Graph theory for fused cubic clusters of water dodecamer

Qicun Shi, Sabre Kais, Joseph S. Francisco

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)12036-12045
Number of pages10
JournalJournal of Physical Chemistry A
Volume109
Issue number51
DOIs
Publication statusPublished - 29 Dec 2005
Externally publishedYes

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Point groups
graph theory
Graph theory
Crystal symmetry
Hydrogen
Psychological Techniques
Water
apexes
symmetry
Electron energy levels
water
Hydrogen bonds
Oxygen
Scanning
Atoms
oxygen atoms
theorems
energy levels
diagrams
hydrogen bonds

ASJC Scopus subject areas

  • Physical and Theoretical Chemistry

Cite this

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

In: Journal of Physical Chemistry A, Vol. 109, No. 51, 29.12.2005, p. 12036-12045.

Research output: Contribution to journalArticle

Shi, Qicun ; Kais, Sabre ; Francisco, Joseph S. / Graph theory for fused cubic clusters of water dodecamer. In: Journal of Physical Chemistry A. 2005 ; Vol. 109, No. 51. pp. 12036-12045.
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