Physical Chemistry , 1st ed.

system that is recognized by spectroscopists. All are IR-active, so ammonia will

absorb infrared radiation having four characteristic frequencies.

Figure 14.33 shows the normal vibrations for benzene, C 6 H 6. For benzene,

3 N6 equals 30, so we expect to have up to 30 different vibrations. Some of

the vibrations are degenerate, so there are less than 30 separate vibrations.

However,only fourvibrations are IR-active, since only four of them involve a

changing dipole moment. (With respect to Figure 14.33, the IR-active vibra-

tions are  4 , 12 , 13 , and  14 .) This is possible because the benzene molecule

has many symmetry elements. Generally speaking, the higher the symmetry of

14.14 Vibrational Spectroscopy of Nonlinear Molecules 499

 1  2  3  5

 6  7  8  9  10

 11  12  13  14  15

 16  17  18  19  20

+

+

+

+

+ +

+ +

+ +

+ +

• 
  

  –

  
  


• – –

+

+

+ +

+ +

• –


• –


• 
  


• 
  

+

+

+

+

+

+

+

+

+

+

 4

H

H

H

H

H

H

C

C

C

C

C

C

Figure 14.33 The normal modes of vibration for benzene, C 6 H 6. Due to the high symmetry of

benzene, only four of these vibrations are IR-active.Source:Gerhard Herzberg,Molecular Spectra

and Molecular Structure, Vol. II,1991, Krieger Publishing Company. Adapted with permission.