Example 14.19
Determine the number of IR-active vibrations of carbon tetrachloride, CCl 4 ,
which has Tdsymmetry.
Solution
The steps and symbols are taken from Table 14.5. First, we construct a table
by listing the classes of the symmetry operations in Tdsymmetry:
E 8 C 3 3 C 2 6 S 4 6 d- Determine Nstationaryfor each symmetry class. You should verify that the
following numbers are correct, as this is typically the most challenging
part of the process.
E 8 C 3 3 C 2 6 S 4 6 d
Nstationary 5 2 1 1 3- Determine the angle of rotation for all symmetry classes:
E 8 C 3 3 C 2 6 S 4 6 d
Nstationary 5 2 1 1 3
0° 120° 180° 90° 180°- Evaluate (1 2 cos ):
E 8 C 3 3 C 2 6 S 4 6 d
Nstationary 5 2 1 1 3
0° 120° 180° 90° 180°
1 2 cos 3 0 1 1 1- Determine Nstationary(1 2 cos ), depending on whether the symme-
try operation is considered a proper rotation or an improper rotation:
E 8 C 3 3 C 2 6 S 4 6 d
Nstationary 5 2 1 1 3
0° 120° 180° 90° 180°
1 2 cos 3 0 1 1 1
Nstationary(1 2 cos ) 15 0 1 1 3- Determine r 1 2 cos for each symmetry class:
E 8 C 3 3 C 2 6 S 4 6 d
Nstationary 5 2 1 1 3
0° 120° 180° 90° 180°
1 2 cos 3 0 1 1 1
Nstationary(1 2 cos ) 15 0 1 1 3
r 3 0 1 1 1- Determine t(1 2 cos ) for each symmetry class (again, de-
pending on whether it is a proper or an improper rotation):
14.14 Vibrational Spectroscopy of Nonlinear Molecules 501