1. Application of group theory- Infrared and Raman Activity
by Dr.D.UTHRA Head Department of Physics DG Vaishnav College Chennai-106

2. Application of character table to find the IR and Raman activity of the
given moiety

3. For the molecule or moiety in general, by analysing the symmetry operations it undergoes, find the point group it belongs to
The character table of that point group can be used to find the IR and Raman activity and inactivity of various species of the point group of the moiety under study

4. Condition for IR activity
For proper rotations
∑R (1+2cosθ) χi (R) ≠ 0 (Active)
= 0 (Inactive)
Other than proper rotations
∑R (-1+2cosθ) χi (R) ≠ 0 (Active)
=0 (Inactive)
where,
R - symmetry operation
θ - angle of rotation for R
χi (R) - from the character table

5. Condition for Raman activity
For proper rotations
∑R 2cosθ (1+2cosθ) χi (R) ≠ 0 (Active)
= 0 (Inactive)
Other than proper rotations
∑R 2cosθ (-1+2cosθ) χi (R) ≠ 0 (Active)
= 0 (Inactive)
where,
R - symmetry operation
θ - angle of rotation for R
χi (R) - from the character table

6. For an XY2 bent molecule XY2 bent molecule belongs to C2v point group1 A2 -1 B1 B2 NR 3
Θ(in degrees)
180
2cosθ 2 -2
(1+2cosθ) -
(-1+2cosθ)

7. To find IR activity
A1 species : 3*1 + -1*1 + 1*1 + 1*1 = 4 ≠ 0 ( IR Active)
A2 species : 3*1 + -1*1 + 1*-1 + 1*-1 = 0 ( IR Inactive)
B1 species : 3*1 + -1*-1 + 1*1 + 1*-1 = 4 ≠ 0 ( IR Active)
B2 species : 3*1 + -1*-1 + 1*-1 + 1*1 = 4 ≠ 0 ( IR Active)
Note: There are no vibration present in B1 species for a XY2
bent molecule, though that mode is IR active

8. To find Raman activity All modes of vibration are Raman active
A1 species : 2*3*1 + -2*-1*1 + 2*1*1 + 2*1*1 = 12 ≠ 0
A2 species : 2*3*1 + -2*-1*1 + 2*1*-1 + 2*1*-1 = 4 ≠ 0
B1 species : 2*3*1 + -2*-1*-1 + 2*1*1 + 2*1*-1 = 4 ≠ 0
B2 species : 2*3*1 + -2*-1*-1 + 2*1*-1 + 2*1*1 = 4 ≠ 0
All modes of vibration are Raman active
Note: There are no vibration present in A2 and B1 species for a XY2
bent molecule, though those modes are Raman active

9. Activity of a XY3 pyramidal molecule
molecule belongs to
C3v point group
C3v E
2C3
3σv A1 1 A2 -1 2 NR 4
Θ(in degrees)
120
2cosθ
(1+2cosθ) 3 -
(-1+2cosθ)

10. To find IR activity
A1 species : 3*1 + 0*1*2 +1*1*3 = 6 ≠ 0 ( IR Active)
A2 species : 3*1 + 0*-1*2 +1*-1*3 = 0 ( IR Inactive)
E species : 3*2 + 0*-1*2 + 1*0*3 = 6 ≠ 0 ( IR Active)

11. To find Raman activity
A1 species : 2*3*1 + -1*0*1*2 + 2*1*1*3 = 12 ≠ 0 (Active)
A2 species : 2*3*1 + -1*0*-1*2 + 2*1*-1*3 = 0 (Inactive)
E species : 2*3*2 + -1*0*-1*2 + 2*1*0*3 = 12 ≠ 0 (Active)

12. Try for many other molecules! Enjoy group theory!!
C u in next presentation!!!
-uthra mam