Graph theoretic model

More advanced mathematical aspects of the graph-theoretical models for aromaticity are given in other references [36, 48, 49]. Some alternative methods, beyond the scope of this chapter, for the study of aromaticity in deltahedral molecules include tensor surface harmonic theory [51-53] and the topological solutions of non-linear field theory related to the Skyrmions of nuclear physics [54]. 

Kvasnicka, V. and Posplchal, J. (1989) Two metrics for a graph-theoretical model of organic chemistry. J. Math. Chem. 3, 161-191. 

Garbalena, M., and W. C. Herndon, Optimum Graph-Theoretical Models for Enthalpic Properties of Alkanes. J. Chem. Inf. Comput. Sci., 1992 32, 37-42. 

The topic of the present section is a formulation of an alternative graph-theoretical model of synthons [16,24]. Such an approach makes it possible to build-up all concepts and notions of synthon theory [18-22] in a very transparent and easily understandable level. 

It is our particular aim to describe methods that solve these problems and to show how generators such as MOLGEN can help in all of these situations. In order to fulfill this purpose, we first have to describe the mathematical model used. It is basically a graph theoretical model and so we provide a detailed description of molecular graphs first. 

There are phenomena such as mesomerism or resonance that cannot be described in terms of our graph theoretical model of a molecule. The reason is that it is no longer possible to associate a unique and integral multiplicity to a covalent bond in aromatic structures. Instead, we introduce several resonance structures in order to represent aromatic compounds. Such structures are not generally isomorphic in the sense of Definition 1.17. 

We hope that our criticism of the policies of the Journal of Chemical Information and Modeling will not pass unnoticed, and that in the near future, item 5 of the Guidelines to assist prospective journal authors of manuscripts in the field of QSAR/ QSPR analysis will be eliminated so that the Journal of Chemical Information and Modeling will welcome all chemical modeling, including graph theoretical models, of structure-activity relationships. After all. Journal of Chemical Information and Modeling is a journal of the American Chemical Society, not a journal of Corwin Hansch Society, if there is such ... 

We see that by using the graph theoretical model, we can immediately understand, for example, why 2-methylpentane and 3-methylpentane have the same diamagnetic susceptibility, given by A + 5S + C, which is not apparent from the standard quantum chemical approach. For an extension of this approach to heteroatomic compounds, see ref 628. 

It may be of interest that isoconjugate benzenoid hydrocarbons necessarily have the same RE in Herndon s resonance theory VB model as in the conjugated circuits model, but generally they will have different RE in the HMO model and the TRE model, mentioned earlier. This clearly points to not only numerical but also conceptual differences between different graph theoretical models those based on the adjacency matrix (HMO) and that based on Kekule valence structures and conjugated circuits (VB). 

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