Ab initio plane wave all valence electron based DFT calculations were used to explore the dichotomy of perimeter vs. interior in the electronic and geometric structure of the D6h singlet ground state and D2h lowest triplet state of planar graphene hydrocarbon molecules with crenellated (arm chair) edges and the general formula C6[3m(m-1)+1] H6(2m-1) where m = 2, ..., 6. The largest molecule C546H66 was 4.78 nm across and contained 2250 valence electrons. These molecules are nominally "fully benzenoid hydrocarbons". However with increasing size, the core of central atoms abandoned any fully benzenoid geometry they had in small systems and organized into single layer graphite (graphene) structure. The perimeter atoms of the crenellation adopted a conjugated geometry with unequal bonds and between core and perimeter there were some C6 rings retaining remnants of aromatic sextet-type properties. Compared to a zigzag edge the crenellated edge conferred stability in all the systems studied as measured by the singlet homo-lumo level gap BG0 and the singlet-lowest triplet energy gap ΔEST. For the largest crenellated system (m = 6) BG0 and ΔEST were approximately 0.7 eV, larger in value than for similarly sized hexagonal graphenes with zigzag edges. Triplet states were identified for all the molecules in the series and in the case of the m = 2 molecule hexabenzocoronene C42H18, two conformations with D2h symmetry were identified and compared to features on the triplet state potential energy surface of benzene.
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