Machine learning the quantum topology of chemical bonds

Chemical bonding can be characterized within quantum chemical topology (QCT), which provides a real-space description via the topological analysis of the electron density and the electron localization function (ELF). While QCT has traditionally been applied on a molecule-by-molecule basis, recent advances in machine learning (ML) and the availability of large quantum chemical datasets now enable bonding analysis at scale. Here, we integrate ELF-based topological descriptors with ML to establish a data-driven framework for mapping chemical bonding across the QM9 dataset. Wavefunctions computed at the B3LYP/6-31G(2df,p) level were used to extract ELF basin populations, which were paired with geometric and bonding descriptors to construct a bond-level dataset. Statistical analysis revealed relationships between ELF populations, bond lengths, and local chemical environments. Regression models were trained to predict ELF electron populations directly from molecular geometry. The best performance was obtained when local environmental descriptors were included, reducing the prediction error by a factor of two relative to models using only the bond type and bond length. These results demonstrate that real-space bonding parameters, such as bond electron populations, can be predicted from simple structural features, enabling scalable and interpretable exploration of chemical bonding across large chemical spaces.