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Internet Electronic Journal of Molecular Design - IEJMD, ISSN 1538-6414, CODEN IEJMAT
ABSTRACT - Internet Electron. J. Mol. Des. July 2005, Volume 4, Number 7, 434-490

My Life-Long Journey in Mathematical Chemistry
Danail Bonchev
Internet Electron. J. Mol. Des. 2005, 4, 434-490

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Abstract:
The special issue of the Internet Electron. J. Mol. Des. represented a challenge to summarize the ideas and results, which I regard important in my 35 years research in the area of mathematical chemistry, and to look ahead to the paths mathematical chemistry might follow in the future. The importance of such an analysis stems from the generality of the methods used and their potential for a variety of applications. Topological patterns in molecular structures are identified and characterized quantitatively in four major classes: branching, cyclicity, centrality, and complexity. It is shown that it is through these patterns that topology controls the properties of molecules, polymers, and crystals. The direct relationships derived between the Wiener number, radius of gyration, and viscosity of polymers offer for the first time the chance to experimentally determine a topological index. Information theory was demonstrated as a method capable of capturing the essence of molecular and atomic structure, and to be a tool for investigating structure-property relationships. The predictions of the nuclear binding energies of nuclides of chemical elements 101-108, which we made 25 years ago, were recently confirmed with a relative standard deviation of only 0.1%. The overall connectivity indices and the information index for the vertex degree distribution were shown to be adequate measures of complexity of molecules and biological networks. Also reported are methods for classification, coding, enumeration and complexity assessment of chemical reaction networks. Mathematical chemistry is shown as a powerful tool for characterization of chemical structures with a variety of applications.

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