### Abstract

The stable structures of the fused cubic water cluster (H _{2}O) _{12} are examined using graph theoretical techniques and ab initio calculations. The calculations are obtained by scanning the symmetry of digraph structures of hydrogen-bond network spanning 12 oxygen atom vertexes. Using the Pólya theorem the cycle index expressions for 12 vertexes and 20 edges of a cuboid in point-group symmetry D _{4h} are developed. A total of 91 energy-allowed fused cubic structures are obtained, which are classified by 8 point-group symmetries: 1 D _{2h}, 2 S _{4}, 5 C _{4}, 1 D _{2}, 11 C _{2}, 10 C _{i}, 1 C _{s}, and 60 C _{1}. An energy level diagram of the structures reveals 14 bands that correspond to 14 unique two-colored graphs derived from the distributions of four free hydrogens of the cluster.

Original language | English |
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Pages (from-to) | 12036-12045 |

Number of pages | 10 |

Journal | Journal of Physical Chemistry A |

Volume | 109 |

Issue number | 51 |

DOIs | |

Publication status | Published - 29 Dec 2005 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physical and Theoretical Chemistry

### Cite this

*Journal of Physical Chemistry A*,

*109*(51), 12036-12045. https://doi.org/10.1021/jp0550154

**Graph theory for fused cubic clusters of water dodecamer.** / Shi, Qicun; Kais, Sabre; Francisco, Joseph S.

Research output: Contribution to journal › Article

*Journal of Physical Chemistry A*, vol. 109, no. 51, pp. 12036-12045. https://doi.org/10.1021/jp0550154

}

TY - JOUR

T1 - Graph theory for fused cubic clusters of water dodecamer

AU - Shi, Qicun

AU - Kais, Sabre

AU - Francisco, Joseph S.

PY - 2005/12/29

Y1 - 2005/12/29

N2 - The stable structures of the fused cubic water cluster (H 2O) 12 are examined using graph theoretical techniques and ab initio calculations. The calculations are obtained by scanning the symmetry of digraph structures of hydrogen-bond network spanning 12 oxygen atom vertexes. Using the Pólya theorem the cycle index expressions for 12 vertexes and 20 edges of a cuboid in point-group symmetry D 4h are developed. A total of 91 energy-allowed fused cubic structures are obtained, which are classified by 8 point-group symmetries: 1 D 2h, 2 S 4, 5 C 4, 1 D 2, 11 C 2, 10 C i, 1 C s, and 60 C 1. An energy level diagram of the structures reveals 14 bands that correspond to 14 unique two-colored graphs derived from the distributions of four free hydrogens of the cluster.

AB - The stable structures of the fused cubic water cluster (H 2O) 12 are examined using graph theoretical techniques and ab initio calculations. The calculations are obtained by scanning the symmetry of digraph structures of hydrogen-bond network spanning 12 oxygen atom vertexes. Using the Pólya theorem the cycle index expressions for 12 vertexes and 20 edges of a cuboid in point-group symmetry D 4h are developed. A total of 91 energy-allowed fused cubic structures are obtained, which are classified by 8 point-group symmetries: 1 D 2h, 2 S 4, 5 C 4, 1 D 2, 11 C 2, 10 C i, 1 C s, and 60 C 1. An energy level diagram of the structures reveals 14 bands that correspond to 14 unique two-colored graphs derived from the distributions of four free hydrogens of the cluster.

UR - http://www.scopus.com/inward/record.url?scp=30344439814&partnerID=8YFLogxK

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U2 - 10.1021/jp0550154

DO - 10.1021/jp0550154

M3 - Article

VL - 109

SP - 12036

EP - 12045

JO - Journal of Physical Chemistry A

JF - Journal of Physical Chemistry A

SN - 1089-5639

IS - 51

ER -