The Molecular Orbitals of Benzene

Cyclobutadiene has never been isolated and purified. It undergoes an extremely fast Diels-Alder dimerization. To avoid the Diels-Alder reaction, cyclobutadiene has been prepared at low concentrations in the gas phase and as individual molecules trapped in frozen argon at low temperatures. This is not the behavior we expect from a molecule with exceptional stability  

In 1911, Richard Willstatter synthesized cyclooctatetraene and found that it reacts like a normal polyene. Bromine adds readily to cyclooctatetraene, and permanganate oxidizes its double bonds. This evidence shows that cyclooctatetraene is much less stable than benzene. In fact, structural studies have shown that cyclooctatetraene is not planar. It is most stable in a tub conformation, with poor overlap between adjacent pi bonds. 

Show the product of the Diels-Alder dimerization of cyclobutadiene. (This reaction is similar to the dimerization of cyclopentadiene, discussed in Section 15-11.) 

Visualizing benzene as a resonance hybrid of two Kekule structures cannot fully explain the unusual stability of the aromatic ring. As we have seen with other conjugated systems, molecular orbital theory provides the key to understanding aromaticity and predicting which compounds will have the stability of an aromatic system. 

Cyclobutadiene and cyclooctatetraene have alternating single and double bonds similar to those of benzene. These compounds were mistakenly expected to be aromatic. 

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Example 6.2-1 This example discusses the molecular orbitals of benzene.The numbering system used for the atoms is shown in Figure 6.3. The point group of benzene is... 

Figure 6.4. Energy-level diagram for the molecular orbitals of benzene evaluated in the Huckel approximation.

The molecular orbitals of benzene are schematically represented in Fig. 3. The first excited state of benzene cannot be described by one electron configuration, due to the degeneracy of the highest occupied molecular orbitals (HOMOs) and the lowest unoccupied molecular orbitals (LUMOs). The Si state of benzene (B2u) can be represented as 4>24>4 - 4>35 and the S2 or state (Biu) as 4>24>5 - 4)3(t,4-... 

Energy diagram of the molecular orbitals of benzene. Benzene s six 77 electrons fill the three bonding orbitals, leaving the antibonding orbitals vacant. 

Figure 7.17a shows the molecular orbitals of benzene. If you were to attempt a simple explanation for the electronic transitions in benzene, you would conclude that there are four possible transitions but each transition has the same energy. You would predict that the ultraviolet spectrum of benzene consists of one absorption peak. However, owing to electron-electron repulsions and symmetry considerations, the actual energy states from which electronic transitions occur are somewhat modified. Figure 7.17b shows the energy-state levels of benzene. Three electronic transitions take... 

Having considered the molecular orbitals of benzene, it is now useful to view an electrostatic potential map of the van der Waals surface for benzene, also calculated from quantum mechanical principles (Fig. 14.5). We can see that this representation is consistent with our understanding that the tt electrons of benzene are not localized but are evenly distributed around the top face and bottom face (not shown) of the carbon ring in benzene. 

Eig. 11.4. The molecular orbitals of benzene and their electronic occupation in the ground state. The shading indicates the atomic orbital amplitudes on each site. The site labelling defines the particle-hole transformation rule, eqn (11.7). 

The raw material for a calculation of the molecular orbitals of benzene is six Ip orbitals in a ring. Linear combination of these atomic orbitals leads to a set of six molecular orbitals three bonding and three antibonding. Their symmetries and relative energies are shown in Figure 13.10. 

For example, to locate the molecular orbitals of benzene, inscribe a hexagon in a circle, vertex down as shown in Figure 13.19, with the nonbonding line dmding the circle exactly in half. 

FIGURE 13.19 The relative energies of the molecular orbitals of benzene derived from a Frost circle. 

Fig. 42b. Rq>resentation ot the molecular orbitals of benzene. The possible combinations of benzene and metal orbitals in bis-v-benzene chromium...

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