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Internet Electronic Journal of Molecular Design - IEJMD, ISSN 1538-6414, CODEN IEJMAT
ABSTRACT - Internet Electron. J. Mol. Des. April 2004, Volume 3, Number 4, 182-188

Topological Aspects Beyond the Hückel Theory
István László
Internet Electron. J. Mol. Des. 2004, 3, 182-188

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Abstract:
Starting from a problem of the density of states of carbon atoms, the extension of Sachs theorem to tight-binding methods, containing atoms of several atomic orbitals, is presented. The concept of topologically determined electronic energy levels will be reviewed. Necessary and sufficient conditions for non-existence of Sachs graphs is given and connection between Sachs graphs and matching problems will be studied. The methods of graph theory and linear algebra are used. It was demonstrated that the topological arrangement of atoms can guarantee the existence of stable electronic energy levels. These levels are stable in the presence of off-diagonal disorder of the Hamiltonian matrix. Graph theoretical methods can be extended beyond the Hückel theory to more sophisticated tight-binding methods.

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