Abstract
We have previously studied molecular fuzzy symmetry and mainly focused on the fuzzy point group symmetry and less on the fuzzy space group symmetry.As a kind of one-dimensional linear fuzzy periodic molecule, polyynes have been studied by us.Although the fuzzy symmetry of their molecular skeletons has been comprehensively investigated, the study of their molecular orbital (MO) has been limited to a few typical molecules because of the tedious calculations involved.In this work, we characterized the MO fuzzy symmetry of different kinds of polyyne molecules systematically and we found correlations between the fuzzy symmetry parameter of the MOs of the polyyne molecules and the number of carbon atoms.In addition, we also analyzed the MOs of related systems such as the cumulative polyene.Although their molecular structures are non-linear, the carbon atoms within the π-MO are linearly positioned and could still be analyzed using the fuzzy group G11 .Finally, on the basis of the Born-Karman approximation (one-dimensional periodic symmetry group containing n units is isomorphic with the Cn point group), the symmetry and the fuzzy symmetry of the MOs of the full carbon ring molecules were investigated.We, therefore, endeavored to characterize the one-dimensional periodic fuzzy symmetry for these molecules.
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