Physical Chemistry , 1st ed.

moment. If it does, the rotation will provide an oscillating electromagnetic

field on the order of the light’s oscillating field, and then the light and the mol-

ecule will interact. Figure 14.7 illustrates this interaction. In order to observe

absorption or emission of light due to pure rotational transitions, the mole-

cule musthave a permanent dipole moment. (The phrase “pure rotational

transitions” is crucial, since the several types of motions of a molecule can in-

teract—“mix”—and seemingly violate such simple statements. We will con-

sider some examples later.) The presence of a permanent dipole moment is

sometimes referred to as a gross selection rule,since it relies on a general prop-

erty of a molecule rather than a specific wavefunction of the molecule. More

specific selection rules, based on wavefunctions, will be considered shortly.

Example 14.7

Which of the following molecules will absorb or emit light due to rotational

energy transitions?

a.Methane, CH 4

b.Hydrogen chloride, HCl

c.Wa t e r, H 2 O

d.Carbon dioxide, CO 2

e.Acetylene, C 2 H 2

f.Hydrogen cyanide, HCN

g.Benzene, C 6 H 6

Solution

a.Methane has no permanent dipole moment; therefore it will not show pure

rotational energy transitions.

b.HCl has a permanent dipole moment and so will exhibit pure rotational

energy transitions.

c.H 2 O will.

d.CO 2 will not.

e.C 2 H 2 will not.

f.HCN will.

g.C 6 H 6 will not.

This gross selection rule is general and considers a general property of the

molecule. What about specific transitions between rotational quantum levels?

Can any two rotational wavefunctions be involved in a transition, or is there a

restriction on what wavefunctions can interact via absorption or emission of a

photon? There is indeed a restriction, and it has to do with the fact that a pho-

ton has angular momentum. (This was alluded to in Chapter 9 when dis-

cussing Arthur Compton’s experiments with X rays and their frequency change

upon interaction with atoms.) Photons have one unit of angular momentum

(they have s1), and so the law of conservation of angular momentum re-

quires that the total angular momentum of an initial state (molecule pho-

ton) must equal the total angular momentum of the final state (the molecule

after it has absorbed or emitted the photon). The law of conservation of an-

gular momentum thus requires that the absorption or emission of a photon

must be accompanied by the change of the Jquantum number by 1, either an

increase of 1 (for absorption) or a decrease of 1 (for emission). One can write

the following quantum-mechanical selection rule for rotational transitions:

J 1 (14.18)

472 CHAPTER 14 Rotational and Vibrational Spectroscopy

rot  light
Figure 14.7 This series of drawings shows how
the frequency of light and the frequency of rota-
tional motion are equal if light is to be absorbed.