Physical Chemistry , 1st ed.

molecules, since MJdoes not affect the rotational energy it will have no effect

on the rotational spectrum unless the molecules are subjected to a strong elec-

tric field (that is, the Stark effect). Since the selection rule for Kis that it must

remain unchanged (K0), the difference in the rotational energies is dic-

tated solely by changes in J:

EE(J)→E(J 1)E(J 1) E(J)  2 B(J 1) (14.24)

This equation is for absorption of electromagnetic radiation by either a pro-

late or an oblate top, where Bis the rotational constant that appears twice in

the three rotational constants for a symmetric top (remember, one of the ro-

tational constants is unique and different from the other two). This is the same

expression we determined for linear molecules. Again, the quantum number J

refers to the lower-energy state involved in the transition.

This suggests that we can determine little more about the structure of sym-

metric tops other than a single rotational constant, even though symmetric

tops have two distinct rotational constants. If molecules acted like perfect rigid

rotors, this would be the case. But they’re not perfect, and that does allow us

to obtain additional information from a real spectrum. We will get to this in

the next section.

By definition, molecules that are spherical tops do not have a permanent di-

pole moment, so they do not have a pure rotational spectrum. However, un-

der some conditions they may have rotational absorptions superimposed in

their vibrational spectrum.

478 CHAPTER 14 Rotational and Vibrational Spectroscopy

Electric

field off

Electric

field on

J  4

MJ  0

MJ  4

MJ  1

MJ  2

MJ  3

J  3

MJ  3

MJ  0

MJ  1

MJ  2

 

0

100

200

300

400

500

600

**

**

**

*

*

*

*

*

++

++

++

++

+

+

+

2.0

v (GHz)

8.0

Intensity (arbitrary units)

0.0 2.0 4.0 6.0

Figure 14.14 Imposition of an electric field

can complicate an otherwise “simple” spectrum.

For a diatomic molecule, the selection rule MJ

now dictates the possible transitions.

Figure 14.15 A real spectrum, showing the Stark effect on benzonitrile, C 6 H 5 CN. The and

* signs mark signals that are splitting due to the electric field.Source:Reprinted with permission

from The American Chemical Society.