π Molecular Orbitals of 1,3-Butadiene

1,3-butadiene is a four-carbon conjugated system where each carbon is sp2-hybridized with an unhybridized p orbital containing one electron. These four p orbitals combine to form four π molecular orbitals: two bonding (ψ1 and ψ2) and two antibonding (ψ3 and ψ4). The four π electrons occupy the two lowest-energy bonding orbitals.

In ψ1, the lowest-energy molecular orbital, all four p orbitals overlap in-phase, creating bonding interactions between all adjacent carbons. This continuous π system explains the partial double-bond character of the C2–C3 bond and the stabilization gained from electron delocalization throughout the conjugated system.

A node is a region of zero electron density where no bonding interaction occurs between atoms. In ψ2, an out-of-phase overlap between C2 and C3 creates one node. As molecular orbital energy increases from ψ1 to ψ4, the number of nodes increases incrementally, and bonding interactions decrease correspondingly.

The four π electrons in 1,3-butadiene occupy the two lowest-energy bonding molecular orbitals, ψ1 and ψ2, following the aufbau principle. ψ2 is the highest occupied molecular orbital (HOMO), while ψ3 is the lowest unoccupied molecular orbital (LUMO), making these frontier orbitals critical for reactivity in cycloaddition reactions.

Conjugated dienes like 1,3-butadiene have lower heats of hydrogenation than isolated or cumulated dienes, indicating greater stability. This enhanced stabilization results from electron delocalization across the continuous π system formed by in-phase overlap of all four p orbitals, distributing electron density and lowering overall energy.

Molecular orbital energy increases directly with the number of nodes. ψ1 has zero nodes and lowest energy, ψ2 has one node, ψ3 has two nodes, and ψ4 has three nodes with highest energy. This relationship reflects decreased bonding character and increased antibonding character as energy increases.

According to molecular orbital theory, the number of molecular orbitals formed equals the number of atomic orbitals combined. Since 1,3-butadiene has four sp2-hybridized carbons, each contributing one unhybridized p orbital, a linear combination produces exactly four π molecular orbitals with distinct energies and bonding characteristics.