Ir spectroscopy
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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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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


V(r)

r

Potential Energy Curve


Harmonic Approximation


m1

m2

Centre of mass

does not move!

Vibration of a diatomic molecule


Quantum Mechanics of vibration


Transition Moment = Integral

Transition Moment Integral

Selection Rule

Must have an oscillating dipole moment

Initial state

Final

state


Morse Potential


3

2

1

0

Blue –ALLOWED

Red – NOT


3

2

1

0


Morse Potential


Electric field + vibrating diatomic molecule


Vibrating Rotating Diatomic


Change to polar

co-ordinates

Z

x

Y

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

0

0

Anti-Stokes

J

EJ

12B

3

2

6B

1

2B

0

0

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


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