Physical Chemistry , 1st ed.

in, one out with respect to the center atom. This type of motion is called an
asymmetric stretching vibration.It is IR-active, because a small dipole moment
is produced during the course of the vibration (where the outside atoms are
different distances from the center). Finally, the vibration labeled  2 has the
center atom moving up-and-down while the outside atoms are moving down-
and-up. The normally linear molecule becomes slightly bent during the course
of this motion, and so this is called a bending motion. It, too, is IR-active: the
molecule becomes bent and the overall dipole moment is no longer eliminated
by symmetry. The interesting thing about this motion is that the bend can be
either up-and-down or in-and-out, two directions that are 90° apart. These
motions are perpendicular to each other and so represent a pair ofdoubly de-
generatevibrational modes. They have the same frequency of vibration, and the
same irreducible representation label. CO 2 is said to have a doubly degenerate
bending motion (IR-active), a symmetric C–O stretching motion (IR-inactive),
and an asymmetric C–O stretching motion (IR-active).
The asymmetric triatomic linear molecule also has a doubly degenerate
bending motion labeled  2. (The numbering of the normal modes follows a
system we won’t get into here.) The other two motions correspond roughly to
a stretching vibration between the left outside atom and the center atom, as
well as a stretching vibration between the right outside atom and the center
atom. So for HCN, we will have a doubly degenerate bending motion, and then
two modes that are roughly described as an H–C stretching vibration and a
C–N stretching vibration.
Because this one vibration is doubly degenerate, it must be counted twice
in the summation that relates D 0 and Defor polyatomic molecules. In larger
molecules, degenerate vibrations must be summed the appropriate number of
times to get the correct numerical relationship between D 0 and De.

Example 14.17

Roughly describe the four normal modes of the following linear molecules.

a.Carbon disulfide, CS 2

b.Hydrogen hypochlorite, HClO

c.Beryllium fluoride, BeF 2

d.The ethynyl radical, HCC

Solution

a.CS 2 has a symmetric C–S stretch, an asymmetric C–S stretch, and a dou-

bly degenerate bending motion.

14.12 Vibrational Spectroscopy of Diatomic and Linear Molecules 495

 1 A B A  1 A B C

 2 A B A  2 A B C

 3 A B A  3 A B C

Figure 14.30 Normal modes of vibration for symmetric (ABA) and asymmetric (ABC) lin-
ear triatomic molecules. In both cases, the vibrations labeled  2 are doubly degenerate, since there
are two equivalent vibrations that are perpendicular to each other. For the symmetric molecule,
only  2 is IR-active. For the ABC molecule, all three vibrations are IR-active.