Graph-theory approach, chemical bonding

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. 

Graph-Theory derived Approach Ideas derived from topology and graph-theory are used to model the skeleton chemical bonding in clusters. 29-33... 

This article may be found in some way unusual and non-traditional. First, it approaches the problem of aromaticity from the chemical graph theory point of view rather than the traditional approaches based on experimental evidence as the support for the notion of aromaticity and theoretical approaches based on molecular orbital (MO) theory or valence bond (VB) theory. The article challenges non-struc-tural approaches (both experimental and theoretical) as contributing to the confusion rather than clarification of aromaticity. The presentation is focused on the aromaticity of benzenoid and non-benzenoid hydrocarbons, almost ignoring 99% or more of the chemistry involving heteroatoms. 

In trying to clarify the notion of aromaticity, one confronts several dilemmas. Should aromaticity be a qualitative concept or quantitative Should aromaticity be characterized by structural attributes or by molecular properties Is the valence bond approach or molecular orbital theory more suitable for definition of aromaticity Could chemical graph theory offer better insights into aromaticity than the traditional quantum chemical approaches We will address these dilemmas in the following sections. 

The first question was answered by Network Thermodynamics (e.g. Oster et al., 1973 Schnakenberg, 1977 Peusner, 1985) adopting the bond graph technique. This approach benefits from the formal correspondence between certain interpretations of nonequilibrium thermodynamics and of electrical network theory. Adopting the notions of chemical impedance , chemical capacity and chemical inductance , chemical reactions as well transport processes can be represented by networks obeying KirchhofFs current and voltage laws. 

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