Within the BET framework, a reaction becomes modeled as a gradient dynamical system, with the electron localization function (ELF) serving as the time-independent "potential function". ELF acts as a quantum probe for visualizing the Pauli exclusion principle. It is well known that ELF maxima correlate with predictions from the valence-shell electron pair repulsion theory (VSEPR), providing thus a solid connection to Lewis bonding ideas in terms of valence, bonds, core, and lone pairs concepts. The topographical analysis of ELF is independent of the theoretical level of theory, and indeed, such a function has also been approximately obtained from electron densities derived from X-ray diffraction data. The BET approach enables us to identify distinct, neighboring structural stability domains (SSDs), each featuring a unique set of nondegenerate critical points. Every SSD can, in principle, be associated with a given bonding state of the evolving system. The abrupt change from one state to another can be traced back to a bifurcation catastrophe in the form of the potential originated by a small change in parameters on which the function depends. Considering Thom's conceptual foundation for these polynomials (unfoldings), it is necessary to highlight that merely counting changes in the number and type of Morse critical points separating adjacent SSDs is insufficient for determining the associated parametric unfolding.