CHEM 515 Spectroscopy Vibrational Spectroscopy I.

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Transcript of CHEM 515 Spectroscopy Vibrational Spectroscopy I.
CHEM 515Spectroscopy
Vibrational Spectroscopy I
2
Rotational, Vibrational and Electronic Levels
3
Molecular Vibrations of CO2
4
Harmonic Oscillator Approximation
Selection rule
Δv = ± 1
5
Harmonic Oscillator Approximation
• At lower energies, the harmonic oscillator model determines the quantum levels quite well. Deviations become more significant at higher energy levels.
6
Types of Potential Function Curves
V V
R R
Dissociatve
Nondissociatve
1330 cm1 667 cm1
7
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.
8
Anharmonicity
• Deviations due to anharmonicity become more clear at – higher energy
levels (v), and
– larger x = r – re values that correspond to dissociation.
9
Anharmonicity
• Electrical anharmonicity: (electrical properties, dipole moment and polarizability).
• Mechanical anharmonicity: (nature of molecular vibration).
Selection rule because of the effect of anharmonicity:
Δv = ± 1, ± 2, ± 3, …
10
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.
11
Vibrational Spectrum of HCl
ν (cm1)
v
Vibrational spectrum of HCl is based on the harmonic oscillator model with ωe = 2989 cm
1.
12
Vibrational Spectrum of HCl
13
Vibrational Spectrum of HCl
14
Vibrational Spectrum of HCl
15
Morse Potential
16
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.
17
Morse Potential
• It also accounts for the anharmonicity of real bonds and the nonzero transition probability for overtones and combinations.
18
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.
19
Dissociation Energy from Spectroscopic Data
20
BirgeSponer Diagram
21
BirgeSponer Diagram
22
VibrationRotation Spectra
Energy increases
23
VibrationRotation Spectra
Infrared spectrumΔJ = ±1
Raman spectrumΔJ = 0 , ±2
24
VibrationRotation Infrared Spectrum of HCl
• νvib is different for H35Cl and H37Cl molecules due to the slight difference in their reduced masses.
au
au
972.036
35ClH35
974.038
35ClH37
25
VibrationRotation 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.
26
VibrationRotation Infrared Spectrum of HCl
B2B2B2B2 B2 B2 B2 B2B4
Band centerH35Cl
Band centerH37Cl
27
VibrationRotation 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.
B2B2B2B2 B2 B2 B2 B2B4
28
VibrationRotation 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.
29
VibrationRotation Infrared Spectrum of HCl
B2B2B2B2 B2 B2 B2 B2B4Approximation of B
values
30
VibRot Infrared Spectrum of Nitric Oxide
• Exceptions to the infrared ΔJ ≠ 0 selection rule are found for some diatomic molecules such as NO.
Qbranch
Pbranch
Rbranch
31
VibRot 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 cm1
B1 = 5.279890 cm1
32
Raman Stokes and AntiStokes Transitions
v
v
v
33
RotVib Raman Spectrum of Carbon Oxide
• Selection rule for Raman transitions in diatomic molecules is ΔJ = 0, ±2.
B4B4
B12
34
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.