The Model of a Supermolecule with Dodecahedral Symmetry

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  • 正十二面体対称性を有する超分子の分子モデル
  • セイ 12メンタイ タイショウセイ オ ユウスル チョウブンシ ノ ブンシ モデル

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Abstract

The molecule given in Figure 2 shows dodecahedral symmetry. It is constructed with a symmetrically unique structure (Figure 3) which resides on the edge of the virtual dodecahedral skeleton. In order to generate all the coordinates, a symmetrically unique fragment structure is rotationally transformed in three ways : (1) 72 degree about z-axis, (2) 180 degree about y-axis and (3) 2φ about y-axis, where 2φ is the angle between two normals which run through the center of the two juxtaposing faces. In order to generate all the connectivity from the fragment structure, the numbering of the whole molecule should be expressed with a parameter related to the number of atoms in the fragment structure. In general, the fragment structure can be expressed as in Figure 4 and the numbering of all the atoms can be expressed with a parameter n (= k-2). This parametrization of the numbering made it possible to generate all the connectivity required for the construction of the dodecahedral structure.<BR>A newly developed program was written in a script language, Perl. It takes the structural data of a fragment as an input and generates the structural data of the corresponding dodecahedronic molecule. This program is useful especially when the fragment structure contains a hydrogen bond or coordination bond. For such a molecule, molecular mechanics or the molecular orbital method cannot be fully utilized for the construction of the model.

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