大学化学 >> 2020, Vol. 35 >> Issue (9): 209-213.doi: 10.3866/PKU.DXHX201910004

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立体角在结构化学中的应用

马忠杰()   

  • 收稿日期:2019-10-08 录用日期:2020-02-25 发布日期:2020-03-05
  • 通讯作者: 马忠杰 E-mail:1120192290@bit.edu.cn

Application of Solid Angle in Structural Chemistry

Zhongjie Ma()   

  • Received:2019-10-08 Accepted:2020-02-25 Published:2020-03-05
  • Contact: Zhongjie Ma E-mail:1120192290@bit.edu.cn

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摘要：

使用立体角概念，说明由一种或几种多面体组合，达到三维无隙结构充分必要条件。本文给出常见正多面体、常见阿基米德半正多面体顶角的立体角以及二面角，并结合结构化学实例分析阐述。在空间中须满足各立体角之和等于4π（sr），故通过简单的加和，即可判断无隙堆积的可能性，得知每个点的共用情况，进而推导出空间结构。运用这种方法，可以对一些尚不存在的结构进行大胆的预测。

关键词: 立体角, 多面体, 结构化学

Abstract:

The concept of solid angle is used to explain the necessary and sufficient conditions for a three-dimensional gapless structure to be achieved by combining one or several polyhedrons. In this paper, the solid angle and dihedral angle of the common regular polyhedron and the common Archimedean semi regular polyhedron are presented, and the examples of structural chemistry are analyzed. In space, the sum of solid angles must be equal to 4π(sr), so by simply adding, we can judge the possibility of gapless accumulation, know the common situation of each point, and then deduce the space structure. By using this method, we can predict some structures that do not exist yet.

Key words: Solid angle, Polyhedral, Structural chemistry

MSC2000: 

  • G64