The non-rigid molecule group theory (NRG) in which the dynamical symmetry operations are defined as physical operations is a new field in chemistry. 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 a subgroup of order 324 without inversions (see J. Math. Chem. 28(4) (2000) 377–388). In this work, a computational method is described, by means of which it is possible to calculate the symmetry group of molecules. We study the full non-rigid group (f-NRG) of Sponge and Pina molecules with C 2 and C i point groups, respectively. It proved that these are groups of order 162 and 13122 with 54 and 3240 conjugacy classes, respectively. The character tables of these groups are also computed.
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References
Smeyers Y.G. (1992). Adv. Quantum Chem. 24: 1
Y.G. Smeyers, in: Structure and Dynamics of Non-Rigid Molecular Systems, ed. Y.G. Smeyers (Kluwer Academic, Dordrecht, 1995), p. 121.
Smeyers Y.G., Senent M.L., Botella V., Moule D.C. (1993). J. Chem. Phys. 98: 2754
Van der Avoird (1993). J. Chem. Phys. 98: 5327
Smeyers Y.G., Villa M., Senent M.L. (1998). J. Mol. Spect. 191: 232
Vivier-Bunge A., Uct V.H., Smeyers Y.G. (1998) J. Chem. Phys. 109: 2279
Longuet-Higgins H.C. (1963). Mol. Phys. 6: 445
Bunker Ph.R. (1979). Molecular Symmetry in Spectroscopy. Academic Press, New York
Isaacs I.M. (1978). Character theory of finite groups. Academic Press, New york
James G., Liebeck M. (1993). Representations and Characters of Groups. Cambridge University Press, Cambridge
Lomont J.S. (1959). Applications of Finite Groups. Academic Press Inc., New York
Smeyers Y.G., Villa M. (2000). J. Math. Chem. 28(4): 377
Stone A.J. (1964). J. Chem. Phys. 41: 1568
Ashrafi A.R., Hamadanian M. (2003). Croat. Chem. Acta 76(4): 299
Ashrafi A.R., Hamadanian M. (2004). J. Appl. Math. & Comput. 14: 289
Hamadanian M., Ashrafi A.R. (2003). Croat. Chem. Acta 76(4): 305
Moghani G.A., Ashrafi A.R., Hamadanian M. (2005). J. Zhejian Univ. SCI. 6(2): 222
Ashrafi A.R. (2005). MATCH Commun. Math. Comput. Chem. 53: 161
Schönert M., Besche H.U., Breuer Th., Celler F., Eick B., Felsch V., Hulpke A., Mnich J., Nickel W., Pfeiffer G., Polis U., Theißen H., Niemeyer A. (1995). GAP, Groups, Algorithms and Programming. Lehrstuhl De für Mathematik, RWTH, Aachen
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Darafsheh, M.R., Farjami, Y., Ashrafi, A.R. et al. Full Non-rigid Group of Sponge and Pina. J Math Chem 41, 315–326 (2007). https://doi.org/10.1007/s10910-006-9076-y
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DOI: https://doi.org/10.1007/s10910-006-9076-y