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IR Spectroscopy

IR Spectroscopy. Wave length ~ 100 m m to 1 m m Wave number ~ 100 to 10,000 cm -1 Frequency ~ 3 x 10 12 to 3 x 10 14 Hz Energy ~ 1 kJ to 100 KJ /mole. HCl absorptions. 2885.9 cm -1 fundamental band strong

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IR Spectroscopy

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  1. IR Spectroscopy Wave length ~ 100 mm to 1 mm Wave number ~ 100 to 10,000 cm-1 Frequency ~ 3 x 1012 to 3 x 1014 Hz Energy ~ 1 kJ to 100 KJ /mole

  2. HCl absorptions • 2885.9 cm-1 fundamental band strong • 5668.1 cm-1 first overtone weak • 8347.0 cm-1 second overtone • 10923.1 cm-1 third overtone • 13396.0 cm-1 fourth overtone

  3. V(r) r Potential Energy Curve

  4. Harmonic Approximation

  5. m1 m2 Centre of mass does not move! Vibration of a diatomic molecule

  6. Quantum Mechanics of vibration

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

  8. Morse Potential

  9. 3 2 1 0 Blue –ALLOWED Red – NOT

  10. 3 2 1 0

  11. Morse Potential

  12. Electric field + vibrating diatomic molecule

  13. Vibrating Rotating Diatomic

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

  15. Up to second order in v and J

  16. Selection Rule Initial state Final state

  17. J EJ 3 12B 2 6B 1 2B 0 0 Anti-Stokes J EJ 12B 3 2 6B 1 2B 0 0 2B 4B P Q R

  18. IR Spectrum of CO2

  19. 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 CO2 - 667 cm-1 We denote normal modes as

  20. Symmetric Stretch of CO2 1330 cm-1

  21. Antisymmetric Stretching of CO2, 2349 cm-1

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

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

  24. Benzene

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