Are There Only Fold Catastrophes in the Diels–Alder Reaction Between Ethylene and 1,3-Butadiene?

Abstract

This work revisits the topological characterization of the Diels-Alder reaction between 1,3-butadiene and ethylene. In contrast to the currently accepted rationalization, we here provide strong evidence in support of a representation in terms of seven structural stability domains separated by a sequence of 10 elementary catastrophes, but all only of the fold type, i.e., C4H6 + C2H4 :[FF]F † -0 : C6H10. Such an unexpected finding provides fundamental new insights opening simplifying perspectives concerning the rationalization of the CC bond formation in pericyclic reactions in terms of the simplest Thom's elementary catastrophe, namely the one-(state) variable, one-(control) parameter function.

Unraveling the Bonding Nature Along the Photochemically Activated Paterno‐Büchi Reaction Mechanism

“…However, this assignation has been uniquely carried out based on the number of attractors and even basins that changed along a reaction path, leading to incorrect classification of catastrophic events and misinterpretations of bonding phenomena. [38] According to our previous investigation, the classification of the catastrophe associated with forming the C2À C3 bond was determined by calculating the determinant of the Hessian matrix, det(H), at a9, a8, and s7* CPs. The value of det H ij À � for a9 and s7* tends to zero when the reacting system approaches the bifurcation point, indicating the degeneration of these CPs into a wandering point.…”

“…More specifically, we appeal to the topology analysis of the electron localization (ELF) function [23,[30][31][32] combined with Thom's catastrophe theory [33] as a theoretical background for elucidating underlying key bonding events. [20,28,[34][35][36][37][38][39] The ELF constitutes a measure of pair localization on the real-space, associated with seminal Lewis-like notions on the chemical bond. Notably, its topology in terms of basins of attractors and critical points provides a piece of valuable information about valence-shell structure representing essential concepts related to chemical thinking.…”

“…[31,[46][47][48][49] Hence, a reaction mechanism can be interpreted as a sequence of electronic rearrangements characterized by ELF topology resulting from different nuclear displacements along of reaction pathway. [26,38,50,51] Within such an approach, those smooth displacements leading to sudden changes on ELF topology are typically associated with bonding changes (i. e., bond breaking/formation and pairing reordering), and indeed, can be adequately characterized via Thom's elementary bifurcation catastrophes. [20,38,50] The outstanding achievement of these ideas is collected in the so-called bonding evolution theory.…”

“…[26,38,50,51] Within such an approach, those smooth displacements leading to sudden changes on ELF topology are typically associated with bonding changes (i. e., bond breaking/formation and pairing reordering), and indeed, can be adequately characterized via Thom's elementary bifurcation catastrophes. [20,38,50] The outstanding achievement of these ideas is collected in the so-called bonding evolution theory. A wide variety of chemical reactions have been studied within this framework [28,[34][35][36]38,39,52,53] allowing us to gain a detailed understanding of the electronic rearrangement featuring a given mechanism.…”

“…[20,38,50] The outstanding achievement of these ideas is collected in the so-called bonding evolution theory. A wide variety of chemical reactions have been studied within this framework [28,[34][35][36]38,39,52,53] allowing us to gain a detailed understanding of the electronic rearrangement featuring a given mechanism.…”