π Molecular Orbitals of the Allyl Radical

An allyl radical contains three π electrons distributed across its three molecular orbitals. The first two electrons occupy ψ1, the lowest energy bonding orbital, while the third electron occupies ψ2, a singly occupied molecular orbital (SOMO). This three-electron configuration distinguishes the radical from the allyl cation, which has two electrons, and the allyl anion, which has four electrons.

A SOMO (singly occupied molecular orbital) is a molecular orbital containing exactly one unpaired electron. In allyl radicals, ψ2 functions as the SOMO because it holds the third π electron. The SOMO is also the highest occupied molecular orbital (HOMO) in the radical system, making it crucial for understanding the radical's reactivity and electronic structure.

All three allyl systems—cation, anion, and radical—share identical molecular orbital frameworks with nodes passing through the central carbon in ψ2 and between carbons in ψ3. The key difference lies in electron occupancy: the cation has two π electrons in ψ1, the radical has three electrons distributed between ψ1 and ψ2, and the anion has four electrons filling both ψ1 and ψ2. This variation affects their HOMO-LUMO characteristics.

Allyl radicals are more stable than alkyl radicals because the unpaired electron is delocalized across all three carbons of the conjugated system, with electron density concentrated at the terminal carbons. This delocalization, confirmed by both molecular orbital theory and resonance structures, distributes the radical character and reduces the energy penalty of having an unpaired electron.

Allyl radicals react primarily at the terminal carbons, not the central carbon. This regioselectivity arises because the unpaired electron density is concentrated at the terminal positions due to the delocalization of the third π electron across the conjugated system. The molecular orbital representation and resonance structures both support this terminal carbon reactivity pattern.

In allyl radicals, the HOMO and LUMO are different orbitals: ψ2 (the SOMO) is the HOMO, while ψ3 is the LUMO. In contrast, allyl cations and anions have different HOMO-LUMO pairs because their electron occupancy differs. This distinction affects how allyl radicals participate in molecular orbital-based reactions and their reactivity patterns.

Allyl radicals form as intermediates during halogenation of alkenes when a halogen adds to the allylic carbon rather than the double bond itself. The three sp2-hybridized carbons in the allyl system each contribute an unhybridized p orbital that combines to form the three π molecular orbitals characteristic of the allyl radical intermediate.