Chapter 10: Conjugation in Alkadienes and Allylic Systems

p Molecular Orbitals of 1,3-Butadiene

• 1,3-Butadiene contains two conjugated double bonds.
• It is built from 4 sp² hybridsed C atoms, each contributing a p orbital containing 1 electron.
• An alternative way to consider "building" the p molecular orbitals is by combining the p molecular orbitals of two ethene molecules.
• This requires that we make an in-phase and an out-of-phase combination for both the p and p* of ethene.
• Either way, we end up with 4 molecular orbitals.

• Notice how the number of nodes and the number of anti-bonding interactions increases as you go up the diagram above.

The diagram to the right shows the relative energies of the p molecular orbitals of 1,3-butadiene (derived from ethene) and the electron configuration.  The horizontal center line denotes the energy of a C atomic p orbital. Orbitals below that line are bonding those above are anti-bonding. We now have 4 electrons to arrange, 1 from each of the original atomic p orbitals. These are all paired in the two stabilized p bonding orbitals, p1 and p2.  The highest occupied molecular orbital or HOMO is p2 in 1,3-butadiene (or any simple conjugated diene). In contrast, the anti-bonding p* orbitals contain no electrons. The lowest unoccupied orbital or LUMO  is p3 in 1,3-butadiene (or any simple conjugated diene).

The relative energies of these orbitals can be accounted for by counting the number of bonding and anti-bonding interactions in each:

• p1 has bonding interactions between C1-C2, C2-C3 and C3-C4
• Overall = 3 bonding interactions
• p2 has bonding interactions between C1-C2 and C3-C4 but anti-bonding between C2-C3
• Overall = 1 bonding interaction
• p3 has bonding interactions between C2-C3 but anti-bonding between C1-C2 and C3-C4
• Overall = 1 anti-bonding interaction
• p4 has anti-bonding interactions between C1-C2, C2-C3 and C3-C4
• Overall = 3 anti-bonding interactions