Planar molecules, permutational symmetry

Planar molecules, permutational symmetry electronic wave function, 681-682 rotational wave function, 685-687 vibrational wave function, 687-692... 

In this particular case, the point group can be described as a set of permutations of the labels 0,1,2,3 of the comers of the tetrahedron or as symmetry operations of this polyhedron. However, we should carefully note that the representation of symmetry operations as permutations of comers, or atoms, is not generally unique. For example, in the case of a planar molecule both the reflection in the plane and the identity mapping are represented by the identity permutation, although they are different symmetry operations. consists of all 24 permutations of the corners of the tetrahedron,... 

The other two principal planar moments and expressions for b and c are given by cyclic permutations of a, b, c. Equations of the form of Eq. (11) are known as the Kraitchman equations. Special cases arise for molecules with various symmetry elements. For substitution of an atom in a linear molecule, the magnitude of the a coordinate of the substituted atom is... 

As a first example, we shall discuss (Figure 3, Thble 1) the benzene molecule (planar regular hexagcm) which has 12 symmetry operations (expressed as cyclic permutations). 

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