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

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Presentation on theme: "Application of group theory- Infrared and Raman Activity by Dr.D.UTHRA Head Department of Physics DG Vaishnav College Chennai-106."— Presentation transcript:

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 (1+2cosθ) ∑ R (1+2cosθ) χ i (R) ≠ 0 (Active) = 0 (Inactive) Other than proper rotations (-1+2cosθ) ∑ R (-1+2cosθ) χ i (R) ≠ 0 (Active) =0 (Inactive) where, R - symmetry operation θ - angle of rotation for R χ i (R) - from the character table

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

6 For an XY 2 bent molecule XY 2 bent molecule belongs to C 2v point group C 2v E C2 C2 C2 C2 σvσvσvσv σv ’σv ’σv ’σv ’ A1A1A1A A2A2A2A2 11 B1B1B1B1 1 1 B2B2B2B2 1 1 NRNRNRNR 3113 Θ(in degrees) cosθ (1+2cosθ) 3-- (-1+2cosθ) --11

7 To find IR activity A 1 species : 3*1 + -1*1 + 1*1 + 1*1 = 4 ≠ 0 ( IR Active) A 2 species : 3*1 + -1*1 + 1*-1 + 1*-1 = 0 ( IR Inactive) B 1 species : 3*1 + -1*-1 + 1*1 + 1*-1 = 4 ≠ 0 ( IR Active) B 2 species : 3*1 + -1*-1 + 1*-1 + 1*1 = 4 ≠ 0 ( IR Active) XY 2 Note: There are no vibration present in B 1 species for a XY 2 bent molecule, though that mode is IR active

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

9 XY 3 pyramidal molecule belongs to C 3v point group Activity of a XY 3 pyramidal molecule C 3v E 2C 3 2C 3 3σv3σv3σv3σv A1A1A1A1 111 A2A2A2A2 11 E 2 0 NRNRNRNR 412 Θ(in degrees) cosθ 22 (1+2cosθ) 30- (-1+2cosθ) --1

10 To find IR activity A 1 species : 3*1 + 0*1*2 +1*1*3 = 6 ≠ 0 ( IR Active) A 2 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 A 1 species : 2*3*1 + -1*0*1*2 + 2*1*1*3 = 12 ≠ 0 (Active) A 2 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 -uthra mam


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