Linking Electron Density Symmetry and Bond Polarity Through Catastrophe Theory in Bonding Evolution Analysis

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 bond formations and scissions using parametric polynomials derived from catastrophe theory (CT) is critical for gaining further insights into chemical bonding and reactivity. However, most of the applications of BET conduct this association without considering the robust mathematical basis supporting BET. Consequently, misinterpretations and incorrect results have arisen due to the inherent ambiguity of such oversight. The proper use of BET involves calculating the Hessian matrix at potentially degenerate critical points of the electron localization function (ELF) and measuring their relative distances along a reactive coordinate. This methodical approach tailors 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.