A Density Functional Theory Study of Ground and Low-Lying Excited Electronic States in Defective Graphenes

Electronic states of graphenes, whose carbon atoms are terminated by hydrogen atoms (hydrogenated graphene, denoted H-graphene) and defective graphene (one carbon atom was removed from H-graphene, denoted D-graphene) have been investigated by density functional theory. The sizes of graphenes examined in the present study were n = 7, 14, 19, 29, 37, 44, and 52; where n is the number of benzene rings in the graphene. The excitation energies of H-graphenes were gradually decreased as a function of the number of rings. In D-graphene, new energy levels for the first and second excited states appeared as low-lying excited states. It was found that the formation of defect sites in graphene produces large decreases in the excitation energies for third and higher excited states. The highest occupied molecular orbital and lowest unoccupied molecular orbital (LUMO) in H-graphene were widely delocalized over the graphene surface. On the other hand, LUMO in D-graphene was localized only in the defect sites. The effects of vacancy defects on both the ground and excited electronic states of graphene were discussed on the basis of theoretical results.