Chemistry Reference
In-Depth Information
as a precursor for the production of the
C
1
molecule atropine, Figure 3.4e. Atropine is an
auxiliary drug used in anaesthesia to control secretions by the salivary and gastric glands
during operations on these areas of the body.
If a molecule has only an inversion centre present it has
C
i
symmetry. Examples of
this point group are less common, but substituted ethanes such as (1
S
,2
R
)-1,2-dichloro-
1,2-difluoroethane (Figure 3.5a) can take on conformations with
C
i
symmetry, and some
bimetallic complexes, such as the general structure shown in Figure 3.5b, also fall into this
classification.
(a)
(b)
Cl
H
X
L
F
L
X
X
i
M
M
i
C
i
X
L
F
X
H
X
C
i
L
Cl
(1
S
,2
R
)-1,2-dichloro-1,2-difluoroethane
Figure 3.5
Molecular structures with C
i
symmetry: (a) a particular conformation of (1S,2R)-
1,2-dichloro-1,2-difluoroethane; (b) a bridged transition metal complex shown with nonspe-
cific metal centre M and ligand L,X labels.
3.5 The Cyclic Groups:
C
n
,
S
n
Cyclic groups contain only operations derived from the repeated application of a single
rotational symmetry operation. The point group is
C
n
if the repeated operation is a simple
rotation, and we have the point group
S
n
if it is an improper rotation axis. In both cases the
subscript denotes the order of the axis.
All the operations in a cyclic group commute with one another, because a product of two
operations can easily be written as the root operation applied multiple times. For example:
C
n
m
C
n
l
=
C
n
m
+
l
=
C
n
l
C
n
m
(3.1)
A group with this property is termed Abelian.
C
2
, the simplest of the
C
n
groups, is another example in which there is only a single
operation other than
E
present, since
C
2
is its own inverse.
For groups containing axes we will use a group order of 4 to generate our typical objects.
The
C
4
example is shown in Figure 3.6a and the
S
4
object is shown in Figure 3.6b. The
identification convention for the points introduced for the earlier examples is also used
here. However, the points are arranged so that the light and dark grey shaded ones are on
the symmetry axis and the black and white points are not. Since the points on the axis are
not affected by the rotation operation, the grey points do not generate any new images.
However, the black and white points form sets of four points: the initial one (marked 1
in Figure 3.6a) and three symmetry images that correspond to the
C
4
1
,
C
2
=
C
4
2
and
C
4
3
operations which define the columns of the character table (Figure 3.7a). The
C
4
1
, rotation
by 90
◦
clockwise, and
C
4
3
, rotation by 90
◦
anticlockwise, turn out to have equivalent effects
