10.4 Stability of the Allyl Radical: Resonance Revisited

Stability and Reactivity of the Allyl Radical

Stability of the allyl radical

The allyl radical is unusually stable because its unpaired electron isn't stuck on one carbon. Instead, it spreads across a conjugated π system of three sp2-hybridized carbons. This delocalization lowers the radical's energy significantly compared to a localized radical.

• Two resonance structures can be drawn for the allyl radical, placing the unpaired electron on either terminal carbon
  • The true structure is a hybrid of these two forms, with the radical character shared equally between the two end carbons
• Overlap of the three 2p orbitals (one on each carbon) creates this conjugated system
  • All three 2p orbitals must be parallel for effective overlap, so all three carbons are sp2-hybridized and the system is planar
• Resonance stabilization energy is estimated at ~14–16 kcal/mol relative to a comparable non-conjugated radical
  • This is measured by comparing bond dissociation energies: breaking an allylic C–H bond requires less energy than breaking a comparable primary C–H bond

Note the distinction: the allyl radical is a three-carbon system ($\text{CH}_2\text{=CH–CH}_2\cdot$), not 1,3-butadiene. Butadiene is a four-carbon conjugated diene and a different species entirely.

Electron delocalization in the allyl radical

Molecular orbital (MO) theory gives a more complete picture than resonance structures alone. The three parallel 2p orbitals on the allyl system combine to form three molecular orbitals:

1. Bonding MO ($\psi_1$): Lowest energy. All three 2p orbitals have constructive overlap. Electron density is spread across all three carbons.
2. Non-bonding MO ($\psi_2$): Intermediate energy. There is a node at the central carbon, so electron density sits only on the two terminal carbons.
3. Antibonding MO ($\psi_3$): Highest energy. Nodes between each pair of adjacent carbons. This orbital is empty in the allyl radical.

The allyl radical has three π electrons total. Two fill $\psi_1$ and the third (the unpaired electron) occupies $\psi_2$. Because $\psi_2$ has a node at the central carbon, the unpaired electron density is distributed equally between the two terminal carbons. This matches what the resonance structures predict: the central carbon carries no radical character, while each terminal carbon carries half.

This even distribution of electron density is why bromination of an allyl radical can occur at either end of the system.

Products of allylic bromination

Allylic bromination (typically using NBS as the bromine source) proceeds through an allylic radical intermediate. Because the radical is delocalized, bromine can bond to either terminal carbon of the allyl system, often giving a mixture of products.

Symmetric allyl radicals produce only one product. For example, allylic bromination of propene generates a symmetric allyl radical, so attack at either end gives the same compound (3-bromopropene).

Unsymmetric allyl radicals produce two different products. The ratio depends on the relative stability of the radical at each end:

• Tertiary radical character > secondary > primary (same stability order as for carbocations and other radicals)
• The more substituted end of the allyl system bears more of the radical character, and bromine adds preferentially to that position

For example, allylic bromination of 2-butene generates an allyl radical where one resonance form places the radical on a secondary carbon and the other on a primary carbon. The secondary radical is more stable, so the product from bromine adding to the secondary position (1-bromo-2-butene) is favored over the primary product (3-bromo-1-butene).

A larger stability gap between the two resonance forms leads to a more skewed product ratio. When one end is tertiary and the other is primary, you'll see a strong preference for the product arising from the tertiary radical.

Factors affecting radical stability

Three effects work together to stabilize radicals. They all share a common theme: spreading out the unpaired electron.

• Conjugation: An unpaired electron adjacent to a π system can delocalize into that system. The more extended the conjugation, the greater the stabilization. This is exactly why the allyl radical is more stable than an isolated primary radical.
• Hyperconjugation: Alkyl groups adjacent to a radical center stabilize it through overlap of their C–H (or C–C) σ bonds with the half-filled p orbital. This is why tertiary radicals are more stable than secondary, which are more stable than primary: more adjacent σ bonds means more hyperconjugative stabilization.
• Delocalization (general): Any mechanism that spreads unpaired electron density over more atoms lowers the system's energy. Conjugation and hyperconjugation are both specific types of delocalization.

The overall radical stability order to remember: