16.5:
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.
16.5:
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.
