Delocalization of {pi}-electrons in graphene, fullerene and carbon nanotubes
Abstract
Full text: Carbon nanostructures have caused an explosive interest among scientists around the world thanks to its unique properties. Incredible properties of these structures have discovered tremendous prospects of their use in electronics, medicine and many other areas. Nowadays, the number of articles and papers on these structures are in the hundreds, that only testifies their relevance to the scientific community. The Nobel Prizes were awarded in 1997 and 2010 for the discovery and study of fullerenes and graphene respectively. But the question of electron delocalization in carbon nanostructures, which is of great theoretical interest, has not been so far fully resolved. Definition of aromaticity of these structures remains open. Comparative trends of the electronic and energetic properties among all three forms of nanostructures, as graphene, fullerene and nanotube have a great theoretical and practical interest. In this report we presents computer simulation results of theoretical investigation of delocalization of pi-electrons, as well as structural, electronic and energetic properties of graphene, fullerenes and carbon nanotubes. Here we considered single and double-layer graphenes, fullerenes with the number of atoms of 60 and 80, the nanotubes of armchair, zig-zag and chiral configurations. We used MNDO PM3, ab-initio HF and DFT with B3LYP basis for computer simulation. Obtained results show that the band gap of a double-layer graphene is wider than for monolayer graphene evidently due to the formation of bonds between the pz-orbitals of the boundary atoms of the layers and the partial compensation of dangling bonds. The energy of formation of fullerene per atom does not depend on the size of fullerene. However, the HOMO-LUMO gap decreases from C60 to C80. In nanotubes with armchair configuration the gap narrowed while the tube diameter decreased, which can be explained by increasing of the angular strengths between the bonds in small diameter tubes. Among nanotubes, the spiral tubes have a severe departure of the size of the HOMO-LUMO gap, which caused actually by the break of long-range order in these structures. A comparative study of the graphene, fullerenes and nanotubes shows that the widest HOMO-LUMO gap is for the fullerenes and narrowest - for graphene. The work is supported by F.3-12 grant of the Fund of Support of Basic Researches of the Academy of Sciences of Uzbekistan. (author)