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

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

Potential Energy Curve V(r) r

Harmonic Approximation

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

Quantum Mechanics of vibration

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

Morse Potential

2 1 3 Blue –ALLOWED Red – NOT

2 1 3

Morse Potential

Electric field + vibrating diatomic molecule

Vibrating Rotating Diatomic

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

Up to second order in v and J

Selection Rule Initial state Final state

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

IR Spectrum of CO2

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

Symmetric Stretch of CO2 1330 cm-1

Antisymmetric Stretching of CO2, 2349 cm-1

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

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

Benzene