Abstract

This chapter presents a brief discussion regarding the relationship between the symmetry of the electron-pair density and elementary catastrophe unfoldings. Such a link arises naturally within the bonding evolution theory framework by explicitly considering the behavior of the Hessian matrix at potentially degenerate critical points as well as its relative distances around the topological bifurcation. Accumulated evidence concerning rupture/formation of simple bonds along a reaction pathway indicates that cusp catastrophes emerge when high symmetry electron density distributions persist with respect to a plane perpendicular to the forming/breaking sigma bond. However, in the most general cases implying any degree of asymmetry, the fold catastrophe will be the observed signature. This sufficient condition allows predicting the correct unfolding to be assigned in every chemical change involving sigma bonds from visually inspecting the molecular geometry of the case at hand. It seems, therefore, that the assignation of the unfolding describing a key chemical event is not just simply a “technical detail,” as suggested by some reviewers. We emphasize that electron density symmetry properties strongly condition the number of critical points involved in any topographical change and, hence, the degree of the associated unfolding, as straightforwardly derived from the formal basis supporting catastrophe theory within the dynamical system model framework.