1. IR Spectroscopy Wave length ~ 100 mm to 1 mm
Wave number ~ 100 to 10,000 cm-1
Frequency ~ 3 x to 3 x 1014 Hz
Energy ~ 1 kJ to 100 KJ /mole

2. HCl absorptions 2885.9 cm-1 fundamental band strong
cm first overtone weak
cm second overtone
cm third overtone
cm fourth overtone

3. Potential Energy Curve
V(r) r

4. Harmonic Approximation

5. Vibration of a diatomic molecule
Centre of mass
does not move!

6. Quantum Mechanics of vibration

9. Must have an oscillating dipole moment
Selection Rule
Must have an oscillating dipole moment
Initial state
Final
state
Transition Moment = Integral
Transition Moment Integral

10. Morse Potential

11. 2 1 3
Blue –ALLOWED
Red – NOT

12. 2 1 3

13. Morse Potential

15. Electric field + vibrating diatomic molecule

18. Vibrating Rotating Diatomic

19. Variables can be separated!
Change to polar
co-ordinates x Y Z
Variables can be separated!

21. Up to second order in v and J

22. Selection Rule
Initial state
Final
state

23. J EJ 3
12B 2 6B 1 2B
Anti-Stokes J EJ
12B 3 2 6B 1 2B 2B 4B P Q R

26. IR Spectrum of CO2

27. Polyatomic molecules Normal Modes Center of mass does not move
Motion is in Phase
All atoms vibrate with same frequency
3N-6 Normal Modes
Bending mode of CO cm-1
We denote normal modes as

28. Symmetric Stretch of CO2 1330 cm-1

29. Antisymmetric Stretching of CO2, 2349 cm-1

30. Vibrational energy of a polyatomic
Each Normal Modes = A Hamonic Oscillator
Energy of one hamonic Oscillator is known!

31. State of the molecule specified by
Wave function:
Selection Rule: Only one of
can change

39. Benzene