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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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