## Full Non-Rigid Group Theory and Symmetry of Melamine (2005)

Venue: | JOURNAL OF THE IRANIAN CHEMICAL SOCIETY |

### BibTeX

@MISC{Ashrafi05fullnon-rigid,

author = {A. R. Ashrafi and M. Hamadanian},

title = {Full Non-Rigid Group Theory and Symmetry of Melamine },

year = {2005}

}

### OpenURL

### Abstract

The non-rigid molecule group (NRG) theory in which the dynamic symmetry operations are defined as physical operations is a new field in chemistry. Smeyers, in a series of papers, applied this notion to determine the character table of restricted NRG of some molecules. For example, Smeyers and Villa computed the r-NRG of the triple equivalent methyl rotation in pyramidal trimethylamine with inversion and proved that the r-NRG of this molecule is a group of order 648, containing two subgroups of order 324 without inversion [5]. In this work, a simple method is described, through which it is possible to calculate character tables for the symmetry group of molecules. We study the full NRG of melamine, and prove that it is a groups of order 48, with 27 and 10 conjugacy classes. Also, we compute the symmetry of melamine and prove that it is a non-abelian groups of order 6. The method can be generalized to apply to other non-rigid molecules.

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(Show Context)
Citation Context ...estigate the f-NRG and symmetry of melamine (2,4,6-triamino-1,3,5-triazine). We prove that the fNRG of melamine has order 48 with 10 conjugacy classes. Throughout this paper, the notation is standard =-=[11,12]-=- and all groups considered are assumed to be finite. EXPERIMENTAL Let us recall some definitions and notations. An automorphism of a graph G is a permutation g of the vertex set 136 Full Non-Rigid Gro... |

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(Show Context)
Citation Context ... and the same weight for the nuclei in the same equivalence classes. The topic of perceiving the symmetry of a graph through the automorphism group of the graph has been studied in considerable depth =-=[13]-=-. However, the connection between the graph automorphism problem and the symmetry of a molecule has not been explored in as much detail. Longuet-Higgins has shown a more desirable representation of mo... |

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(Show Context)
Citation Context ...estigate the f-NRG and symmetry of melamine (2,4,6-triamino-1,3,5-triazine). We prove that the fNRG of melamine has order 48 with 10 conjugacy classes. Throughout this paper, the notation is standard =-=[11,12]-=- and all groups considered are assumed to be finite. EXPERIMENTAL Let us recall some definitions and notations. An automorphism of a graph G is a permutation g of the vertex set 136 Full Non-Rigid Gro... |

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(Show Context)
Citation Context ...interest and importance to develop simple methods of calculating these character tables, which are needed for the classification of wave functions, determination of selection rules, and so on. Lomont =-=[3]-=- has given two methods for calculating character tables. These are satisfactory for small groups, but both of them require a knowledge of the class constant and hence of the group multiplication table... |

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(Show Context)
Citation Context ...e analysis of the symmetry properties of physical systems. The symmetry properties of rigid molecules are well known and so it is natural to investigate non-rigid molecules. According to Y.G. Smeyers =-=[1]-=-, the non-rigid molecule group (NRG) is strictly defined as the complete set of the molecular conversion operations, which commute with a given nuclear Hamiltonian operator, limited to large amplitude... |

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(Show Context)
Citation Context ...own that the automorphism group of the Euclidean graph of a molecule is the PI group of the molecule [7]. Our computations were carried out using the “Groups, Algorithms and Programming” (GAP) system =-=[14]-=-. GAP is a free and extensible software package for computation in discrete abstract algebra, in which you can write your own programs in the GAP language, and use them in the same way the programs wh... |