Bonding evolution theory

The study of chemical reactions requires the definition of simple concepts associated with the properties ofthe system. Topological approaches of bonding, based on the analysis of the gradient field of well-defined local functions, evaluated from any quantum mechanical method are close to chemists intuition and experience and provide method-independent techniques [4-7]. In this work, we have used the concepts developed in the Bonding Evolution Theory [8] (BET, see Appendix B), applied to the Electron Localization Function (ELF, see Appendix A) [9]. This method has been applied successfully to proton transfer mechanism [10,11] as well as isomerization reaction [12]. The latter approach focuses on the evolution of chemical properties by assuming an isomorphism between chemical structures and the molecular graph defined in Appendix C. 

The Bonding Evolution Theory, briefly presented in Appendix B, provides a description of the bonding features of a system, along with their evolution accompanying a reaction path. It relies on the variation of the ELF topological profile as a function of nuclear coordinates. The ELF makes a partition of the molecular space into open sets having a... 

In the previous equation, the sum runs over all critical points of the gradient dynamical system. In the Bonding Evolution Theory, the critical points form the molecular graph. In this graph, they are represented according to the dimension of their unstable manifold. Thus, critical points of / = 0, are associated with a dot, these with I = 1 are associated with a line, these with / = 2 by faces, and finally these with 7=3 by 3D cages. 

The combined path integral with the non-linear and electronic density aspects fully qualify our analytical results as a reliable framework within which the electronic localization targeting the bonding evolution theory to be further developed. 

A topological study ofthe electron transfer in Li + Clj system and of the three-electron bond created through this transfer has been achieved, based on the topological concepts of Bonding Evolution Theory. Our results suggest that the dual cusp catastrophe characterizes the diabatic surface crossings which are subjacent in the classical adiabatic analysis ofthe overall reaction path. 

Berski S, Andres J, Silvi B, Domingo LR (2006) New findings on the Diels—Alder Reactions. An analysis based on the bonding evolution theory. J Phys Chem A 110 13939-13947... 

Gonzalez-Navarrete P, Sensato F, Andres J, Longo E (2014) Oxygen atom transfer reactions from mimoun complexes to sulfides and sulfoxides. A bonding evolution theory analysis. J Phys Chem A... 

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