Periodicity-dependent long range coulomb on-site repulsion in hydrogen adsorbed graphene: A DFT plus U study

The long rang Coulomb on-site repulsion between pi electrons in hydrogen (H) adsorbed graphene has been studied based on DFT + U calculations. This study demonstrates that the rigidity of pi electronic structure of graphene is partially destroyed in the cases of H adsorption due to the introduction of un-paired electron in this system. The softness of pi conjugation is largely depending on the concentrations as well as the periodicity of H adsorption. Due to the destruction of the rigidity of pi conjugation, the Coulomb on-site repulsion increases. The results show that the Coulomb on-site repulsion between pi electrons is very sensitive to the periodicity of H adsorption. A considerable enhancement of Coulomb on-site repulsion occurs for the systems with 3n x 3n peroidcity. More importantly, the strength and the patterns of Coulomb on-site repulsion in the graphene plane are significantly size-dependent, which further induces the band gap opening at Fermi level. Especially for 6 x 6 system, the on-site repulsion induces a stabilized non-ferromagnetic state. Our results reveal for the first time that the considerable long rang Coulomb on-site repulsion between pi electrons exists which plays an important role in the electronic characteristics of H adsorbed graphene. The finding in this investigation provides new insight into the many-body interaction between localized impurities with delocalized pi electrons in graphene related materials.