Download CHEM 515 Spectroscopy Vibrational Spectroscopy I

CHEM 515
Spectroscopy
Vibrational Spectroscopy I
Rotational, Vibrational and Electronic Levels
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Molecular Vibrations of CO2
3
Harmonic Oscillator Approximation
Selection rule
Δv = ± 1
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Harmonic Oscillator Approximation
• At lower energies,
the harmonic
oscillator model
determines the
quantum levels quite
well. Deviations
become more
significant at higher
energy levels.
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Types of Potential Function Curves
1330 cm-1
V
667 cm-1
V
R
Dissociatve
R
Non-dissociatve
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Force Constant
• The force constant is a
measure of the
strength of the spring
(or chemical bond)
connecting two
particles.
The force constants is
proportional to the
bond order.
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Anharmonicity
Vv
Harmonic
oscillator
Anharmonic
oscillator
2
1
• Deviations due to
anharmonicity become
more clear at
– higher energy levels
(v), and
– larger x = r – re
values that
correspond to
dissociation.
0
r0
Bond distance
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Anharmonicity
Vv
Harmonic
oscillator
Anharmonic
oscillator
2
Selection rule because of the
effect of anharmonicity:
1
0
r0
• Electrical anharmonicity:
(electrical properties,
dipole moment and
polarizability).
• Mechanical
anharmonicity: (nature of
molecular vibration).
Δv = ± 1, ± 2, ± 3, …
Bond distance
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Types of Vibrational Transitions
• The intensity of Δv= ±1
transitions is stronger
than that for Δv= ±2, ±3,
… transitions.
• Both electrical and
mechanical
anharmonicity
contribute to the
intensities of Δv= ±2, ±3,
… transitions.
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Vibrational Spectrum of HCl
Vibrational spectrum of HCl is based on the
harmonic oscillator model with ωe = 2989 cm-1.
v
ν (cm-1)
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Vibrational Spectrum of HCl
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Vibrational Spectrum of HCl
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Vibrational Spectrum of HCl
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Morse Potential
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Morse Potential
• It is a better
approximation for
the vibrational
structure of the
molecule than the
quantum harmonic
oscillator because it
explicitly includes
the effects of bond
breaking, such as the
existence of unbound
states.
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Morse Potential
• It also accounts for
the anharmonicity
of real bonds and
the non-zero
transition
probability for
overtones and
combinations.
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Morse Potential
• Morse function is
not well behaved
where r  0 or
x  – re . Although
V(x) becomes large
but is doesn’t go to
infinity.
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Dissociation Energy from Spectroscopic Data
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Birge-Sponer Diagram
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Birge-Sponer Diagram
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Vibration-Rotation Spectra
Energy increases
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Vibration-Rotation Spectra
Infrared spectrum
ΔJ = ±1
Raman spectrum
ΔJ = 0 , ±2
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Vibration-Rotation Infrared Spectrum of HCl
• νvib is different for
H35Cl and H37Cl
molecules due to the
slight difference in
their reduced
masses.
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 H35Cl 
 0.972 au
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35
 H37Cl   0.974 au
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Vibration-Rotation Infrared Spectrum of HCl
• The lines due to
H35Cl transitions are
more intense because
the isotopic
abundance ration of
H35Cl to H37Cl
molecules is 3:1.
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Vibration-Rotation Infrared Spectrum of HCl
2B 2B 2B 2B
4B
2B
2B 2B
2B
Band center
H35Cl
Band center
H37Cl
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Vibration-Rotation Infrared Spectrum of HCl
2B 2B 2B 2B
4B
2B
2B 2B
2B
• The rotational constant B slightly decreases as
going to higher vibrational levels. This results in
decrease of the gaps between transition lines as
one goes to higher frequencies.
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Vibration-Rotation Infrared Spectrum of HCl
• The rotational constant B slightly decreases as
going to higher vibrational levels. This results in
decrease of the gaps between transition lines as
one goes to higher frequencies.
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Vibration-Rotation Infrared Spectrum of HCl
Approximation of B
values
2B 2B 2B 2B
4B
2B
2B 2B
2B
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Vib-Rot Infrared Spectrum of Nitric Oxide
R-branch
Q-branch
P-branch
• Exceptions to the infrared ΔJ ≠ 0 selection rule are
found for some diatomic molecules such as NO.
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Vib-Rot Infrared Spectrum of the DCl
Molecule
• νvib(HCl) > νvib(DCl)
because of the
differences in force
constants and
reduced massed
between the two
molecules.
• B0 = 5.392263 cm-1
B1 = 5.279890 cm-1
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Raman Stokes and Anti-Stokes Transitions
v
v
v
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Rot-Vib Raman Spectrum of Carbon Oxide
12 B
4B
4B
• Selection rule for Raman transitions in diatomic
molecules is ΔJ = 0, ±2.
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Gross Selection Rule of Infrared Vibrational
Spectroscopy
• The gross selection rule
for infrared vibrational
spectroscopy states that
electric dipole moment of
the molecule must change
when the atoms are
displaced.
• The molecule need NOT
to have permanent dipole
moment in order to be
infrared active.
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