Effects of shape, size, and pyrene doping on electronic properties of graphene nanoflakes

Effects of size, shape, and pyrene doping on electronic properties of graphene nanoflakes (GNFs) were theoretically investigated using density functional theory method with PBE, B3PW91, and M06-2X functionals and cc-pVDZ basis set. Two shapes of zigzag GNFs, hexagonal (HGN) and rhomboidal (RGN), were considered. The energy band gap of GNF depends on shape and decreases with size. The HGN has larger band gap energy (1.23-3.96 eV) than the RGN (0.13-2.12 eV). The doping of pyrene and pyrene derivatives on both HGN and RGN was also studied. The adsorption energy of pyrene and pyrene derivatives on GNF does not depend on the shape of GNFs with energies between 21 and 27 kcal mol^-1. The substituent on pyrene enhances the binding to GNF but the strength does not depend on electron withdrawing or donating capability. The doping by pyrene and pyrene derivatives also shifts the HOMO and LUMO energies of GNFs. Both positive (destabilizing) and negative (stabilizing) shifts on HOMO and LUMO of GNFs were seen. The direction and magnitude of the shift do not follow the electron withdrawing and donating capability of pyrene substituents. However, only a slight shift was observed for doped RGN. A shift of 0.19 eV was noticed for HOMO of HGN doped with 1-aminopyrene (pyNH₂) and of 0.04 eV for LUMO of HGN doped with 1-pyrenecarboxylic acid (pyCOOH). Graphical Abstract HOMO and LUMO Energies of pyrene/pyrene derivatives doped Graphene Nanoflakes.