## Abstract

Ab initio plane wave based all valence electron DFT calculations with geometry optimization are reported for the electronic structure of planar zigzag edged triangular shaped graphene molecules C_{m* * 2 + 4 m + 1} H_{3 m + 3} where the zigzag ring number m = 2, ..., 15. The largest molecule C_{286}H_{48} has a 3.8 nm side length and retains D_{3h} symmetric geometry. The zone in the middle of the molecules, where the geometry and electronic properties resemble infinite single sheet graphite (graphene), expands with increasing ring number m, driving deviations in geometry, charge and spin to the perimeter. If a molecule is viewed as a set of nested triangular rings of carbon, then the zone where the lattice resembles an infinite sheet of graphene with CC = 142 pm, extends to the middle of the penultimate ring. The radial bonds joining the perimeter carbon atoms to the interior are long CC = 144 pm, except near the three apexes where the bonds are shorter. Isometric surfaces of the total charge density show that the two bonds joined at the apex have the highest valence charge. The perimeter CC bonds establish a simple pattern as the zigzag number increases, which shares some features with the zigzag edges in the D_{2h} linear acenes C_{4m+2}H_{2m+4} and the D_{6h} hexangulenes C_{6 m* * 2} H_{6 m} but not the D_{6h} symmetric annulenes (CH)_{(2 m - 1)* 6}. The two CC bonds forming each apex are short (≈139 pm), next comes one long bond CC ≈ 142 pm and a middle region where all the CC bonds have length ≈141 pm. The homo-lumo gap declines from 0.53 eV at m = 2 to approximately 0.29 V at m = 15, the latter being larger than found for linear or hexagonal shaped graphenes with comparable edge lengths. Across the molecule the charge on the carbon atoms undergoes a small oscillation following the bipartite lattice. The magnitude of the charge in the same nested triangle decreases monotonically with the distance of the row from the center of the molecule. These systems are predicted to have spin polarized ground states with S = 1/2(m - 1), in accord with the theorems of Lieb for a bipartite lattice with unequal numbers of sub-lattice carbon atoms. The magnitude of the spin on the atoms increases monotonically from the center to the edges, this effect being greatest on the majority A-sub lattice atoms. The spins are delocalized, not confined to specific atoms as might result in geometries stabilized by islands of aromatic resonance. In the largest systems the magnetic non-bonding levels (NBL) occur as a narrowly distributed set of homos close to the Fermi level, separated from the lower lying valence bond manifold by a gap of about 1 eV. The NBL are a set of disjoint radical orbitals having charge only on atoms belonging to the A-lattice and this charge is concentrated on the perimeter and penultimate row atoms.

Original language | English |
---|---|

Pages (from-to) | 1-15 |

Number of pages | 15 |

Journal | Chemical Physics |

Volume | 354 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - 2008 Dec 10 |

Externally published | Yes |

## Keywords

- Density functional theory (DFT)
- Disjoint radical
- Graphene
- Non-Kekulé structure
- Non-bonding level (NBL)
- Organic magnetism
- Polycyclic hydrocarbon
- Triangulenes

## ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

## Fingerprint

Dive into the research topics of 'Geometry, bonding and magnetism in planar triangulene graphene molecules with D_{3h}symmetry: Zigzag C

_{m* * 2 + 4 m + 1}H

_{3 m + 3}(m = 2, ..., 15)'. Together they form a unique fingerprint.