Symmetries and fuzzy symmetries of graphene molecules

In this paper, we will investigate the fuzzy layer group symmetries of two-dimensional (2D) periodic molecules. Here, we select several graphene molecules as typical examples to discuss. For these two-dimensional graphene molecules, their MO energies, symmetries and fuzzy symmetries are preliminarily studied. In addition, we especially make a detailed comparison between the zigzag and armchair graphene molecules. These studies will develop a theoretical framework that will help us to investigate the fuzzy symmetries of various layer group molecules as well as molecules with 3D periodic structure.