How do magnetic, structural, and electronic criteria of aromaticity relate to HOMO - LUMO gap? An evaluation for graphene quantum dot and its derivatives

The purpose of our study is to theoretically calculate the HOMO - LUMO gaps and aromaticity indices (HOMA, PDI, FLU, MCBO, PLR, Shannon, and NICS) for graphene quantum dot molecule and its seventeen derivatives. The correlation between the HOMO - LUMO gap and each aromaticity index was established for the core and petal rings. The linear correlation coefficient for the petal ring is: NICS(1) (0.7181) > PLR (0.6910) > PDI (0.6740) > FLU (0.6098) > MCBO (0.5294) > HOMA (0.3846) > Shannon (0.1498); and that for the core ring is: Shannon (0.4846) > MCBO (0.3765) > PLR (0.3334) > PDI (0.2647) > FLU (0.2356) > NICS (1) (0.2072) > HOMA (0.0529). All calculated aromaticity indices show that the petal ring is more aromatic than the core ring. A better correlation between the HOMO - LUMO gap and the energetic or electronic delocalization criterion than the structural criterion was observed for the investigated molecules.