TY - JOUR
T1 - Geometry, bonding and magnetism in planar triangulene graphene molecules with D3h symmetry
T2 - Zigzag Cm* * 2 + 4 m + 1 H3 m + 3 (m = 2, ..., 15)
AU - Philpott, Michael R.
AU - Cimpoesu, Fanica
AU - Kawazoe, Yoshiyuki
N1 - Funding Information:
All the calculations were performed on the IMR Super Computer. MRP thanks the Center for Computational Materials Science for their warm hospitality and financial support. The authors thank the staff of the SR8000 Supercomputer Facility, Institute of Materials Research (IMR), Tohoku University, for their dedicated and enthusiastic support. MRP is a Japan Society for the Promotion of Science visiting professor at IMR and a visiting scholar in the group of W.A. Lester at the Kenneth Pitzer Theory Centre, Department of Chemistry, University of California Berkeley. FC acknowledges support from grant CNCSIS UEFISCU “Idei” 174/2007.
PY - 2008/12/10
Y1 - 2008/12/10
N2 - 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 Cm* * 2 + 4 m + 1 H3 m + 3 where the zigzag ring number m = 2, ..., 15. The largest molecule C286H48 has a 3.8 nm side length and retains D3h 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 D2h linear acenes C4m+2H2m+4 and the D6h hexangulenes C6 m* * 2 H6 m but not the D6h 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.
AB - 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 Cm* * 2 + 4 m + 1 H3 m + 3 where the zigzag ring number m = 2, ..., 15. The largest molecule C286H48 has a 3.8 nm side length and retains D3h 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 D2h linear acenes C4m+2H2m+4 and the D6h hexangulenes C6 m* * 2 H6 m but not the D6h 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.
KW - Density functional theory (DFT)
KW - Disjoint radical
KW - Graphene
KW - Non-Kekulé structure
KW - Non-bonding level (NBL)
KW - Organic magnetism
KW - Polycyclic hydrocarbon
KW - Triangulenes
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U2 - 10.1016/j.chemphys.2008.08.015
DO - 10.1016/j.chemphys.2008.08.015
M3 - Article
AN - SCOPUS:56949103131
SN - 0301-0104
VL - 354
SP - 1
EP - 15
JO - Chemical Physics
JF - Chemical Physics
IS - 1-3
ER -