Chemistry Reference
In-Depth Information
(a)
H
H
CCC
H
H
σ
d
D
2d
C
2
′
C
2
′
σ
d
C
2
&
S
4
D
5d
(b)
Fe
Fe
C
2
σ
d
σ
d
C
2
C
2
σ
d
C
2
C
5
&
S
10
C
2
σ
d
σ
d
Figure 3.21
Example molecules belonging to D
n
d
point groups (a) propa-1,2-diene, D
2d
,
(b) ferrocene, D
5d
.
The axial symmetry elements for ferrocene are shown in Figure 3.21b along with the
dihedral mirror planes. Since the principal axis in this case is
C
5
, ferrocene belongs to the
D
5d
point group.
It should be noted that if any of our example molecules had a slightly different 'twist'
along the principal axis, then the dihedral mirror planes would no longer be valid and the
symmetry would be reduced to
D
n
.
Molecules in
D
n
h
point groups are shown in Figure 3.22. Ethene is a classic exam-
ple of
D
2h
symmetry, and the
C
2
axes and mirror planes are overlaid on this molecule in
Figure 3.22a. This group contains only
C
2
axes, and none has the collinear
S
4
axis we used
to identify the principal axis in the
D
2d
example. Hence, the designation of the vertical
direction for the ethene molecule is an arbitrary choice from the three possibilities. This
is recognized in the headings of the character table by assigning each of the
C
2
axes to a
Cartesian axis direction,
X
,
Y
or
Z
, rather than giving one a higher priority than the other
two. The usual convention with planar molecules, when such ambiguity arises, is to set
Z
perpendicular to the molecular plane and then
X
and
Y
are set as shown in Figure 3.22a.
Labelling of the mirror planes follows the same convention and all planes and axes meet
at a central point, which is the site of an inversion centre.
