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., C<sub>4</sub>H<sub>6</sub> + C<sub>2</sub>H<sub>4 </sub>: 1–7– [FF]F[F<sup>†</sup>F<sup>†</sup>][F<sup>†</sup>F<sup>†</sup>][FF]F<sup>†</sup>–0 : C<sub>6</sub>H<sub>10</sub>. 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.

On the Nature of Bonding in the Photochemical Addition of Two Ethylenes: C-C Bond Formation in the Excited State?

“…20,22,23,25,26,30,34 Certainly, a defying quest from the experimental point of view. 18,19,60 Regarding a more subtle formal detail, our findings also confirm recent conclusions that bonding events in asymmetric electronic interactions as the thermal 4s+2s Diels-Alder reaction 44 and the photochemically induced 2s+2s cycloaddition of two ethylenes via MECI can be rationalized in terms of the simplest Thom's universal unfolding. [43][44][45] The most favorable 2s+2s (face to face) reaction mode involving a rhomboidal conical intersection S1/S0 can be represented through the sequence of six abrupt variations in the shape of the electron pair distribution (as characterized by the ELF topology), defining five clear ELF-MG sets of configurations.…”

“…The ELF molecular graphs reveal that the change in ELF topology can formally be associated with two simultaneous changes in the ELF topology, 45 each located in the double CC bonds region. As recently emphasized for the Diels-Alder reaction, 44 the sudden changes in the ELF topology can be here also precisely associated to the simplest elementary Thom's universal unfolding. 42,43,45 Here, simply we establish that the sudden change in the ELF topology is associated to the annihilation of a maximum (a) and a saddle (s) in the C=C bonding region (i.e., a2+s1 in the case of C1C2, and a2+s4 in the case of C3C4) as revealed in Figure 1.…”

“…Our groups are currently working to determine if the observed features constitute a general signature in the realm of pericyclic reactions. 44,50,52…”

“…The identification of the bond breaking/bond formation events along the path was carried out following the analysis of the determinant of the Hessian, as recently discussed. 44 The ELF function was calculated based on the first-order density matrix obtained from MC-SCF calculations, using the expression recently derived within the TD-DFT approach. 50…”

“…In particular, key bonding events (e.g., bond formation and bond-breaking), as well as the electron rearrangement along any chemical reaction, can be suitably represented by a sequence of ELF-based molecular configurations (ELF-MG) separated by abrupt changes in the shape of electron pair delocalization. 39,[42][43][44] In this work, we…”