To end this chapter, we deal with one more question which MOs allow us to answer: how flexible is a molecule? The answer depends on the molecule of course, but more importantly it depends on the type of bond. You may be aware that many alkenes can exist in two forms, cis and trans, also called Z and E (see Chapter 17). These two forms are not usually easy to inter convert—in other words the C=C double bond is very rigid and cannot rotate. If we look at the bonding in but-2-ene we can see why. The π bond is made up of two parallel p orbitals. To rotate about the π bond requires those orbitals to lose their interaction, pass through a state in which they lie perpendicular, and finally line up again. That transitional, perpendicular state is very unfavorable because all of the energy gained through π bonding is lost. Alkenes are rigid and do not rotate.

Compare that situation with butane. Rotating about the middle bond doesn’t break any bonds because the σ bond is, by defi nition, cylindrically symmetrical. Atoms connected only by a σ bond are therefore considered to be rotationally free, and the two ends of butane can spin relative to one another.

The same comparison works for ethylene (ethene) and ethane: in ethylene all the atoms lie in a plane, enforced by the need for overlap between the p orbitals. But in ethane, the two ends of the molecule spin freely. This difference in rigidity has important consequences throughout chemistry, and we will come back to it in more detail in Chapter 16.