Drawpictorialrepresentations (as in Figures16-4 and 16-6) for the three bonding MOs and the two nonbonding MOs of cyclooctatetraene. The antibonding MOs are difficult to draw, except for the all-antibonding MO.
(a) Draw the molecular orbitals for the cyclopropenyl case.

(Because there are three p orbitals, there must be three MOs: one all-bonding MO and one degenerate pair of MOs.)
(b) Draw an energy diagram for the cyclopropenyl MOs. (The polygon rule is helpful.) Label each MO as bonding, nonbonding, or antibonding, and add the nonbonding line. Notice that it goes through the approximate average of the MOs.
(c) Add electrons to your energy diagram to show the configuration of the cyclopropenyl cation and the cyclopropenyl anion. Which is aromatic and which is antiaromatic?
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Key Concepts
Molecular Orbitals (MOs)
Aromaticity and Antiaromaticity
Energy Diagrams
Explain why each compound or ion should be aromatic, antiaromatic, or nonaromatic.
(d)
(e)
(f) the [20]annulene dication
One of the following compounds is much more stable than the other two. Classify each as aromatic, antiaromatic, or nonaromatic.
a. Use the polygon rule to draw an energy diagram (as in Figures 16-5 and 16-7) for the MOs of a planar cyclooctatetraenyl system.
b. Fill in the eight pi electrons for cyclooctatetraene. Is this electronic configuration aromatic or antiaromatic? Could the cyclooctatetraene system be aromatic if it gained or lost electrons?
Repeat Problem 16-10 for the cyclopentadienyl ions. Draw one all-bonding MO, then a pair of degenerate MOs, and then a final pair of degenerate MOs. Draw the energy diagram, fill in the electrons, and confirm the electronic configurations of the cyclopentadienyl cation and anion.
Explain why each compound or ion should be aromatic, antiaromatic, or nonaromatic.
(a)
(b)
(c)
