Point Groups

Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 78)


In Sect. 2.2, we considered the symmetry groups of an equilateral triangle and a square as elementary examples of a group. These groups, which consist of rotations and reflections, are called, in general, point groups. Point groups describe the microscopic symmetry of molecules and the macroscopic symmetry of crystals. They are therefore frequently used in studying electronic states and vibrations of molecules as well as the symmetry of the macroscopic properties of crystals. In this chapter, we describe point groups, their notation, and their irreducible representations. Applications to molecules are given in Chaps. 9 and 10.


Irreducible Representation Point Group Mirror Plane Mirror Reflection Symmetry Operation 
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  1. 8.1
    G. Herzberg: Molecular Spectra and Molecular Structure, Vol. 3: Electronic Spectra and Electronic Structure of Polyatomic Molecules (Van Nostrand, New York 1966) 9.1Google Scholar

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© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  1. 1.Japan Women’s UniversityBunkyo-ku, Tokyo 112Japan
  2. 2.Department of Physics, School of Science and TechnologyMeiji UniversityTama-ku, Kawasaki 214Japan

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