results indicate that ELF derived graphs provide a physically grounded representation that introduces useful inductive bias even in low data regimes.