The simple two p-orbital overlap scheme can be expanded to conjugated
systems. We start by considering 1,3-butadiene, the simplest conjugated
system. Because 1,3-butadiene has four atomic orbitals, four molecular
orbitals must result. Figure 5.19 shows the atomic and molecular orbitals
of 1,3- butadiene and the corresponding energy levels. Like ethylene, only
the π MO are shown, which result from the overlap between unhybridized
p-orbitals on the carbons. The MOs resulting from s-bonds are not
shown.
The important aspect of Figure 5.19 is the π ! π* transitions. Notice that
the f 2 ! f 3 * transition in 1,3-butadiene is much smaller than the f 1 !
f 2 * transition in ethylene. As the number of p-orbitals increases in a
conjugated system, the energy gap, ΔE, between the HOMO and the
LUMO becomes progressively smaller. Figure 5.20 shows the MO energy
levels of ethylene and the first three conjugated systems: 1,3-butadiene;
1,3,5-hexatriene; and 1,3,5,7-octatetraene. The vertical arrows emphasize
the HOMO–LUMO transitions. Further, the energy difference between the
Antibonding orbital (Ψ 2 *)
C
C
C
C
C
C
Bonding orbital (Ψ 1 )
Atomic orbital (φ 1 )
Atomic orbital (φ 2 )
π π*
Figure 5.18 A partial MO
energy-level diagram for ethylene emphasizing the π
bonding (Ψ 1 ) and antibonding
(Ψ 2 ) MOs. MOs are constructed by the linear combination of the AOs of
ethylene, in this illustration the
unhybridized p-orbitals (ϕ 1 and
ϕ 2 ) on each carbon atom.
The two electrons from each
p-orbital are placed in the
bonding MO (Ψ 1 ). The MOs due
to σ-bonding are not shown.
SIMPLE MODELS DESCRIBING ELECTRONIC STRUCTURE 171