16.2c Pi Molecular Orbitals the Allyl System

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Pi Molecular Orbitals of the Allyl System

Whether one speaks of the allyl cation, allyl radical, or allyl anion there are three adjacent carbon atoms involved in the pi system and the combination of a p orbital from each of these three atoms will result in three pi molecular orbitals: ψ1, ψ2, and ψ3*, (also referred to as π1, π2, and π3*).

allyl system pi molecular orbitals

In the allyl system, ψ1 is a bonding molecular orbital, ψ2 is a nonbonding molecular orbital, and ψ3* is an antibonding molecular orbital.  Nonbonding pi molecular orbitals are generally present in conjugated systems with an odd number of atoms.  They will generally be the median molecular orbital from an energy standpoint and electrons in a nonbonding molecular orbital can be thought of as energetically equivalent to nonbonding electrons on a Lewis structure.   This makes them higher energy than bonding electrons and lower energy than antibonding electrons. 

The orbital diagrams will be identical for the ally cation, allyl radical, and allyl anion.  The major difference will be which orbitals are occupied and the identity of the HOMO and LUMO.

The orbitals are arranged in the following table in order of increasing energy.  It can also be seen that the number of vertical nodes in a molecular orbital increases as the energy increases. ψ1 has zero vertical nodes and they increase incrementally until ψ3* which has 2 vertical nodes.  It should also be pointed out that these vertical nodes are always arranged symmetrically in the molecular orbital diagrams.

Pi Molecular Orbitals of the Allyl Cation

The allyl cation has two pi electrons and ψ1 is the Highest Occupied Molecular Orbital (HOMO) and ψ2 is the Lowest Unoccupied Molecular Orbital (LUMO).

allyl cation structure
ψ3 / π3* - 2
ψ2 / π2 LUMO 1
ψ1 / π1 HOMO 0

Pi Molecular Orbitals of the Allyl Radical

The allyl radical has 3 pi electrons.  Some identify ψ2 as the HOMO and ψ3* as the LUMO, while others prefer to use the term SOMO (Singularly Occupied Molecular Orbital) to designate ψ2 instead of using the traditional HOMO/LUMO designations.

allyl radical structure
ψ3 / π3* LUMO 2
ψ2 / π2 HOMO or SOMO 1
ψ1 / π1 - 0

Pi Molecular Orbitals of the Allyl Anion

The allyl anion has four pi electrons and ψ2 is the Highest Occupied Molecular Orbital (HOMO) and ψ3* is the Lowest Unoccupied Molecular Orbital (LUMO).

allyl anion
ψ3 / π3* LUMO 2
ψ2 / π2 HOMO 1
ψ1 / π1 - 0