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Fuzzy ta/2 symmetries of straight chain conjugate polyene molecules

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Abstract

On the basis of our recent studies on the molecular fuzzy point group symmetry, we further probe into the more complicated planar one-dimensional fuzzy periodic molecules—straight chain conjugate polyene. Except for the fuzzy translation transformation, the space transformation of the fuzzy screw rotation and the glide plane will be referred to. In addition, other fuzzy point symmetry transformation lain in the space transformation is discussed. Usually there is a correlation between the fuzzy symmetry characterization caused by the transition of the point symmetry elements and by certain space symmetry transformation. For the molecular orbital, the irreducible representation component is analyzed besides the membership function of the fuzzy symmetry transformation. Also, we inquire into the relativity between some molecular property and the fuzzy symmetry characterization.

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References

  1. Mezey P G, Maruani J. A continuous extension of the symmetry concept for quasi-symmetric structures using fuzzy-set theory. Mol Phys, 1990, 69(1): 97–113

    Article  CAS  Google Scholar 

  2. Mezey P G, Maruani J. The fundamental syntopy of quasi-symmetric systems: Geometric criteria and the underlying syntopy of a nuclear configuration space. Int J Quantum Chem, 1993, 45(2): 177–187

    Article  CAS  Google Scholar 

  3. Mezey P G. Generalized chirality and symmetry deficiency. J Math Chem, 1998, 23(1): 65–84

    Article  CAS  Google Scholar 

  4. Maruani J, Mezey P G. Le concept de «syntopie»: une extension continue du concept de symétrie pour des structures quasi-symétriques à l’aide de la méthode des ensembles flous. Compt Rend Acad Sci Paris (Série II), 1987, 305: 1051–1054

    Google Scholar 

  5. Maruani J, Toro-Labbé A. Le modèle de la syntopie et l’état de transition de réactions chimiques: fonctions d’appartenance et coefficients de Brönsted pour l’isomérisation cis-trans. Compt Rend Acad Sci Paris (Série IIb), 1996, 323: 609–615

    CAS  Google Scholar 

  6. Mezey P G. Quantum chemistry of macromolecular shape. Int Rev Phys Chem, 1997, 16, 361–388

    Article  CAS  Google Scholar 

  7. Zabrodsky H, Peleg S, Avnir D. Continuous symmetry measures. 2. symmetry groups and the tetrahedron. J Am Chem Soc, 1993, 115, 8278–8289

    Article  CAS  Google Scholar 

  8. Avnir D, Zabrodsky H, Hel-Or H, Mezey P G. Symmetry and chirality: continuous measures. In: Paul von Ragué Schleyer, ed. Encyclopaedia of Computational Chemistry, vol 4. Chichester: Wiley, 1998. 2890–2901

    Google Scholar 

  9. Chauvin R. Chemical algebra. I: Fuzzy subgroups. J Math Chem, 1994, 16(1): 245–256

    Article  CAS  Google Scholar 

  10. Chauvin R. Chemical algebra. II: Discriminating pairing products”. J Math Chem, 1994. 16(1): 257–258

    Article  CAS  Google Scholar 

  11. Zhou X Z, Fan Z X, Zhan J J. Application of Fuzzy Mathematics in Chemistry. Changsha: National University of Defence Technology Press, 2002. 325–349

    Google Scholar 

  12. Zhao X Z, Xu X F. The molecular fuzzy symmetry (in Chinese). Acta Phys Chim Sci, 2004, 20(10): 1175–1178

    CAS  Google Scholar 

  13. Zhao X Z, Xu X F, Wang G C, Pan Y M, Cai Z S. Fuzzy symmetries of molecule and molecular orbital: characterization and simple application. Mol Phys, 2005, 103(24): 3233–3241

    Article  CAS  Google Scholar 

  14. Xu X F, Wang G C, Zhao X Z, Pan Y M, Liang Y Y, Shang Z F. Fuzzy symmetries for linear molecules and their molecular orbitals. J Math Chem, 2007, 41(2): 143–160

    Article  CAS  Google Scholar 

  15. Zhao X Z, Xu X F, Wang G C, Pan Y M, Shang Z F, Li R F. The fuzzy D2h-symmetries of ethylene tetra-halide molecules and their molecular orbitals. J Math Chem, 2007, 42(2): 265–288

    Article  CAS  Google Scholar 

  16. Zhao X Z, Wang G C, Xu X F, Pan Y M, Shang Z F, Li R F, Li Z C. The fuzzy D6h-symmetries of azines molecules and their molecular orbitals. J Math Chem, 2008, 43(2): 485–507

    Article  CAS  Google Scholar 

  17. Zhao X Z, Shang Z F, Wang G C, Xu X F, Li R F, Pan Y M, Li Z C. Fuzzy space periodic symmetries for polyynes and their cyanocompounds. J Math Chem, 2008, 43(3): 1141–1162

    Article  CAS  Google Scholar 

  18. Zhao X Z, Shang Z F, Sun H W, Chen L, Wang G C, Xu X F, Li R F, Pan Y M, Li Z C. The fuzzy symmetries for linear tri-atomic B⋯A⋯C dynamic systems. J Math Chem, 2008, 44(1): 46–74

    Article  CAS  Google Scholar 

  19. Zhao X Z, Xu X F, Shang Z F, Wang G C, Li R F. Fuzzy symmetry characteristics of propadine molecule. Acta Phys Chim Sci, 2008, 24(5): 772–780

    Article  CAS  Google Scholar 

  20. Zhao C D. Quantum Chemistry of Solids (in Chinese). 2nd ed., Beijing: Higher Education Press, 2003. 51–54,197–204

    Google Scholar 

  21. Wang R H, Gao K X. Symmetry Group of Crystallography (in Chinese). Beijing: Science Press, 1990. 348–349

    Google Scholar 

  22. Jiang M Q. The Rule of Homologous Linearity of Organic Compounds (in Chinese). Beijing: Science Press, 1980. 129–144

    Google Scholar 

  23. Kutzelnigg W. Zur behandlung der bindungsalternierung als störung in der Hückelschen MO-Theorie. Theor Chim Acta, 1966, 4(5): 417–433

    Article  CAS  Google Scholar 

  24. Sondheimer F, Ben-Efralm D A, Wolovsky R. Unsaturated macrocyclic compounds. XVII. The prototropic rearrangement of linear 1,5-enynes to conjugated polyenes. The synthesis of a series of vinylogs of butadiene. J Am Chem Soc, 1961, 83(7): 1675–1681

    Article  CAS  Google Scholar 

  25. Frisch M J, Trucks G W, Schlegel H B, Scuseria G E, Robb M A, Cheeseman J R, Zakrzewski V G, Montgomery Jr, Stramann R E, Burant J C, Dapprich J M, Daniels A D, Kudin K N, Strain M C, Farkas O, Tomasi J, Barone V, Cossi M, Cammi R, Mennuggi B, Pomelli C, Adamo C, Clifford S, Ochterski J, Petersson G A, Ayala P Y, Cui Q, Morokuma K, Malick D K, Rabuck A D, Raghavachari K, Foresman J B, Cioslowski J, Ortiz J V, Baboul A G, Stefanov B B, Liu G, Liashenko A, Piskorz P, Komaromi I, Gomperts R, Martin L R, Fox D J, Keith T, Al-Laham M A, Peng C Y, Nanayakkara A, Gonzalez C, Challacombe M, Gill P M W, Johnson B, Chen W, Wong M W, Andres J L, Gonzalez C, Head-Gordon M, Replogle E S, Pople J A. Gaussian 98, Revision A.3. Pittsburgh: Gaussian, Inc., 1998

    Google Scholar 

  26. Kittel C. Introduction to Solid State Physics. 8th ed. New York: John Wiley and Sons, 2004. 169–200

    Google Scholar 

  27. Cotton F A. Translated by Liu W C, You X Z, Lai W J. Chemical Application of Group Theory (in Chinese). 3rd ed. Fuzhou: Fujian Science and Technology Press, 1999. 81–92

    Google Scholar 

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Authors and Affiliations

  1. College of Chemistry, Nankai University, Tianjin, 300071, China

    Yun Li, XueZhuang Zhao, XiuFang Xu, ZhenFeng Shang, Zhen Zhou, ZunSheng Cai, GuiChang Wang & RuiFang Li

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  1. Yun Li
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  2. XueZhuang Zhao
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  3. XiuFang Xu
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  4. ZhenFeng Shang
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  7. GuiChang Wang
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  8. RuiFang Li
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Correspondence to XueZhuang Zhao or GuiChang Wang.

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Li, Y., Zhao, X., Xu, X. et al. Fuzzy ta/2 symmetries of straight chain conjugate polyene molecules. Sci. China Ser. B-Chem. 52, 1892–1910 (2009). https://doi.org/10.1007/s11426-009-0284-8

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  • DOI: https://doi.org/10.1007/s11426-009-0284-8

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