Bonding Evolution Theory in Ground and Electronically Excited States: Mathematical Foundations and Consequences for Understanding Reactivity

This review analyses the chemical bonding and reactivity implications of recent findings concerning the rigorous application of the bonding evolution theory (BET) to describe electron rearrangements in cycloaddition reactions in the ground and electronically excited states. Computational evidence shows that characterizing formations and scissions of chemical bonds through parametric polynomials derived from catastrophe theory (CT) is critical to gaining further insights into chemical bonding and reactivity. However, most of the insofar application of BET conducts this association without considering the robust mathematical basis supporting BET. Consequently, misinterpretations and incorrect results have arisen because of the inherent ambiguity of such an oversight. The proper utilization of BET involves the calculation of the Hessian matrix at potentially degenerate critical points of the electron localization function (ELF) and measuring their relative distance along a reactive coordinate. This methodical approach is tailored to incorporate key CT concepts into the original BET framework, thereby recovering the rigor of the latter. The systematic application of these steps has led to various unexpected outcomes, including the correlation between electron density symmetry and CT’s polynomials, the interplay between these polynomials and the heterolytic/homolytic character of bond breakages, and a CT-based model for scaling bond polarity. These discoveries underscore the relevance of adhering to concepts and highlight that rationalizing electron reorganizations using CT’s functions is far from a technical subtlety.