Chemistry Reference
In-Depth Information
the molecular plane. We also take
Y
to be in the molecular plane, and so
X
must be per-
pendicular to it. The full labels for the mirror planes of water become
σ
v
(
XZ
) and
σ
v
(
YZ
),
but it is common to omit the Cartesian parts of these labels.
Some molecules have multiple axes and mirror planes. For example, boron trifluoride
(BF
3
) is a planar molecule with a
C
3
axis perpendicular to the plane and passing through
the boron atom, as shown in Figure 1.12. However, there are also
C
2
axes in the plane of
the molecule which run along each of the B
F bonds.
C
3
F
2
F
2
F
2
C
2
F
2
F
3
B
F
3
B
B
F
3
B
F
3
F
1
C
2
F
1
F
1
C
2
F
1
Figure 1.12
The rotational symmetry elements of BF
3
. To the left is a flying wedge drawing
looking from the side of the molecule in the same orientation as the perspective ball-and-
stick model below it. The C
2
axes are shown with the molecule viewed looking down on the
molecular plane.
The highest order axis present is taken to be the principal axis and gives us the 'vertical'
direction. So, BF
3
has three vertical mirror planes, each of which contains a B F bond; an
example of a vertical mirror plane in BF
3
is shown in Figure 1.13a. The
C
3
operations will
move the fluorine atoms between these planes, but each will always contain one fluorine
atom and reflect the other two into one another. So, although there are three vertical planes,
they are identical, requiring only the single label
σ
v
operations. The
plane of the molecule for BF
3
is also a plane of symmetry, as illustrated in Figure 1.13b.
This contains all three of the B F bonds, but not the principal axis. In fact, the plane is
perpendicular to the
C
3
axis, i.e. the plane is horizontal and so is labelled
σ
v
, and there are three
σ
h
.
(a)
(b)
σ
v
σ
h
Figure 1.13
The two types of symmetry plane for BF
3
: (a) an example of a vertical plane;
(b) the horizontal plane
σ
h
.
