16.2a Pi Molecular Orbitals 1,3-Butadiene
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Pi Molecular Orbitals
For drawing the pi molecular orbitals for a given pi system it is important to remember the following:
- The number of pi molecular orbitals is equal to the number of atoms contributing a p orbital to the pi system.
- The lowest pi molecular orbital will have zero vertical nodes. Each successive pi molecular orbital as energy increases will have one additional vertical node.
- The Highest Occupied Molecular Orbital or HOMO is the highest energy pi molecular orbital that has any electrons in it. It gets a special name as part of the Frontier Molecular Orbitals as the electrons in this orbital are the most likely to be donated if/when the molecule as a nucleophile.
- The Lowest Unoccupied Molecular Orbital or LUMO is the lowest energy empty pi molecular orbital. It gets a special name as part of the Frontier Molecular Orbitals as this orbital is the most likely to accept electrons if/when the molecule acts as an electrophile.
Pi Molecular Orbitals of Ethylene
In ethylene there are two adjacent carbon atoms involved in the pi system and the combination of a p orbital from each of these atoms will result in two pi molecular orbitals: ψ1 and ψ2*, (also referred to as π1 and π2*).
ψ1 is a bonding molecular orbital, is occupied in the ground state, and is the Highest Occupied Molecular Orbital (HOMO). ψ2* is an antibonding molecular orbital, is unoccupied in the ground state, and is the Lowest Unoccupied Molecular Orbital (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 ψ2* has 1 vertical node. It should also be pointed out that these vertical nodes are always arranged symmetrically in the molecular orbital diagrams which will become more evident with larger pi systems.
| ψ2* / π2* |  | HOMO | 1 |
| ψ1 / π1 |  | - | 0 |
Pi Molecular Orbitals of 1,3-Butadiene
With a single sigma bond separating the pi bonds of 1,3-butadiene it is a conjugated system and some of the pi electron density will be delocalized between carbons 2 and 3 rather than just between 1 and 2 and 3 and 4. There are four adjacent carbon atoms involved in the pi system and the combination of a p orbital from each of these atoms will result in four pi molecular orbitals: ψ1, ψ2, ψ3*, and ψ4* (also referred to as π1, π2, π3*, and π4*).
ψ1 and ψ2 are bonding molecular orbitals and are occupied in the ground state with ψ2 being the Highest Occupied Molecular Orbital (HOMO). ψ3* and ψ4* are antibonding molecular orbitals and are unoccupied in the ground state with ψ3* being the Lowest Unoccupied Molecular Orbital (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 ψ4* which has 3 vertical nodes. It should also be pointed out that these vertical nodes are always arranged symmetrically in the molecular orbital diagrams.
| ψ4 / π4* |  | - | 3 |
| ψ3 / π3* |  | LUMO | 2 |
| ψ2 / π2 |  | HOMO | 1 |
| ψ1 / π1 |  | - | 0 |
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