### 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