The Point Groups Used with Molecules - Molecular Symmetry - page 49

and so do not generate any images. The resulting six-point object has C s symmetry. It is
not the simplest case; we could have chosen a plane containing three of the points for
example, but it illustrates the relationship between the new structure and the C 1 object we
used as the starting point.
The third nonaxial group contains only the identity operator and inversion centre i , and
this point group is given the symbol C i . An example of a C i object generated from the
C 1 structure of Figure 3.3a is shown in Figure 3.3c. We have chosen to place the inversion
centre at the top right point in the generating structure, and so this point occurs only once in
the resulting object. The other three points generate new positions in the C i object through
the action of the inversion operation. Each of these pairs of points would hold an atom of
the same chemical element, and it is an arbitrary choice which we consider as the 'original'
and which the 'generated' point.

3.4.1 Examples of Molecules for the Nonaxial Groups: C s , C i , C 1
There are many molecules that conform to the C s point group; for example, dichloroflu-
oromethane (Figure 3.4a) and secondary amines such as N(CH 3 ) 2 H (Figure 3.4b). More
complex examples include tropinone, Figure 3.4c and d, which is a natural product used

(a)

(b)

F

σ h σ h

N

H 3 C

Cl

H

H

H 3 C
dimethylamine

C s

C s

Cl

dichlorofluoromethane

(c) (d)

O N

C s

tropinone

(e)

OH

O

C 1

σ h N

O

atropine

Figure 3.4 Example molecules conforming to the nonaxial group C s ; each molecule has only
a mirror plane and E as symmetry element. Tropinone, structure (c), is shown as a three-
dimensional model in (d) and is a precursor to the C 1 (only symmetry element E) molecule
shown as (e).