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of the light frequency (ν) or the wavelength (λ) at which light is absorbed gives the oscillator frequency. As shown in the figure, ΔE = 667 cm-1 for the bending modes of carbon dioxide. The two bending modes have the same frequency because they only differ by the direction of the bend. (We can write the energy or frequency in wave numbers [cm-1] by dividing the energy, ΔE, by ch.) The frequency of light absorbed by the CO2 bends is almost exactly at the peak of the Earth’s black body spectrum. It is much easier (takes less energy) to bend a chemical bond than to stretch it. The carbon dioxide symmetric and asymmetric stretches are at much higher frequency. Neither contributes significantly to absorption of the Earth’s black body radiation.

FIGURE 17.3. Top: A potential energy curve showing the energy as a function of the bond lengths with the vibrational quantum levels. Only the first few energy levels are shown. Bottom: The lowest vibrational energy level (n = 0) and the first excited level (n = 1) for the CO2bending modes (Figure 17.2.). This transition (arrow) will absorb the Earth’s black body radiation (see Figure 17.1).

CO2 GREENHOUSE EFFECT IS QUANTUM MECHANICAL

The important point is that at the most fundamental level, CO2’s contribution to the greenhouse effect and to global climate change is inherently quantum mechanical. First, the bonds that are broken and made in burning natural gas, oil, or coal are determined by the quantum mechanics that give us molecular orbitals, which control the bond strengths. The bond strengths determine the amount of energy that is released per CO2 produced. At an even more fundamental level, the shape of the black body spectrum emitted by the Earth is determined by quantum effects. Black body radiation was discussed in Chapters 4 and 9. Planck’s explanation of the shape of the black body spectrum and how it changes with the temperature of a hot object was the first application of quantum theory. The CO2 absorption centered at 667 cm-1 is a result of the quantized vibrational energy levels of molecules, a purely quantum effect. The CO2 bending modes have their quantized n = 0 to n = 1 vibrational transition at a key frequency in the Earth’s black body spectrum. While massive power plants, vast numbers of cars, trucks, and planes, burning of rain forests, etc. produce the greenhouse gas CO2, it is the quantum interaction between CO2 and the Earth’s infrared black body radiation that produces the greenhouse effect.

18

Aromatic Molecules

IN CHAPTERS 13 AND 14 we discussed double bonds, and in Chapter 16 we saw that double bonds play a fundamental role in determining the biological properties of fats. Some of the fat molecules discussed, the polyunsaturated fats, have several double bonds, but these double bonds are always separated by a number of single bonds. For example, Figure 16.5 shows a ball-and-stick model of DHA, a polyunsaturated fat with six double bonds. As can be seen, there are two single bonds between each double bond. In this chapter, we will see the wide-ranging impacts of multiple double bonds that are not separated by several single bonds. Quantum theory shows that the nature of the bonding found in the molecule benzene and a vast number of other “aromatic” molecules can explain electrical conductivity in metals, as well as the differences among metals, semiconductors, and insulators that will be discussed in Chapter 19. To understand aromatic molecules and electrical conductivity in metals, it is necessary to discuss the nature of the molecular orbitals that arise when identical atomic orbitals from many atoms interact to form MOs.

BENZENE: THE PROTOTYPICAL AROMATIC MOLECULE

Figure 18.1 shows a diagram of benzene, which is composed of six carbon atoms and six hydrogen atoms. Experiments have determined that benzene is a perfect hexagon with all of the atoms, carbons, and hydrogens in a plane. The angle formed by the bonds from one carbon to its two nearest neighbors is exactly 120°, and the angle formed by the bond of a hydrogen to a