16.4:
π Molecular Orbitals of the Allyl Cation and Anion
Recall that 1,3-butadiene is a four-carbon conjugated system. In comparison, the allyl cation and anion are three-carbon conjugated systems.
A linear combination of the three unhybridized atomic p orbitals in allylic systems gives three π molecular orbitals.
The lowest energy molecular orbital, ψ1, is formed by an in-phase overlap of all p orbitals and is entirely bonding.
ψ2 has one node passing through the central carbon. Since there is no overlap between adjacent carbons, this is a nonbonding orbital and energetically similar to the atomic orbitals.
ψ3 is entirely antibonding with three out-of-phase p orbitals forming two nodes.
The two π electrons of the allyl cation fill up ψ1, which becomes the HOMO, making ψ2 the LUMO.
In comparison, the allyl anion has four π electrons distributed between ψ1 and ψ2, where ψ2 is the HOMO and ψ3 the LUMO.
Interestingly, in both systems, the charge is concentrated on the end carbons, which agrees with the resonance picture.
16.4:
π Molecular Orbitals of the Allyl Cation and Anion
An allyl group is a three-carbon conjugated system where the sp³-hybridized allylic carbon is bonded to a CH=CH2 group via a single bond. Allyl anions can be obtained by treating propene with a strong base that can deprotonate methyl groups. Allyl cations are formed as intermediates during substitution reactions involving allylic halides. In both cases, the hybridization of the allylic carbon changes from sp3 to sp2, giving rise to a carbon chain with three sp2-hybridized carbons, each with an unhybridized p orbital.
A linear combination of the three atomic p orbitals gives three molecular orbitals, ψ1, ψ2, and ψ3. ψ1 is the bonding molecular orbital, ψ2 is a nonbonding orbital characterized by a node passing through the central carbon, whereas ψ3 is an antibonding molecular orbital with two nodes. The molecular orbital frameworks of the allyl anion and cation are identical and differ only in the number of π electrons. The allyl cation has two π electrons in ψ1, whereas the allyl anion has four π electrons distributed between ψ1 and ψ2.
