π Molecular Orbitals of 1,3-Butadiene

1,3-Butadiene is a conjugated system with four sp² hybridized carbons, each with an unhybridized p orbital containing one electron.

A linear combination of the four unhybridized atomic p orbitals gives rise to four π molecular orbitals, two bonding and two antibonding.

The four π electrons occupy the two lowest molecular orbitals, ψ₁ and ψ₂.

ψ₂ is the highest occupied molecular orbital or HOMO, and ψ₃ is the lowest unoccupied molecular orbital or LUMO.

Notice that ψ₁ is formed by an in-phase overlap of all four p orbitals leading to bonding interactions between all adjacent carbons. This explains the partial double-bond character of the C2–C3 bond and the stabilization gained from electron delocalization.

In ψ₂, the out-of-phase overlap between C2 and C3 gives rise to a node, a region of zero electron density with no bonding interaction.

As the energy of the molecular orbitals increases from ψ₁ to ψ₄, the number of nodes increases incrementally, and the bonding interaction decreases.