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Internet Electronic Journal of Molecular Design - IEJMD, ISSN 1538-6414, CODEN IEJMAT
| ABSTRACT - Internet Electron. J. Mol. Des. July 2002, Volume 1, Number 7, 351-359 |
Computing the Permanent of the Adjacency Matrix for Fullerenes
Francisco Torrens
Internet Electron. J. Mol. Des. 2002, 1, 351-359
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Abstract:
Novel carbon allotropes, with finite molecular structure, including
spherical fullerenes are nowadays currently produced and
investigated. These compounds have beautiful architectures and show
unusual properties that are very promising for the development of
nanotechnologies. The Kekulé structure count and permanent of the
adjacency matrix are computed for these molecules. A method for
computation of the permanent of the adjacency matrix is herein
optimized for fullerenes. The method finds exact values for
permanents of adjacency matrices up to 60x60. The results provide
linear and non-linear correlations between different structural
parameters involving the presence of contiguous pentagons,
ln[per(A)]/ln K, ln K and ln[per(A)]. A method for
computing the permanent of the adjacency matrix is optimized for fullerenes. As
ln[per(A)]/ln K can be related with thermodynamic stability, this
aspect of chemistry could be useful for designing or predicting
unknown fullerenes and their structure. The non-linear correlation for
ln[per(A)]/ln K is improved. The variance decreases 49% and the risk
of co-linearity diminishes. The software programs are available on
request from the author (Francisco.Torrens@uv.es) and are free for
academics.
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