Page 731 - Advanced Organic Chemistry Part A - Structure and Mechanisms, 5th ed (2007) - Carey _ Sundberg

714 3 4 5
α – 2β α – 1.62β
CHAPTER 8 α – β
α
Aromaticity α + 0.62β
α + 2β α + 2β α + 2β
6 7
α – 2β α – 1.80β
α – β
α – 0.45β
α + β α + 1.25β
α + 2β α + 2β

8 9
α – 2β α – 1.87β
α – 1.41β α – β
α
α + 1.41β α + 0.35β
α + 1.53β
α + 2β α + 2β
Fig. 8.1. HMO energies for conjugated planar ring systems
of three to nine carbon atoms.

destabilize the molecule. The dramatic difference in properties of cyclobutadiene
(extremely unstable) and benzene (very stable) are explicable in terms of these HMO
diagrams.
α – 2β α – 2β
α – β
α
α + β
α + 2β α + 2β
cyclobutadiene benzene
E = 4α + 4β E = 6α + 8β
Cyclobutadiene has two bonding electrons, but the other two electrons are
unpaired because of the degeneracy of the two nonbonding orbitals. The two electrons
in the nonbonding levels do not contribute to the stabilization of the molecule. The
total HMO energy is 4 + 4 , which is the same as for two isolated double bonds.
Furthermore, as these electrons occupy a high-energy orbital, they are particularly
available for chemical reactions. As we shall see shortly, experimental evidence
indicates that cyclobutadiene is rectangular rather than square. This modifies somewhat
the orbital picture from the simple HMO pattern, which applies to a square geometry.
The two nonbonding levels are no longer degenerate, so cyclobutadiene is not predicted
to have unpaired electrons. Nevertheless, higher-level calculations agree with the
Hückel concept in predicting cyclobutadiene to be an extremely unstable molecule
with a high-lying HOMO. We will see that several methods of analysis indicate that
cyclobutadiene is not only highly reactive, but is also less stable than an isolated diene.
Cyclobutadiene is called antiaromatic. 2
Simple Hückel calculations on benzene, in contrast, place all the electrons
in bonding MOs. The -electron energy of the benzene molecule is calculated by
2
R. Breslow, Acc. Chem. Res., 6, 393 (1973).