Bonding and magnetism in high symmetry nano-sized graphene molecules: linear acenes C_4m+2H_2m+4 (m = 2,... 25); Zigzag Hexangulenes C_6m**2H_6m (m = 2,... 10); Crenelated Hexangulenes C_{6(3m**2-3m+1)}H_6(2m-1) (m = 2,...6); zigzag triangulenes C_m**2+4m+1H _6m (m = 2,... 15)

Plane wave based ab initio DTF all valence electron spin polarized calculations are reported for the electronic structure and geometry of differently shaped graphene molecules. These polycyclic hydrocarbon molecules comprise four series: D_2h symmetric linear polyacenes C _4m+2H_2m+4 (m = 2,..., 25); D_6h hexagulenes with zigzag edges C_6**2H_6m (m = 2.....,10); D _6h hexagulenes with crenelated edges C _{6(3m**2-3m+i)}H_6(2m-1) (m = 2,..., 6); D _3h zigzag edged triangulenes C_m**2+4m+1H _6m (m = 2.... 15). The systems variously display ground states that are spin paired singlet (S = 0), singlet anti-ferromagnetically ordered diradical and spin polarized S = 1 /2(m - 1). Molecules with zigzag edges show evidence of electron derealization along the perimeters with some bond alternation at the corners. In the acenes the spin paired singlet state of the short members switches to a singlet diradical at m % 7-8 and this remains as the ground state for larger m. In contrast the triangulenes are magnetic and the atomic charge and spin density changes monotonically with distance from center to perimeter. In the hexagonal systems the development of a graphene core region, where the C-C bonds are 142 pm, extends to within a few C-C bonds of the perimeter atoms. Zigzag hexagulenes have a spin paired singlet ground state for m ≤ 8 and a singlet diradical ground state for larger m. When hexagulenes are substitutionally doped with boron or nitrogen, acceptor or donor levels appear that track the valence or conduction band edges with increase in zigzag number. This result suggests the possibility of building several semiconductor device structures into the same graphene molecule.