π Moleculaire orbitalen van het allylkation en anion

Recall that 1,3-butadiene is a four-carbon conjugated system. In comparison, the allyl cation and anion are three-carbon conjugated systems.

A linear combination of the three unhybridized atomic p orbitals in allylic systems gives three π molecular orbitals.

The lowest energy molecular orbital, ψ₁, is formed by an in-phase overlap of all p orbitals and is entirely bonding.

ψ₂ has one node passing through the central carbon. Since there is no overlap between adjacent carbons, this is a nonbonding orbital and energetically similar to the atomic orbitals.

ψ₃ is entirely antibonding with three out-of-phase p orbitals forming two nodes.

The two π electrons of the allyl cation fill up ψ₁, which becomes the HOMO, making ψ₂ the LUMO.

In comparison, the allyl anion has four π electrons distributed between ψ₁ and ψ₂, where ψ₂ is the HOMO and ψ₃ the LUMO.

Interestingly, in both systems, the charge is concentrated on the end carbons, which agrees with the resonance picture.