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Internet Electronic Journal of Molecular Design - IEJMD, ISSN 1538-6414, CODEN IEJMAT
ABSTRACT - Internet Electron. J. Mol. Des. July 2006, Volume 5, Number 7, 364-375

The Evolution of the Valence Delta in Molecular Connectivity Theory
Lionello Pogliani
Internet Electron. J. Mol. Des. 2006, 5, 364-375

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Abstract:
The evolution of a fundamental parameter in Kier and Hall molecular connectivity theory, the valence delta δv, is followed from its beginnings till its most recent definitions. This parameter, which was initially based on quantum concepts (atomic number, and valence electrons), is now solely based on concepts belonging to general and complete graphs, like multiple edges, and self-connections of pseudographs, and order and regularity of complete graphs. Furthermore, the hydrogen content of a molecule, which was implied in hydrogen suppressed chemical graphs, is now directly encoded into the valence delta. These two new features of the valence delta allow to graph differentiate among atoms of any type. The model quality of the newly defined valence delta is tested with three properties of three different classes of compounds: side-chain molecular volume, and isoelectric point of amino acids, and boiling points of amines plus boiling points of alcohols. The model of the composite class [amines + alcohols], which seems to behave as a new property underlines the peculiar character of the new valence delta. A new valence delta number, which includes hydrogen perturbation, is defined. The defined hydrogen perturbation makes no use of any new graph concept because it is the ratio between two different valence delta numbers. The ratio is always smaller than one and can be fine-tuned thanks to an exponential parameter. A model of three properties with and without hydrogen perturbation is presented. The model, which is achieved with different values for the exponential parameter, underlines the advantages and characteristics of this kind of perturbation. The hydrogen perturbation throughout the present model study is not only property-dependent, but also N-dependent, i.e., dependent on the number of studied compounds.

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