New insights from a bonding evolution theory based on the topological analysis of the electron localization function

This chapter reviews some basic ideas behind the so-called bonding evolution theory (BET) framework, i.e., the combined topological analysis of the electron localization function (ELF) and Thom's catastrophe theory. Discussion is focused on recent applications within the realm of both thermal and photochemically-induced pericyclic reactions. We stress that the correctness of the representation of the local character of the Electron Localization Function (ELF) will depend on correctly identifying the associated elementary catastrophe. This fact demands the ability to identify the control parameters. Hence, we explore the idea of following the evolution of the determinant of the Hessian matrix and the relative mobility of specific critical points as a proper tool for identifying the type of bifurcation catastrophe featuring any chemical bonding event.