Towards a Unified Fold-Cusp Model for Bond Polarity Scaling: Electron Rearrangements in the Pyrolytic Isomerization of Cubane to Cyclooctatetraene

This study meticulously examines the criteria for assigning electron rearrangements along the intrinsic reaction coordinate (IRC) leading to bond formation and breaking processes during the pyrolytic isomerization of cubane (CUB) to 1,3,5,7 cyclooctatetraene (COT) from both thermochemical and bonding perspectives. The computed gas phase activation enthalpies obtained using state-of-the-art DFT functionals strongly align with experimental values. Notably, no cusp-type function was detected in the initial thermal conversion step of CUB to bicyclo[4.2.0]octa 2,4,7 triene ( as evidenced by examining the modulus of the Hessian determinant at all potentially degenerate critical points (CPs) and their relative distances. Contrary to previous reports, all relevant fluxes of the pairing density must be described in terms of fold unfolding. The transannular ring opening in the second step highlights characteristics indicative of a cusp-type catastrophe, facilitating a direct comparison with fold features. This fact underscores the critical role of density symmetry persistence near topographical events in determining the type of bifurcation. A fold cusp unified model for scaling the polarity of chemical bonds is proposed, integrating ubiquitous reaction classes such as isomerization, bimolecular nucleophilic substitution, and cycloaddition. The analysis reveals that bond polarity index (BPI) values within the [0, 10-5] au interval correlate with cusp unfolding, whereas fold spans over a broader [10-3, ∞) au spectrum. These insights emphasize that the cusp polynomial is suitable for describing chemical processes involving symmetric electron density distributions, particularly those involving homolytic bond cleavages; in contrast, fold characterizes most chemical events The elucidated unified model accurately captures the CUB to COT stepwise reaction mechanism, as illustrated by the sequence of catastrophes describing ELF topology changes along the IRC. The rigorous application of BET and identifying unfoldings that describe crucial electron rearrangements are highlighted as essential for understanding and predicting chemical reactivity.