Fuzzy Symmetries for Linear Molecules and their Molecular Orbitals

Xu, Xiufang; Wang, Gui‐Chang; Xin, Zhao; Pan, Yinming; Liang, Yong; Shang, Zhenfeng

doi:10.1007/s10910-006-9065-1

Cited by 7 publications

(7 citation statements)

References 15 publications

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“…In the terminal cell, there may be a few H atoms in the position of C atoms. When the atomic criterion Y J is changed to Y GJ through the symmetry transformation, Ĝ , the membership functions [12][13][14] of the molecule M related to the symmetry transformation Ĝ is…”

Section: Computational Detailsmentioning

confidence: 99%

“…Here 1/Dn is the normalizing factor. For the molecular skeleton, the atomic number is the atomic criterion [12][13][14] . Thereby, for the conjugate polyene molecules, H-(C 2 H 2 ) n -H, the Dn value of the related membership function in the eq.…”

Section: Computational Detailsmentioning

confidence: 99%

“…In the above equation, Y is related to Ψ ρ , and the square of LCAO coefficients is used as the AO criteria in the discussion of MO fuzzy symmetry [12][13][14] , that is: …”

Section: Computational Detailsmentioning

confidence: 99%

“…In our previous papers, some methods [12,13] for studying the fuzzy symmetry feature of molecules and molecular orbitals (MO) were provided. Through these methods, we analyzed the fuzzy symmetry characterization of the static and dynamic molecules [14][15][16][17][18][19] . However, most of them dealt with the fuzzy point symmetry transformation characterization, and in case of the fuzzy space symmetry, only polyyne and its cyanide have been taken as examples to discuss the fuzzy one-dimensional periodic linear molecules [17] .…”

Section: Introductionmentioning

confidence: 99%

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Fuzzy ta/2 symmetries of straight chain conjugate polyene molecules

Xin

et al. 2009

Sci. China Ser. B-Chem.

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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.conjugate polyene, one-dimensional fuzzy periodic transformation, the membership function, irreducible representation component

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Section: Computational Detailsmentioning

confidence: 99%

Section: Computational Detailsmentioning

confidence: 99%

“…In the above equation, Y is related to Ψ ρ , and the square of LCAO coefficients is used as the AO criteria in the discussion of MO fuzzy symmetry [12][13][14] , that is: …”

Section: Computational Detailsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Fuzzy ta/2 symmetries of straight chain conjugate polyene molecules

Xin

et al. 2009

Sci. China Ser. B-Chem.

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“…Where a ρ ( ja, iao) expresses the iaoth atomic orbital of the jath atom. The membership function of ρ -MO about theĜ symmetry transformation is denoted as [12][13][14][15]:…”

Section: Fuzzy Symmetry Calculations Of π -Momentioning

confidence: 99%

Symmetries and fuzzy symmetries of graphene molecules

Xing

Xin

et al. 2012

J Math Chem

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In this paper, we will investigate the fuzzy layer group symmetries of two-dimensional (2D) periodic molecules. Here, we select several graphene molecules as typical examples to discuss. For these two-dimensional graphene molecules, their MO energies, symmetries and fuzzy symmetries are preliminarily studied. In addition, we especially make a detailed comparison between the zigzag and armchair graphene molecules. These studies will develop a theoretical framework that will help us to investigate the fuzzy symmetries of various layer group molecules as well as molecules with 3D periodic structure.

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