π Molecular Orbitals of the Allyl Radical

Allyl radicals are three-carbon conjugated systems. They are readily formed as intermediates in halogenation reactions of alkenes involving the addition of halogen to the allylic carbon instead of the double bond. As seen in allyl cations and anions, each of the three sp²-hybridized carbon atoms in allyl radicals has an unhybridized p orbital. These orbitals combine to give three π molecular orbitals.

The allyl systems have identical molecular orbitals but differ in the number of π electrons. While the allyl cations and anions have two and four π electrons, respectively, allyl radicals are systems with three π electrons. Irrespective of the ion or the radical, the first two electrons occupy the bonding molecular orbital, ψ₁. The difference arises in the electron occupancy of the nonbonding molecular orbital, ψ₂, which is unoccupied in the allyl cation, singly occupied in the radical, and fully occupied in the anion. Accordingly, the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) vary across the allyl system. Since the HOMO in allyl radicals is singly occupied, it is also referred to as the singly occupied molecular orbital, or SOMO, as shown below.