Fuzzy Symmetry Characteristics of Propadine Molecule

Abstract

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 2 h , D 2 d , and D 2 were considered. Using the D 4 h point group, which is the minimal point group including all symmetry elements of D 2 h , D 2 d , and D 2, we can analyze the fuzzy symmetry for this process. The elements included in D 4 h point group can be classified to four subsets: (i) G0—it includes all the elements in D 2 point group, also belongs to all the above three point groups of D 2 h , D 2 d , and D 2; (ii) G1—it includes the elements in D 2 h point group, but not in D 2 d point group; (iii) G2—it includes the elements in D 2 d point group, but not in D 2 h point group; (iv) G3—it includes the elements in D 4 h point group, but not in D 2 h or D 2 d 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.