In this paper, the fuzzy symmetry of some prototypical linear molecules has been analyzed. The results show that some molecular orbitals (MOs) are less symmetrical but some others are more symmetrical than the molecular skeleton, which the MOs correspond to. The membership functions of space inversion for MOs are closely related to the chemical characteristics of the MOs. Sometimes, although the symmetry of a molecular skeleton is not obvious, however that of some MO is quite obvious. The membership functions of the fuzzy inversion symmetry depend on the choice of the position of the center of inversion. As compared to those of diatomic molecules and linear tri-atomic molecules, the linear polyatomic molecules in which a distinctive fuzzy symmetry of space translation may exist, and thus a significant effect on their properties can be expected.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Dubois D., Prade H. (1980). Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York
Xiao W.S. (1992). Basic Fuzzy Mathematics and its Applications. (In Chinese) Aircraft Industry Press, Beijing p201
Mezey P.G., Maruani J. (1990). Mole. Phys. 69(1): 97
Mezey P.G., Maruani J. (1993) Int. J. Quantum Chem. 45: 177
D.H. Rouvray, Are the concepts of chemsitry all fuzzy? in: Concepts in Chemistry, Ed. D.H. Rouvray (Research Studies Press, Taunton, Somerset, 1997), pp. 1–15.
Pearson R.G. (1976). Symmetry Rules for Chemical Reaction: Orbital Topology and Elementary Processes. John Wiley and sons, New York
Zhao X.Z., Xu X.F. (2004) Acta Physico Chim. Sci. 20(10): 1175 (in Chinese)
Zhao X.Z., Xu X.F., Wang G.C., Pan Y.M., Cai Z.S. (2005). Mol. Phys. 103(24): 3233
Frisch M.J., Trucks G.W., Schlegel H.B. et al. (1998). Gaussian 98, Revision A.3, Gaussian, Inc., Pittsburgh PA
Zadeh L.A. (1965) Inform. Control 8B, 338–353
Baba T., Fukui H. (1999) J. Chemical Phys. 110(1): 131
Rauk A., Armstrong D.A. (2002) J. Phys. Chem. A 106: 400
Shtoff A.V., Reat M., Gusarov S.L. (2001) Eur. Phys. J. D 15(2): 199
Lu S.I. (2001) J. Chemical Phys. 114(9): 3898
Tsuzuki S., Luthi H.P. (2001) J. Chem. Phys. 114(9): 3949
Moore Plummer P.L. (2004) J. Phys. Chem. B 108, 19582
Rajasekar P., Kadossov E.B., Watt T., Materer N.F. (2002) Surf. Sci. 515, 421
Kadossov E.B., Rajasekar P., Materer N.F. (2004) J. Phys. Chem. B 108, 303
Buma W.J., Fanti M., Zerbetto F. (1999) Chem. Phys. Lett. 313, 426
Molder U., Burk P., Koppel I.A. (2002) Int. J. Quantum Chem. 82: 73
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Xu, X., Wang, G., Zhao, X. et al. Fuzzy Symmetries for Linear Molecules and their Molecular Orbitals. J Math Chem 41, 143–160 (2007). https://doi.org/10.1007/s10910-006-9065-1
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10910-006-9065-1