Topology Meets Reactivity: Rationalizing Electron Rearrangements in Cycloadditions Through Thom’s Polynomials and Bonding Evolution Theory

This mini-review discusses recent advances in the rigorous application of Bonding Evolution Theory (BET) to elucidate electron rearrangements in cycloaddition reactions occurring in both ground and electronically excited states. Computational studies reveal that describing bond formation and cleavage through parametric polynomials derived from the Catastrophe Theory (CT) provides a deeper and more coherent understanding of chemical bonding and reactivity. However, several existing BET applications have adopted CT concepts without fully incorporating the mathematical rigor on which BET is based, resulting in conceptual ambiguities and inaccurate interpretations. A proper implementation of BET requires evaluating the Hessian matrix at potentially degenerate critical points (CPs) of the Electron Localization Function (ELF) and assessing their relative evolution along the reaction coordinate. This systematic protocol integrates key CT principles within BET’s original framework, restoring its formal consistency. The resulting analyses have revealed correlations between electron-density symmetry and CT polynomials, relationships between these polynomials and the homolytic or heterolytic character of bond dissociation, and the development of a CT-based model for scaling bond polarity. These findings demonstrate that incorporating CT-derived functions into BET is not merely a formal refinement but a fundamental step toward achieving a more rigorous and predictive understanding of electron rearrangements in cycloadditions.