Experimentally, however, it is observed that there is a significant barrier to rotation about the C₂-C₃ bond, and that the entire molecule is planar. In addition, the C₂-C₃ bond is 148 pm long, shorter than a typical carbon-carbon single bond (about 154 pm), though longer than a typical double bond (about 134 pm).

Molecular orbital theory accounts for these observations with the concept of delocalized pi bonds. In this picture, the four 2p atomic orbitals combine mathematically to form four pi molecular orbitals of increasing energy. Two of these – the bonding pi orbitals – are lower in energy than the p atomic orbitals from which they are formed, while two – the antibonding pi* orbitals – are higher in energy.

The lowest energy molecular orbital, pi₁, has only constructive interaction and zero nodes. Higher in energy, but still lower than the isolated p orbitals, the pi₂ orbital has one node but two constructive interactions – thus it is still a bonding orbital overall. Looking at the two antibonding orbitals, pi₃* has two nodes and one constructive interaction, while pi₄* has three nodes and zero constructive interactions.

By the aufbau principle, the four electrons from the isolated 2p_z atomic orbitals are placed in the bonding pi₁ and pi₂ MO’s. Because pi₁ includes constructive interaction between C₂ and C₃, there is a degree, in the 1,3-butadiene molecule, of pi-bonding interaction between these two carbons, which accounts for its shorter length and the barrier to rotation. The valence bond picture of 1,3-butadiene shows the two pi bonds as being isolated from one another, with each pair of pi electrons ‘stuck’ in its own pi bond. However, molecular orbital theory predicts (accurately) that the four pi electrons are to some extent delocalized, or ‘spread out’, over the whole pi system.

1,3-butadiene is the simplest example of a system of conjugated pi bonds. To be considered conjugated, two or more pi bonds must be separated by only one single bond – in other words, there cannot be an intervening sp³-hybridized carbon, because this would break up the overlapping system of parallel p orbitals. In the compound below, for example, the C₁-C₂ and C₃-C₄ double bonds are conjugated, while the C₆-C₇ double bond is isolated from the other two pi bonds by sp³-hybridized C₅.

A very important concept to keep in mind is that there is an inherent thermodynamic stability associated with conjugation. This stability can be measured experimentally by comparing the heat of hydrogenation of two different dienes. (Hydrogenation is a reaction type that we will learn much more about in chapter 15: essentially, it is the process of adding a hydrogen molecule – two protons and two electrons – to a p bond). When the two conjugated double bonds of 1,3-pentadiene are ‘hydrogenated’ to produce pentane, about 225 kJ is released per mole of pentane formed. Compare that to the approximately 250 kJ/mol released when the two isolated double bonds in 1,4-pentadiene are hydrogenated, also forming pentane.

The formation of synthetic polymers from dienes such as 1,3-butadiene and isoprene is discussed in Section 18.5. Synthetic polymers are large molecules made up of smaller repeating units. You are probably somewhat familiar with a number of these polymers; for example, polyethylene, polypropylene, polystyrene and poly(vinyl chloride).

Figure 13.6: Energy diagram for the hydrogenation of 1,3-butadiene (not to scale).

As the hydrogenation of 1,3-butadiene releases less than the predicted amount of energy, the energy content of 1,3-butadiene must be lower than we might have expected. In other words, 1,3-butadiene is more stable than its formula suggests.

The conjugated diene is lower in energy: in other words, it is more stable. In general, conjugated pi bonds are more stable than isolated pi bonds.

Here is an energy diagram comparing different types of bonds with their heats of hydrogenation (per mole) to show relative stability of each molecule (1 kcal = 4.18 kJ).  (The lower the heat of hydrogenation (per pi bond), the more stable the structure is.)

The stabilization of dienes by conjugation is less dramatic than the aromatic stabilization of benzene. Nevertheless, similar resonance and molecular orbital descriptions of conjugation may be written.

Conjugated pi systems can involve oxygen and nitrogen atoms as well as carbon. In the metabolism of fat molecules, some of the key reactions involve alkenes that are conjugated to carbonyl groups.

MO theory is very useful in explaining why organic molecules that contain extended systems of conjugated pi bonds often have distinctive colors. beta-Carotene, the compound responsible for the orange color of carrots, has an extended system of 11 conjugated pi bonds.