Absolutely Small - Michael D. Fayer [123]
FIGURE 18.1. The geometry of benzene, C6H6. Benzene is planar, and it is a perfect hexagon.
Where Are the Double Bonds?
Figure 18.2 shows two possible double-bonded structures. In both, each carbon makes four bonds. A carbon makes three σ bonds, one to a hydrogen and one to each of the adjacent two carbons. Each carbon also participates in a double bond with one adjacent carbon. The diagrams on the right and left are identical except for the locations of the double bonds.
Two things are wrong with the bonding in benzene depicted in Figure 18.2. In the discussion of double bonds in Chapter 14, Table 14.1 shows that the carbon-carbon double bond length is considerably shorter than the single bond length. In ethylene (double bond) vs. ethane (single bond), the bond lengths are 1.35 Å and 1.54 Å, respectively. So if benzene had alternating double and single bonds, it should have alternating short and long carbon-carbon bonds. However, experiments demonstrate conclusively that benzene is a perfect hexagon; all of the carbon-carbon bond lengths are the same.
If we ignore the diagram’s implied unequal bond lengths, the second problem is the issue of which diagram would be correct, the one on the right or the one on the left? There is no reason to prefer one over the other. An early explanation was that the bonds jumped back and forth between the configuration on the right and the configuration on the left. The jumps were proposed to produce a type of average structure. This idea is in some sense closer to the truth, but the real answer, which then applies to many types of systems, is in the nature of the molecular orbitals that are formed.
FIGURE 18.2. Two possible configurations of double bonds in benzene. In both, each carbon makes four bonds.
Delocalize Pi Bonds
Figure 18.3 is a schematic of the atomic orbitals used to form molecular orbitals in benzene. The top shows the atomic hybrid orbitals used to make the σ bonds. Each carbon uses three sp2 hybrid orbitals to form three σ bonds, one to a hydrogen and one to each of the two adjacent carbon atoms. Forming the three sp2 hybrid atomic orbitals leaves each carbon atom with a leftover p orbital. In the top part of Figure 18.3, take the plane that contains the atoms (the plane of the page) to be the xy plane. Then each of the carbons has an unused pz orbital sticking in and out of the plane of the page. These orbitals are shown in the bottom of the figure. The positive and negative lobes of the pz orbitals are above and below the plane of the ring. In the diagram, the lengths of the bonds between carbon atoms have been exaggerated and the widths of the pz orbitals are reduced so that they can be seen clearly. The pz orbitals actually overlap, as shown more to scale in Figure 14.15.
The six pz atomic orbitals will combine to form molecular orbitals. The six atomic orbitals can contain at most 12 electrons without violating the Pauli Principle. Therefore, the six atomic orbitals will form superpositions to form six molecular orbitals that can also contain at most 12 electrons. The MOs are not associated with a particular atom or even a particular pair of atoms. They are molecular orbitals that span the entire six-carbon system.
In discussing the hydrogen molecule in connection with Figure 12.6, we saw that two atomic orbitals combine to form two molecular orbitals, one bonding MO and one antibonding MO. In Chapter 13, we investigated larger diatomic molecules, such as F2, O2, and N2. In these atoms,