π Molecular Orbitals of the Allyl Radical

Just like the allyl cation and anion, the allyl radical is a three-atom conjugated system.

The molecular orbital framework is identical to that of the ions, with a node passing through the central carbon in ψ₂ and between the carbons in ψ3.

However, the difference lies in the number of π electrons.

Recall that the allyl cation has two π electrons occupying the lowest energy bonding orbital, ψ₁. The anion has four π electrons distributed between the ψ₁ and ψ₂ orbitals.

In comparison, the radical has three π electrons. The first two electrons occupy ψ₁, and the third ψ₂, also called a singly occupied molecular orbital, SOMO.

Notice that the HOMO and LUMO are different for the allyl system.

Much like the ions, the molecular orbital representation of the radical agrees with the resonance picture suggesting that the unpaired electron is delocalized over the three atoms with the electron density concentrated at the terminal carbons.

Consequently, the ions and radicals react at the terminal carbons and are more stable than comparable alkyl counterparts.