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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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