Physical Chemistry , 1st ed.

Therefore, the gross selection rule for vibrations is the presence of a dipole mo-

ment that changes during the course of the vibration: a varying dipole moment

is required.

Note that this does not imply that the molecule must have a permanent di-

pole moment in order to have a vibrational spectrum. Consider the methane

molecule, CH 4. It has no permanent dipole moment, thanks to its tetrahedral

symmetry. However, in the course of the vibrations of the atoms in the mo-

lecule (see Figure 14.26), fleeting dipole moments are present as the atoms dis-

tort the molecule. In this way, not only the magnitude but also the direction

of such fleeting dipole moments is changing. Methane absorbs richly in the in-

frared region of the spectrum due to its vibrations. CO 2 is a linear molecule.

It has no permanent dipole moment, but during the course of some of its mo-

lecular vibrations it has a fleeting nonzero dipole moment that allows for light

to be absorbed. However, for one specific normal mode of CO 2 , there is no net

dipole moment change because both oxygen atoms are moving back and forth

with respect to the carbon atom in phase, by the same amount (this is the

so-called symmetric stretching motion of CO 2 ). This particular vibrational

motion of the molecule is not active in absorbing infrared light. (The vibra-

tional motions of CO 2 are particularly important in carbon dioxide’s behavior

as a greenhouse gas. Even though CO 2 has no permanent dipole moment, it

absorbs energy in the form of infrared light due to its vibrational motions.)

Homonuclear diatomic molecules do not absorb or emit radiation due to

vibrational state transitions. By definition, homonuclear diatomic molecules

have no dipole moment and no changing dipole moment as the two atoms

vibrate. Other methods are necessary to observe vibrational energy levels

directly.

488 CHAPTER 14 Rotational and Vibrational Spectroscopy

 1

H

C

H

H

H

 2

H

C

H

H

H

 3

H

C

H

H

H

 4

H

C

H

H

H

Figure 14.26 Normal modes of vibration for methane, CH 4. Although methane does not have

a permanent dipole moment, some of the vibrations distort the molecule so that a fleeting di-

pole moment is present. These vibrations absorb infrared light and appear in a vibrational spec-

trum of methane.