π Molecular Orbitals of the Allyl Cation and Anion

Three molecular orbitals form from a linear combination of the three unhybridized atomic p orbitals in allylic systems. These are designated ψ1, ψ2, and ψ3, each with distinct bonding characteristics and energy levels that determine electron distribution in allyl cations and anions.

ψ1 is entirely bonding with in-phase p orbital overlap. ψ2 is nonbonding with a node through the central carbon and no adjacent orbital overlap. ψ3 is entirely antibonding with out-of-phase p orbitals forming two nodes. These orbital types determine electron stability and reactivity in allyl species.

The allyl cation has two π electrons filling ψ1, making ψ1 the HOMO and ψ2 the LUMO. The allyl anion has four π electrons distributed between ψ1 and ψ2, with ψ2 as the HOMO and ψ3 as the LUMO. Despite different electron counts, both systems share identical molecular orbital frameworks.

Charge concentration on end carbons reflects the molecular orbital electron distribution. In both cations and anions, the central carbon's p orbital contributes minimally to charge density due to the nonbonding nature of ψ2, which has a node at that position, leaving positive or negative charge localized at the terminal carbons.

The sp³-hybridized allylic carbon in propene converts to sp² hybridization when an allyl cation or anion forms. This change generates three sp²-hybridized carbons, each with an unhybridized p orbital available for π bonding and molecular orbital formation in the conjugated system.

Allyl cations form as intermediates during substitution reactions involving allylic halides. Allyl anions are obtained by treating propene with a strong base that deprotonates methyl groups. Both processes create three-carbon conjugated systems with sp² hybridization and pi molecular orbitals available for bonding.

The allyl cation and anion are three-carbon conjugated systems, while 1,3-butadiene is a four-carbon conjugated system. Both involve linear combinations of unhybridized p orbitals to form molecular orbitals, but allyl systems have three π molecular orbitals compared to butadiene's four, affecting their electronic properties and reactivity.