Chemical graph concept

A key concept in the assessment of molecular similarity based on chemical graphs is that of a maximum common substructure, MCS(G,GJ), of two chem-... 

The chapter is divided into the following sections. First, a brief introduction to group contribution methods is given with a major emphasis on the concept and limitations of this technique. An introduction to the use of chemical graph theory and how it applies to polymers and in particular to the dielectric constant is given next. Application of the method to a number of polyimides is then demonstrated and predictions are compared to experimental results. 

In this review we discuss the scaling properties of topological invariants and the relations between them. First, we recall the basic concepts of the chemical graph theory. Then, we introduce reduced topological invariants and discuss the problem of size extensivity. Following a brief overview of the known approximate relations between topological invariants, we move to considerations of their scaling properties. Finally, we discuss some practical aspects of the present formalism. 

Individual formal valence structures of conjugated hydrocarbons are excellent substrates for research in chemical graph theory, whereby many of the concepts of discrete mathematics and combinatorics may be applied to chemical problems. The lecture note published by Cyvin and Gutman (Cy-vin, Gutman 1988)) outlines the main features of this type of research mostly from enumeration viewpoint. In addition to their combinatorial properties, chemists were also interested in relative importance of Kekule valence-bond structures of benzenoid hydrocarbons. In fact, as early as 1973, Graovac et al. (1973) published their Kekule index, which seems to be one of the earliest results on the ordering of Kekule structures These authors used ideas from molecular orbital theory to calculate their indices... 

The search for pairs of graphs having the same molecular ID number or molecular prime number ID can be viewed as an illnstration of experimental mathematics or, if you wish, experimental chemical graph theory. The concept of molecular ID numbers has been extended later to cover rings [81] and alternative ID numbers were considered [82]. The examination of the discrimination power of molecular identification numbers has been very recently revisited [83-86], clearly indicating that this topic has not yet been completely explored. New indices have outperformed earlier ones and show limits of classical measnres, such as the Balaban index /. 

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. 

Table 53. Concepts of Interest in Chemistry Developed within Chemical Graph Theory, As Well as Concepts Evolving from Early Quantum Chemistry and Which Are of Graph Theoretical Nature...

Chemical graph theory is bound to remain terra incognita for some, who will, undoubtedly, continue to be hostile toward chemical graph theory, curse it, and find it faulty, rather than becoming acquainted with the basic concepts of the field in which they are, at best, novices. One should not underestimate the dangers of the situation in which chemical graph theory found itself, not by its fault. The situation is... 

Not all chemistry textbooks provide a clear description of what stereo- and structural formulas imply. Maybe the concepts of spatial and topological congruence of graphs could contribute to the clarification of the chemical terminology. 

For a better understanding of this type of flame occurrence and for more explicit conditions that define each of these turbulent flame types, it is necessary to introduce the flame stretch concept. This will be done shortly, at which time the regions will be more clearly defined with respect to chemical and flow rates with a graph that relates the nondimensional turbulent intensity, Reynolds numbers, Damkohler number, and characteristic lengths /. 

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. 

---