Axes and centres of symmetry

The fact that the three compounds we have just introduced (along with Feist s acid in the box on p. 319) were chiral might have surprised you, because at first glance they do look quite symmetrical. In fact, they do all have an element of symmetry, and it is only one which is compatible with chirality an axis of symmetry. If a molecule can be rotated through 180° about an axis to give exactly the same structure then it has twofold axial symmetry, or C2 symmetry. Compounds with an axis of symmetry will still be chiral, provided they lack either a plane or a centre of symmetry. 

So far we have used a plane of symmetry as the defining characteristic of an achiral molecule we have said several times that a molecule is chiral if it lacks a plane of symmetry. We are now 

The syn diastereoisomer has no plane of symmetry but you should be able to spot a C2 axis of symmetry running straight through the middle of the ring. The axis is compatible with chirality of course. In this compound both chiral centres are S and it has an enantiomer where both are R. 

The anti diastereoisomer has no plane of symmetry, nor does it have an axis. Instead it has a centre of symmetry. This is marked with a black dot in the middle of the molecule and means that if you go in any direction from this centre and meet, say, an R group, you will meet the same thing if you go in the opposite direction (green arrows). The same thing applies to the brown arrows and, of course, to the ring itself. There is no centre of symmetry in the syn isomer as the green or brown arrows would point to R on one side and H on the other. The anti isomer is superimposable on its mirror image and is achiral. 

---

Recognize the presence of planes, axes and centres of symmetry in a given molecule or object. (Questions 6.1-6.3 and 6.5-6.8)... 

---