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IR Spectroscopy: Molecule Vibration Quantum Mechanics

Explore the fundamentals of IR spectroscopy focusing on molecule vibration, quantum mechanics, transition moments, and selection rules. Learn about Morse potential, polyatomic molecules, normal modes, and energy transitions. Delve into the intricate world of diatomic and polyatomic molecules in this informative guide.

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IR Spectroscopy: Molecule Vibration Quantum Mechanics

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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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