Plan:

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Plan Introduction Description of the
experimental observation Theoretical
explanation Example of a obtained spectra Pure
rotation Rotational energy levels Population of
the rotational state Appearance of rotational
spectra Degeneracy and the stark
effect Rotational Raman spectra Vibration Vibra
tional energy expression and selection
rule Vibration-rotation spectra Vibrational
Raman spectra
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Introduction
Description of the experimental observation
Incident radiation
Elastically scattered radiations The photon
energy is conserved - Rayleigh Scatter -
Inelastically scattered radiations The photon
energy is not conserved - Raman Scatter 1/10 000
000-
Sample
Scattered radiations
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Introduction
Description
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Introduction
Quantum mechanical view of scattering
Virtual State
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Introduction
General aspect of Raman spectra
Pure rotational transitions
Rayleigh line
Stokes lines
Anti-Stokes lines
?excitation
Frequency
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Pure rotation
The expression of the related energy to the
rotation motion
The kinetic energy if a rotating molecule E
½ I ?2 Where ? is the angular velocity
I is the moment of inertia I ? mi ri2
m is the atoms mass
r is the perpendicular distance from he
rotation axis Introducing the angular momentum J
I ? in the energy expression E (Ja2 Jb2
Jc2) / 2I
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Pure rotation
The expression of the related energy to the
rotation motion in a spherical rigid rotors CH4,
SiH4, SF6 ...three equal moment of inertia
Considering J as the magnitude of the angular
momentum, The quantum expression is J2?
J(J1)h2/4?2 J 0, 1,
2, 3, ... E J (J1) h2/8?2 I The
rotation energy, normally expressed in terms of
rotational constant B B h / 8?2 c I cm-1
E hcB J(J1)
The rotational term F is the most used expression
for the description of the rotational state
F E/hc B
J(J1) cm-1
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Pure rotation
The expression of the related energy to the
rotation motion in a symmetric rotors NH3, CH3Cl
...two moment of inertia are equal but different
from the third
Ia I?? and Ib Ic I? F B J (J1)
(A-B) K2 J 0, 1, 2, 3 ... And K
0,?1, ... ?J B h / 8?2 c I ?
cm-1, A h / 8?2 c I ?? cm-1 All
levels with K?0 are doubly degenerate in a
linear rotors CO2, HCl, ... Have only one moment
of inertia
Ia I?? 0 and Ib Ic I?
F B J (J1) J 0,
1, 2, 3 ...
B h / 8?2 c I ? cm-1
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Pure rotation
Population of the rotational state
in case of spherical or linear molecules A
Boltzmann distribution Nj No exp-Bhc (kT)-1 J
(J1) Energetic level degeneracy MJ 0,?1, ...
?J , has 2J1 possible vales corresponding to
different orientations B Rotational state
population Nj No (2J1) exp-Bhc (kT)-1 J
(J1) The maximal population is calculated for
the level satisfying Jmax ½ (kT/2hcB) ½ -1
for spherical and linear rotor In the case of a
symmetric rotor Jmax ½ (4kT/2hcB) ½ -1
B
A
Population NJ/No
Angular momentum quantum number J
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Pure rotation
Appearance of rotational spectra

• The transitions are drawn considering
• ?J 1
• The maximum intensity correspond to the
• maximal population.
• F B Jmax (Jmax1)
• Jmax ½ (kT/2hcB) ½ -1
• Interval between lines correspond to ?F 2B
• B h / 8?2 c I
• I ? mi ri2
• Information about the molecule dimensions

Frequency
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Pure rotation
Stark effect
All rotating molecule orientations (?MJ) have the
same energy. Symmetrical rotor counts (2J1)2
fold degeneracy. An external electric field
partially removed these degeneracy E h c B J
(J1) ? The permanent electric
dipole moment of the molecule E The
external electric field
?2E 2 J(J1)-3MJ2
2hcBJ(J1)(2J-1)(2J3)
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Pure rotation
Rotational Raman spectra
The selection rule in the rotational
Raman transition is that the molecule must be
anisotropically polarisable. Therefore, all
linear molecules are Raman active while the
spherical rotors are Raman inactive. The
specific rotational Raman selection rules are
?J 0, ?2 for a
linear rotors ?J 0, ?1, ?2, ?K 0 for
a symmetric rotors
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Vibration
Energy expression
Re
distance
When the molecular potential energy is
approximated by a parabola V ½ k (R-Re)2 K is
the force constant In this case the energy is
quantized Ev (v ½) ?h/2? where ? (k/?)½
The energy levels are equally-separated by
?h/2?
k1
k2
The vibration term
? ?/2?c

n
G (
v
) (v ½)

k1 gtk2
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Vibration
Energy expression, anharmonicity
E h c G(v)
?e is the anharmonicity constant
Separation between the energy levels
DG(v ½) ? - 2 (v1) ?e ? The some of these
terms gives the dissociation energy (BIRGE-SPONER
extrapolation)


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Vibration
Selection rule
The gross selection The electric dipole moment
of the molecule must change when the atoms are
displaced. The molecule is then able to shake an
electromagnetic field to oscillation. The
molecule need not have a permanent dipole. The
specific selection rule In a harmonic
oscillator Dv ?1 In an anharmonic
oscillator weak 2?0 , 3?0 transitions

are also observed
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Rotation- Vibration
Selection rule Dv 1 DJ 1 and 0 if the
molecule possesses an angular momentum about its
axis. Stokes lines Dv 1 Anti-Stokes lines Dv
-1 P branches DJ -1 Q branches DJ 0 R
branches DJ 1
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The extraction of the force constant The
frequency of the V 0?1 transition Can be
estimated at the middle of J 1?0, and J
0?1 This frequency is ?/2?c with
? (k/m)1/2 k
can be deduced
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The extraction of the Bond Length The
interval between two rotational lines is 2B h
/ (4 c ?2 I) The moment of inertia can be
deduced I m R2 the bond length R can be
deduced
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Vibration
Vibrational Raman spectra
Molecule is vibrational-Raman active if It
polarizability change as the molecule
vibrate The polarizability depends on how
tightly the electrons are bound to the
nuclei Diatomic molecule presents 1 vibration
mode Poly-atomic (N) molecules present 3N-6
vibration modes if they are not linear, and
3N-5 If they are linear.
Selection rule Dv 1 DJ 2 and 0 Stokes
lines Dv 1 Anti-Stokes lines Dv -1 O branch
DJ -2 Q branch DJ 0 All linear molecules
present the Q branch S branch DJ 2
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Stokes lines
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Atmosphere Raman spectrum
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Example of Vibrational Raman spectra CCl4
15 mW of HeNe 632.8 nm radiation
holographic notch filter to reject the Rayleigh
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• Resonance Raman
  Spectroscopy
• The incident excitation radiation coincides
  nearly with the frequency
• of an electronic transition,
• Much greater intensity of scattered radiation
• Greatly simplified Raman spectrum because few
  vibrational modes
• contribute.
• Coherent anti-Stokes
  Raman Spectroscopy
• When two lasers beam frequencies are mixed
  together, several different
• frequencies give arise. Among them ? 2 ?1 -
  ?2
• When scanning with ?2, the matching with any
  stokes lines (?1 D?)
• give rise to the coherent emission
• ? 2 ?1 - ?2 2 ?1 (?1
  D?) ?1 D?
• Useful in case of the existence of competing
  incoherent background.