Pure Rotation

1
Pure Rotation
Rotation term F(J) B J (J1) (A B) K 2
DJ J 2 (J1)2
F(J) /B
J
Term induced by deformation
56
7
Span between energetic levels
D(J?J1)F 2 B (J1)- ...
42
6
30
5
20
4
A h/(8? 2 c I??) B h/(8? 2 c I?) for a
spherical rotor A B For a linear rotor K 0
12
3
2
6
1
2
0
0
Linear or spherical rotor
2
Pure Rotation
IR Molecule must be polar to gave a Pure
rotational spectrum DJ 1 DMJ 0, 1
Raman Molecule must be anisotropically polarizab
le Linear rotor DJ 0, 2 Symmetric rotor DJ
0, 1, 2 DK 0
3
Rotational Raman Spectroscopy Distortion
Stokes
F(J2) - F(J) 2B(2J3) - 4D(2J3)(J23J3)
cm-1
cm-1
D 0
D 0,01
Approximated value of the Centrifugal Distortion
constant in linear molecules D 4 B3/?2 From
the spectrum ?(2?0) 6B 36D ?(3?1) 10B
168D ?(4?2) 14B 364D

D 0,02
cm-1
4
760K
Rotational Raman spectroscopy Temperature
2600K
for spherical and linear rotor Jmax (kT/2hcB)
½ -½
4000K
5
Vibration
i
i
Term induced by The anharmonicity
i
i
i
k is the force constant m is the reduced mass
6
Vibration
IR The electric dipole moment of the molecule
must change when the molecule vibrates Dv 1 DJ
0, 1
Raman The polarizability of the molecule must
change as the molecule vibrates Linear rotor Dv
1 DJ 0, 2
If a molecule has a center of inversion then no
modes can be both infrared and Raman active
7
Energy of the scattered photon
Pure rotational transitions
Rayleigh line
Stokes lines
Anti-Stokes lines
?excitation
Frequency
?i
8
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9
Vibration In the Stokes lines the Q branch
correspond to the transitions characterized by Dv
1 and DJ 0 These branch is formed with a
spaced lines, the span between them is larger in
the direction of the low scattered photon energy.
In the case of V 0?1 and J J?J The span
between lines in the Q branch is
D? 2 (J1)
(B1-B0) Where B0 is the rotational constant in
the ground state and B1 the rotational constant
in the first vibrational excited state. The Q
branch can only inform us how big is the
difference DB The first line J 0 ?0 informs us
about the bond force constant


n
n

(B
-
B
) J (J1)
1
0
i

10
Vibration In the Stokes lines the O branch
correspond to the transitions characterized by Dv
1 and DJ -2 These branch is formed with
spaced lines, the span between them is larger
near from the Q branch. In the case of V 0?1 and
J J?J The span between lines in the O branch
is D? 2
(J-1) B1 2 (J1) B0 The O branch can gave us
the length of the bond in the ground state and in
the excited state.

n
n
B1 (J
-
2) (J
-
1)
-
Bo J (J1)


i

11
Vibration In the Stokes lines the S branch
correspond to the transitions characterized by Dv
1 and DJ 2 These branch is formed with a
spaced lines, the span between them is larger
near from the Q branch. In the case of V 0?1 and
J J?J The span between lines in the S branch
is D? 2
(J3) B1 2 (J1) B0 The S branch can gave us
the length of the bond in the ground state and in
the excited state.

n
?
B
(J2) (J3)

B
J (J1)

1
0
i

12
O-branch
S-branch
Q
2330 cm-1
2286,5 cm-1
2374,7 cm-1
2301,6 cm-1
2358,2 cm-1
2293,9 cm-1
2366,3 cm-1
2342 cm-1
2318 cm-1
2350 cm-1
2310 cm-1
m1,162 10-26kg K 2241 N/m B0 B1 2 cm-1 RN2
0,108 nm
frequency
Central part of the fundamental vibrational Raman
band of 14N2
Label the spectrum, and calculate the Force
constant, rotation constant, bond length and the
distortion constant
13
Central part of the fundamental IR
vibration-rotation band of HBr
P- branch
R- branch
0,31056 eV
0,32434 eV
0,3062 eV
0,3083 eV
0,326226 eV
0,31264 eV
0,32066 eV
0,32264 eV
0,3013 eV
0,3036 eV
0,327925 eV
0,31867 eV
0,329434 eV
0,3149 eV
0,331038 eV
0,332547 eV
0,333962 eV
0,299 eV
0,335566 eV
0,2967 eV
0,336887 eV
0,294 eV
Label the spectrum, and calculate the Force
constant, rotation constant, bond length and the
distortion constant
1 eV ? 8059 cm-1
mHBr 1,6529 10-27 kg