Using topology for understanding your computational results

Abstract The integration of quantum theory (QT) into chemistry has significantly enhanced computational accuracy, yet challenges remain in translating quantum mechanical results into intuitive chemical concepts. Traditional atomic and molecular models, while empirically effective, lack direct representation in Hilbert space, leading to ambiguities in chemical interpretation. Here, we present a summary of topological methods as a bridge between QT and chemical reasoning, focusing on the quantum theory of atoms in molecules (QTAIM) and the electron localization function (ELF). These approaches provide rigorous frameworks for defining atomic and bonding regions, enabling additive decompositions of quantum mechanical observables. By analyzing critical points of the electron density and other scalar fields, we demonstrate how the QTAIM and the ELF offer complementary insights into molecular bonding. As a case study, we examine the electronic structure of carbon suboxide (C 3 O 2 ), revealing that a combined QTAIM-ELF approach resolves discrepancies between two bonding descriptions.