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Internet Electronic Journal of Molecular Design - IEJMD, ISSN 1538-6414, CODEN IEJMAT
| ABSTRACT - Internet Electron. J. Mol. Des. February 2003, Volume 2, Number 2, 96-111 |
Principal Component Analysis of Structural Parameters for Fullerenes
Francisco Torrens
Internet Electron. J. Mol. Des. 2003, 2, 96-111
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Abstract:
Novel carbon allotropes with finite molecular structure,
including spherical fullerenes, are nowadays currently produced
and investigated. The Kekulé structures count and permanent of
the adjacency matrix of these molecules are related to structural
parameters involving the presence of contiguous pentagons. Both
single- and complete-linkage cluster analyses of the structural
parameters allow classifying these parameters. Principal
component analysis (PCA) 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 q parameter (the
number of edges common to two pentagons). PCA clearly
distinguishes three classes of fullerenes. The cluster analysis of
fullerenes is in agreement with PCA classification. Cluster
analysis shows the greatest similarity for the p and r (the number
of vertices common to three pentagons) parameters. Split
decomposition indicates a spurious relationship resulting from
base composition effects. PCA provides three orthogonal factors
F1-F3. The use of only F1
gives an error of 13%. The use F1 and
F2 decreases the error to 3%. PCA groups the fullerenes in three
classes. Some fullerenes with different numbers of atoms belong
to the same class, while some fullerene isomers are members of
different classes. The software programs are available on request
from the author (Francisco.Torrens@uv.es) and are free for
academics.
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