The Fuzzy D2h-symmetries of Ethylene Tetra-halide Molecules and their Molecular Orbitals

Based on our study in relation to the fuzzy symmetry characterization and the application to linear molecule, the fuzzy symmetry of the planar molecules have been analyzed. The prototypical planer molecules we have chosen to study are the C2F3X (X = Cl, Br, and I) and three kinds of C2F2Cl2 isomers. These molecules relate to the fuzzy symmetry in connection with the D2h point group. As we known, the D2h point group includes an identity transformation and seven twofold symmetry transformations but without higher-fold ones. Meanwhile, it is related only to some one-dimensional irreducible representations, but there is not to multi-dimensional irreducible representation. In this paper, the fuzzy symmetries of these molecules and their molecular orbital(MO)s have been studied, such as the membership functions, the representation compositions, the fuzzy correlation diagrams and so on have been analyzed. These analysis methods can be used to analyze the molecular fuzzy symmetries of some other molecule systems, no difficulty.