Nils Walter: Chem 260

Rotational Raman spectroscopy

Experimental setup:

laser

Gross selection rule:anisotropic polarization

(example: H-H)

Specific selection rules:∆∆∆∆J = +2 (Stokes lines)

∆∆∆∆J = -2 (anti-Stokes lines)

Nils Walter: Chem 260

The vibration of molecules

Morse potential2)(

21

eRRkV −=

ννννhvEv

++++====

21

Solution for the harmonic oscillator:

=

µπν k

21

BA

BA

mmmm+

=µeffective mass

A B B

zero point energy

Nils Walter: Chem 260

=

µπν k

21

⇒⇒⇒⇒ 300-3000 cm-1 = Infrared

Vibrational transitions: Infrared spectroscopy

Gross selection rule:the electric dipole

moment of the molecule must change during the vibration

Nils Walter: Chem 260

Specific selection rules

∆∆∆∆v = ±±±±1

In reality: anharmonic oscillator

xe = anharmonicity constant

∆∆∆∆v = ±±±±1, ±±±±2, ±±±±3,...

kTE

lower

upper eNN ∆−

=

D0

Deqev xhvhvE νν

2

21

21

+−

+=

Nils Walter: Chem 260

The vibrating rotor

Born-Oppenheimer approximation:The energies of rotations and vibrations are so

different that Etotal = Erot. + Evib.

∆ ∆ ∆ ∆J = -1 ∆ ∆ ∆ ∆J = +1

Nils Walter: Chem 260

Vibrations of polyatomic molecules:How many are there?Each atom can move along one of three axes:

⇒⇒⇒⇒ 3N possible displacements (= degrees of freedom)⇓⇓⇓⇓

Three degrees of freedom correspond to translational motion:⇒⇒⇒⇒ 3N - 3 degrees of freedom left

⇓⇓⇓⇓Three (/two) degrees of freedom correspond to rotations:

⇒⇒⇒⇒ 3N - 6 (3N - 5 for linear molecule) degrees of freedom left for vibrations

Nils Walter: Chem 260

Vibrations of polyatomic molecules:How can one describe them?

CO2: C-O stretch vibrations are NOTindependent (cannot be excited

independently)

Normal stretch modes (linear combinations of C-O stretches) ARE

independent

inactive activ

e

symmetric antisymmetric:greenhouse gas

Nils Walter: Chem 260

What is all this good for???

←←←← low energy→→→→

Identification of organic compounds!!!B

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