# Polyhedral Phenylacetylenes: The Interplay of Aromaticity and Antiaromaticity in Convex Graphyne Substructures

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Computational Methods

## 3. Results

#### 3.1. Energies of formation

#### 3.2. Link topology

#### 3.3. Cyclic phenylacetylene trimer and conventional Fullerene C${}_{60}$

#### 3.4. Necklace-style phenylacetylenes

#### 3.5. The P1 molecule

#### 3.6. The P2 molecule

#### 3.7. The P4 molecule

#### 3.8. The A1 molecule

#### 3.9. The A4 molecule

## 4. Discussion and Conclusions

## Acknowledgements

## References

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**Figure 3.**Size comparison of polyhedral phenylacetylenes, with fullerene C60 included for comparison. Clockwise from top: C${}_{60}$, P2, P4, A1, A4.

**Figure 4.**NICS maps of the phenylacetylene trimer (top) and the C${}_{60}$ fullerene (bottom) in units of 10-6 (ppm). The same underlying data was used for the two (PA trimer) and three (C${}_{60}$) slices, only the perspective (the orientation and position of the slice plane) is different.

**Figure 5.**NICS maps of a PA hexamer (top) and a PA decamer (bottom), each from two different perspectives.

**Table 1.**Platonic and Archimedean templates for graphyne macrocycles. For the polyhedra marked with an asterisk${}^{\star}$, the sixfold rotational symmetry of the phenyl ring is a poor match for the vertex geometry.

Polyhedron designation (name) | Vertices (C6) | Edges (C2) | Molecular formula |
---|---|---|---|

P1 (tetrahedron) | 4 | 6 | C36H12 |

P2 (cube) | 8 | 12 | C72H24 |

P3 (octahedron) | 6 | 12 | –${}^{\star}$ |

P4 (dodecahedron) | 20 | 30 | C180H60 |

P5 (icosahedron) | 12 | 30 | –${}^{\star}$ |

A1 (cuboctahedron) | 12 | 24 | C120H24 |

A2 (great rhombicosidodecahedron) | 120 | 180 | C1080H360 |

A3 (great rhombicuboctahedron) | 48 | 72 | C432H144 |

A4 (icosidodecahedron) | 30 | 60 | C300H60 |

A5 (small rhombicosidodecahedron) | 60 | 120 | –${}^{\star}$ |

A6 (small rhombicuboctahedron) | 24 | 48 | –${}^{\star}$ |

A7 (snub cube) | 24 | 60 | C264H24 |

A8 (snub dodecahedron) | 60 | 150 | C660H60 |

A9 (truncated cube) | 24 | 36 | C216H72 |

A10 (truncated dodecahedron) | 60 | 90 | C540H180 |

A11 (truncated icosahedron) | 60 | 90 | C540H180 |

A12 (truncated octahedron) | 24 | 36 | C216H72 |

A13 (truncated tetrahedron) | 12 | 18 | C108H36 |

**Table 2.**Heats of formation of the different polyhedra (per carbon atom) considered in this work. The energy of the infinite graphene sheet (marked $\star $) has been taken as reference. Also reported are the number of pi-electrons in C${}_{2}$ triple bonds (4 electrons per C${}_{2}$), and the topology of the acetylene-connections between phenyl rings.

Polyhedron | Formation energy | Number of triple bonds | link |
---|---|---|---|

[kcal/mol per C] | topology | ||

Graphyne sheet | 0.0${}^{\star}$ | n/a | ortho/meta/para |

C${}_{60}$ | -4.31 | n/a | ortho/meta/para |

PA trimer | 0.10 | 3 | ortho |

PA hexamer | 0.71 | $6=2\times 3$ | para |

PA decamer | 0.86 | $16=2\times 2\times 2\times 2$ | ortho/meta/para |

P1 | 3.86 | $6=2\times 3$ | meta |

P2 | 1.56 | $12=2\times 2\times 3$ | meta |

P4 | 0.47 | $30=2\times 3\times 5$ | meta |

A1 | 1.12 | $24=2\times 2\times 2\times 3$ | ortho/meta/para |

A4 | 0.25 | $60=2\times 2\times 3\times 5$ | ortho/meta/para |

© 2009 by the authors; licensee Molecular Diversity Preservation International, Basel, Switzerland. This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license http://creativecommons.org/licenses/by/3.0/.

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**MDPI and ACS Style**

Sebastiani, D.; Parker, M.A.
Polyhedral Phenylacetylenes: The Interplay of Aromaticity and Antiaromaticity in Convex Graphyne Substructures. *Symmetry* **2009**, *1*, 226-239.
https://doi.org/10.3390/sym1020226

**AMA Style**

Sebastiani D, Parker MA.
Polyhedral Phenylacetylenes: The Interplay of Aromaticity and Antiaromaticity in Convex Graphyne Substructures. *Symmetry*. 2009; 1(2):226-239.
https://doi.org/10.3390/sym1020226

**Chicago/Turabian Style**

Sebastiani, Daniel, and Matt A. Parker.
2009. "Polyhedral Phenylacetylenes: The Interplay of Aromaticity and Antiaromaticity in Convex Graphyne Substructures" *Symmetry* 1, no. 2: 226-239.
https://doi.org/10.3390/sym1020226