Chapter 10: Conjugation in Alkadienes and Allylic Systems

π Molecular Orbitals of 1,3-Butadiene

• 1,3-Butadiene contains two double bonds that are conjugated.
  
• It is "built" from 4 sp² hybridsed C atoms, each contributing a p atomic orbital containing 1 electron.
• An alternative way to consider "building" the π molecular orbitals is by combining the π molecular orbitals of two ethene molecules.
• This requires that we make an in-phase and an out-of-phase combination for both the π and π* of ethene.
• Either way, we end up with the same set of 4 π 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 π 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 stabilised pi bonding orbitals, π1 and π2.  The highest occupied molecular orbital or HOMO is π2 in 1,3-butadiene (or any simple conjugated diene). In contrast, the anti-bonding π* orbitals contain no electrons. The lowest unoccupied orbital or LUMO  is π3 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:

• π1 has bonding interactions between C1-C2, C2-C3 and C3-C4
• Overall = 3 bonding interactions
• π2 has bonding interactions between C1-C2 and C3-C4 but anti-bonding between C2-C3
• Overall = 1 bonding interaction
• π3 has bonding interactions between C2-C3 but anti-bonding between C1-C2 and C3-C4
• Overall = 1 anti-bonding interaction
• π4 has anti-bonding interactions between C1-C2, C2-C3 and C3-C4
• Overall = 3 anti-bonding interactions

© Dr. Ian Hunt, Department of Chemistry