Chemistry Reference
In-Depth Information
Figure 2.11c and d show three-dimensional representations of the two enantiomers ori-
entated to emphasize that they are reflections of one another. If you have a modelling kit
you should construct models of the two enantiomers shown in Figure 2.11c and d and
confirm that they cannot be superimposed on one another.
Inspection of Figure 2.11 should concentrate on carbon 4 (C4), which is at the bottom of
the cyclohexene ring in each diagram. If we move from C4 around the ring in a clockwise
direction, we arrive at C6 after two bonds; this is a saturated (
>
CH
2
) carbon centre. Mov-
ing around the ring in the anticlockwise direction from C4 we arrive at C2, which is a
carbon atom in the double bond of the ring, so that the two sections of the six-carbon ring
either side of C4 are different. The other two substituents on C4 are an isopropyl group
and a hydrogen atom, so that the four substituents on C4 are different to one another. This
is one way of generating a chiral molecule; if a molecule contains one centre that has four
different groups attached, in such away that the four groups are not coplanar, the molecule
will be chiral. Since the chirality in this case arises from the substitution patterns possible
at a single atom, e.g. C4 in our example, the atom which is substituted is called a chiral
centre. Swapping any two of the groups at the chiral centre will give the other enantiomer.
However, for carbon centres, the energy required to swap two groups is usually large and
so if a single enantiomer is created it will be stable and so observable.
The use of symmetry in determining which molecules can be chiral can be discussed
based on the fact that enantiomers are related to one another by reflection. Any object
has only one mirror image; it does not matter where the mirror is positioned to reflect
the object. This immediately tells us that a molecule with a plane of symmetry cannot be
chiral, because we generate an identical molecule when it is reflected in the symmetry
plane and so the molecule must be indistinguishable from its mirror image. In fact, if there
is any symmetry operation that links a molecule with its mirror image, then the molecule
cannot be chiral.
Simple mirror planes are not the only symmetry elements that use reflection. If a
molecule possesses an improper rotation axis, then the reflection through the mirror plane
used in the symmetry operation will also link the mirror images. So any molecule contain-
ing an improper rotation axis as a symmetry element cannot be chiral. Also, since
S
2
2
=
i
,
the inversion centre also precludes chirality.
So, the most general statement for identifying molecules that are chiral is that:
Chiral molecules must belong to a point group without mirror planes, improper rotation
axes or the inversion centre.
2.6 Summary
1. Molecules that can undergo an identical set of operations belong to the same symmetry
point group. The idea of a group is really a mathematical abstraction, and for a set of
operations to form a proper group the following must apply:
