Absolutely Small - Michael D. Fayer [126]
Figure 18.7 shows a diagram of naphthalene, with its 10 carbon atoms. Each carbon atom will contribute one pz orbital with one electron to form the delocalized π electron system. The other three carbon valence electrons are used to form the σ bonds. Ten pz atomic orbitals form the π system, so there will be 10 molecular orbitals, five bonding MOs and five antibonding MOs. In naphthalene, none of the MOs is degenerate; each has a different energy. Figure 18.9 displays a schematic of the energy levels of the π MOs of naphthalene. The left-hand side shows the π energy levels with the 10 π electrons filling the five bonding MOs. The antibonding MOs are empty.
The right side of Figure 18.9 illustrates the effect of absorption of light. Because the energy levels are quantized, only certain energies of light can be absorbed by the molecule. In the figure, ΔE is the lowest energy light that can be absorbed. Consider what happens if we shine light on a sample of naphthalene molecules, beginning with light that is too low in energy to be absorbed by the molecules. The energy of the light is E = hν, where h is Planck’s constant and ν is the frequency. So initially, ΔE > hν; the energy separation between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) is greater than the energy of the photons that are impinging on the sample. As a result, they pass through the sample without being absorbed. Now, we start changing the energy of the light to higher energy (red to blue). When hν = ΔE, light is absorbed, which is detected by a decrease in the amount of light that passes through the sample. An electron is excited from the HOMO to the LUMO. This excitation is shown on the right side of Figure 18.9, which has one electron in the HOMO and one electron in the LUMO. In the left-hand side of Figure 18.9, there are two electrons in the HOMO and none in the LUMO.
FIGURE 18.9. A schematic of the naphthalene π molecular orbital energy levels. There are five bonding MOs and five antibonding MOs. The left side shows the 10 p electrons filling the five bonding MOs. The right side shows the result of absorption of light that raises the energy of a bonding electron into an antibonding MO.
The transition from the HOMO to the LUMO is the lowest energy transition. As drawn, the bonding MOs are closer together than the separation between the HOMO and the LUMO. However, an electron cannot be excited from one filled bonding MO to another filled bonding MO. If we try to take an electron from one bonding MO and put it into another bonding MO, the result would be an MO with three electrons in it. Three electrons in an MO violates the Pauli Exclusion Principle. Then in our optical absorption experiment, as the light color is scanned from red to blue (low energy to high energy), the first color (wavelength) that is absorbed corresponds to the energy ΔE. ΔE can be calculated using quantum mechanics. ΔE depends on the structure of the molecule and the interactions of the atomic orbitals that give rise to the molecular orbitals. The quantum calculations can be tested further by comparison to the wavelengths at which absorption of higher energy light takes place as the light is scanned further and further to the blue. This second absorption occurs because light can take an electron from the HOMO to one energy level above the LUMO. Another absorption at even higher energy will occur by exciting an electron from the HOMO to two levels above the LUMO, and so forth.
NAPHTHALENE TREATED AS A PARTICLE IN A BOX PROBLEM
Using modern quantum theory and computers, the structure of naphthalene can be calculated with great accuracy. The theory will give the bond lengths and bond angles. For example, the bond lengths can be calculated to 0.001 nm, that is, a thousandth of a nanometer. The calculations also yield the frequencies at which