Towards a unified fold-cusp model for bond polarity scaling: electron rearrangements in the pyrolytic isomerization of cubane to cyclooctatetraene

Abstract

Context

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. 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 (BOT). 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.

Methods

Geometry optimization and frequency calculations were conducted using various DFT functionals. In line with recent findings concerning the rigorous application of BET, the characterization of bond formations and scissions via unfoldings was carried out by carefully monitoring the determinant of the Hessian matrix at all potentially degenerate CPs and their relative distance. The computed gas-phase activation enthalpies strongly align with experimental values, stressing the adequacy of the chosen levels of theory in describing the ELF topography along the IRC. The BPI was determined using the methodology proposed by Allen and collaborators.