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 D2h, D2d, and D2 were considered. Using the D4h point group, which is the minimal point group including all symmetry elements of D2h, D2d, and D2, we can analyze the fuzzy symmetry for this process. The elements included in D4h 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 D2h, D2d, and D2; (ii) G1-it includes the elements in D2h point group, but not in D2d point group; (iii) G2-it includes the elements in D2d point group, but not in D2h point group; (iv) G3-it includes the elements in D4h point group, but not in D2h or D2d 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.