Fuzzy Symmetry Characteristics of Propadine Molecule

The fuzzy symmetry characteristics for the internal-rotation of propadine were analyzed using the fuzzy symmetry theory for molecule and molecular orbital (MO). In the process of rotation, three different symmetry point groups D_2h, D_2d, and D₂ were considered. Using the D_4h point group, which is the minimal point group including all symmetry elements of D_2h, D_2d, and D₂, we can analyze the fuzzy symmetry for this process. The elements included in D_4h point group can be classified to four subsets: (i) G0—it includes all the elements in D₂ point group, also belongs to all the above three point groups of D_2h, D_2d, and D₂; (ii) G1—it includes the elements in D_2h point group, but not in D_2d point group; (iii) G2—it includes the elements in D_2d point group, but not in D_2h point group; (iv) G3—it includes the elements in D_4h point group, but not in D_2h or D_2d point group. On the basis of the above four subsets, we analyzed the membership functions and the regularity of variation in MOs for the internal-rotation of propadine.