16.2d Pi Molecular Orbitals 1,3,5 Hexatriene

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Pi Molecular Orbitals of 1,3,5-Hexatriene

With a single sigma bond separating the pi bonds of 1,3,5-hexatriene it is a conjugated system and some of the pi electron density will be delocalized between each of the C-C bonds, not just those written as double bonds in the Lewis structure.  There are six adjacent carbon atoms involved in the pi system and the combination of a p orbital from each of these six atoms will result in six pi molecular orbitals: ψ1, ψ2, ψ3, ψ4*, ψ5*, and ψ6* (also referred to as π1, π2, π3, π4*, π5*and π6*).

1,3,5-hexatriene pi molecular orbitals

ψ1, ψ2 and ψ3 are bonding molecular orbitals and are occupied in the ground state with ψ3 being the Highest Occupied Molecular Orbital (HOMO).  ψ4*, ψ5*, and ψ6* are antibonding molecular orbitals and are unoccupied in the ground state with ψ4* 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 ψ6* which has 5 vertical nodes.  It should also be pointed out that these vertical nodes are always arranged symmetrically in the molecular orbital diagrams.

ψ6 / π6* - 5
ψ5 / π5* - 4
ψ4 / π4* LUMO 3
ψ3 / π3 HOMO 2
ψ2 / π2 - 1
ψ1 / π1 - 0