Calculating the symmetry of hexamethylcyclohexane

Authors

  • Ahmad Gholami Department of Mathematics, Faculty of Science, University of Kashan, Kashan,
  • Ali Reza Ashrafi Department of Mathematics, Faculty of Science, University of Kashan, Kashan,
  • Fariba Nazari Department of Chemistry, Faculty of Science, University of Zanjan, Zanjan,

DOI:

https://doi.org/10.20450/mjcce.2007.266

Keywords:

symmetry group, hexamethylcyclohexane, automorphism of groups

Abstract

An Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix. Balasubramanian (1995) computed the Euclidean graphs and their automorphism groups for benzene, eclipsed and staggered forms of ethane, and eclipsed and staggered forms of ferrocene. It was shown by Balasubramanian that the molecular symmetry groups can be obtained as the automorphism groups of edge-weighted Euclidean graphs. In this paper we calculate the atom centers of hexamethylcyclohexane molecule using the chemistry package HyperChem and then compute its symmetry group.

References

W. C. Herndon, in: Studies in Physical and Theoretical Chemistry, Vol. 28, Chemical Applications of Graph Theory and Topology, ed. R.B. King (Elsevier, Amsterdam, 1983) pp. 231–242.

. S. L. Altmann, Induced Representation in Crystal & Molecule, Academic Press, London, 1977.

G. S. Ezra, Symmetry Properties of Molecules, Lecture Notes in Chemistry 28, Springer, 1982.

H. C. Longuet-Higgins, The symmetry group of non-rigid molecules, Mol. Phys. 6, 445–460 (1963).

. P. R, Bunker, Molecular Symmetry in Spectroscop, Academic Press, 1979.

M. Randic, On the recognition of identical graphs representing molecular topology, J. Chem. Phy, 60, 3920– 3928 (1974).

K. Balasubramanian, Graph theoretical perception of molecular symmetry, Chem. Phys. Letters, 232, 415–423 (1995).

K. Balasubramanian, The symmetry groups of non-rigid molecules as generalized wreath products and their representations, J. Chem. Phys. 72, 665–677 (1980).

K. Balasubramanian, The symmetry groups of chemical graphs, Intern. J. Quantum Chem. 21, 411–418 (1982).

K. Balasubramanian, Application of combinatorics and graph theory to spectroscopy and quantum chemistry, Chem.Rev. 85, 599–618 (1985).

K. Balasubramanian, Group theory of non-rigid molecules and its applications, Studies Phys. Theor. Chem. 23, 149–168 (1983).

K. Balasubramanian, Generating functions for the nuclear spin statistics of non-rigid molecules, J. Chem. Phys. 75, 4572–4585 (1981).

K. Balasubramanian, Non-rigid group theory, tunneling splitting and nuclear spin statistics of water pentamer (H2O)5, J. Phys. Chem. 108, 5527–5536 (2004).

K. Balasubramanian, Group theoretical analysis of vibrational modes and rovibronic levels of extended aromatic C48N12 azafullerece, Chem. Phys. Letters 391, 64–68 (2004).

K. Balasubramanian, Nuclear spin statistics of extended aromatic C48N12 azafullerece, Chem. Phys. Letters 391, 69–74 (2004).

A. R. Ashrafi, M. Hamadanian, The full non-rigid group theory for tetraammine platinium(II), Croat. Chem. Acta, 76 (4), 299–303 (2004).

A. R. Ashrafi, On non-rigid group theory for some molecules, MATCH Commun. Math. Comput. Chem. 53, 161– 174 (2005).

G. James, M. Liebeck, Representations and Characters of Groups, Cambridge University Press, 1993.

N. Trinajstić, Chemical Graph Theory, CRC Press, Boca Raton, FL. 1992.

A. Gholami, M. Safaei-Ghomi, A. R. Ashrafi, M. Ghorbani, Symmetry of TetrahydroxyCalix

arenes, J. Serb. Chem. Soc. 71 (10), 1025–1029 (2006).

A. Gholami, A. R. Ashrafi, M. Ghorbani, Symmetry of Benzenoid Chains, Bulletin of the Chemists and Technologists of Macedonia, 25 (1), 23–27 (2006).

Downloads

Published

2007-12-15

How to Cite

Gholami, A., Ashrafi, A. R., & Nazari, F. (2007). Calculating the symmetry of hexamethylcyclohexane. Macedonian Journal of Chemistry and Chemical Engineering, 26(2), 115–124. https://doi.org/10.20450/mjcce.2007.266

Issue

Section

Theoretical Chemistry