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Internet Electronic Journal of Molecular Design - IEJMD, ISSN 1538-6414, CODEN IEJMAT
| ABSTRACT - Internet Electron. J. Mol. Des. August 2003, Volume 2, Number 8, 546-563 |
Principal Component Analysis of New Structural Parameters for Fullerenes
Francisco Torrens
Internet Electron. J. Mol. Des. 2003, 2, 546-563
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Abstract:
Novel carbon allotropes, with finite molecular structure,
including spherical fullerenes are nowadays currently produced
and investigated. The Kekulé structure count and permanent of
the adjacency matrix of these molecules are related to structural
parameters involving the presence of contiguous pentagons. The
close relationship between these parameters suggests considering
also their quotients. Both single- and complete-linkage cluster
analyses of the structural parameters allow classifying these
parameters. PCA (principal component analysis) of the structural
parameters and the cluster analyses of the fullerenes permits
classifying these molecules. Cluster analysis provides a binary
taxonomy of the structural parameters that separates first the
r-r/p from the p-q-q/p parameters.
PCA clearly distinguishes five
classes of fullerenes. The cluster analysis of fullerenes is in
agreement with the PCA classification. Cluster analysis shows
that the greatest similarity is between the q-q/p
and r-r/p pairs of
parameters. Split decomposition indicates a spurious relationship
resulting from base composition effects. PCA provides five
orthogonal factors F1-F5.
The use of F1 gives an error of 28%.
The use F1 and F2
decreases the error to 2%. PCA groups the
fullerenes in five classes. Some fullerenes with different numbers
of atoms belong to the same class, while some fullerene isomers
are members of different classes.
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