Absolutely Small - Michael D. Fayer [125]
THE BENZENE DELOCALIZED PI MOLECULAR ORBITALS
Benzene, naphthalene, and similar molecules are referred to as aromatic molecules. They tend to have a sweet smell. Naphthalene is a mothball, which has a characteristic aromatic smell. Perfumes are more complex aromatic molecules having a number of benzene-like rings, as well as other chemical groups replacing the hydrogen atoms. Small changes in the molecular structure change the aroma, which is what makes one perfume smell different from another.
In Chapter 8, we discussed the particle in a box problem. Figures 8.4 to 8.6 show the particle in a box wavefunctions and energy levels. The wavefunction associated with the lowest energy level has no nodes. The next higher energy state has a wavefunction with one node, the next higher energy state has a wavefunction with two nodes, and so forth. A node is a place where the wavefunction goes to zero, so the probability of finding the electron is zero. The particle in a box is a one-dimensional problem. A node is a point. In Chapter 10, we examined the wavefunctions and the energy levels for a hydrogen atom. Figures 10.2 to 10.6 show representations of the wavefunctions for the 1s, 2s, and 3s hydrogen atom states. The hydrogen atom wavefunctions are three-dimensional. The lowest energy state (1s) has no nodes, the next higher energy state (2s) has a wavefunction with one node. The next higher energy state (3s) has two nodes. These nodes are three dimensional surfaces on which there is zero probability of finding the electron.
The benzene π MOs also have an increasing number of nodes as the energy is increased. Figure 18.8 shows schematics of the benzene π MOs. The shaded areas are the regions of high electron density (high probability of finding electrons) for the π MOs.
FIGURE 18.8. Benzene π molecular orbital energy levels and schematics showing the shapes of the corresponding MOs. As the energy increases, the number of nodes increases. MOs with the same number of nodes have the same energy.
These are three-dimensional electron clouds that extend above and below the plane of the page and do not have sharp boundaries. Also shown are the energy levels with the 6 pz electrons filled in the lowest energy bonding MOs. The lowest energy MO has no nodes. There are two states with the next higher energy. Both of these MOs have one node. The three MOs with no nodes and one node are the bonding MOs. There are also two levels with the next higher energy. These MOs have two nodes. The highest energy MO has three nodes. The three MOs having two and three nodes are the antibonding MOs.
Comparing the schematics of the lowest energy MO with the highest energy MO in Figure 18.8, it can be seen clearly why the former is a bonding MO and the latter is an antibonding MO. The lowest bonding MO has electron density between all of the carbons. The highest antibonding MO has nodes between all of the carbons, so electrons in this MO would not join the carbons together. The pair of bonding MOs, although higher in energy than the lowest energy bonding MO, results in bonding among the carbon atoms. Each of these MOs has one node. The one on the left puts electron density between a pair of carbons on the left and right. The MO on the right puts electron density between three carbon atoms on the top and three on the bottom. In spite of the nodes, these MOs combine with the lowest energy MO to produce the three π bonds that are shared by the six carbons. The two degenerate antibonding MOs have two nodes each. The one on the left clearly does not contribute to bonding because it does not place electron density between any of the carbons. The one on the right puts electron density between two pairs of carbons, but when combined with the one on the right, it does not produce net bonding.
Light Absorption by Aromatic Molecules
Quantum theory can calculate the molecular orbitals of aromatic molecules, as well as their shapes and sizes. There are many ways to test the quantum calculations by comparison