chem 515 spectroscopy vibrational spectroscopy i
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![Page 1: CHEM 515 Spectroscopy Vibrational Spectroscopy I](https://reader033.vdocuments.site/reader033/viewer/2022061323/56649d375503460f94a0fce1/html5/thumbnails/1.jpg)
CHEM 515Spectroscopy
Vibrational Spectroscopy I
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Rotational, Vibrational and Electronic Levels
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Molecular Vibrations of CO2
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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
V V
R R
Dissociatve
Non-dissociatve
1330 cm-1 667 cm-1
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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
• Deviations due to anharmonicity become more clear at – higher energy
levels (v), and
– larger x = r – re values that correspond to dissociation.
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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, …
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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
ν (cm-1)
v
Vibrational spectrum of HCl is based on the harmonic oscillator model with ωe = 2989 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 spectrumΔJ = ±1
Raman spectrumΔJ = 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.
au
au
972.036
35ClH35
974.038
35ClH37
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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
B2B2B2B2 B2 B2 B2 B2B4
Band centerH35Cl
Band centerH37Cl
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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.
B2B2B2B2 B2 B2 B2 B2B4
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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
B2B2B2B2 B2 B2 B2 B2B4Approximation of B
values
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Vib-Rot Infrared Spectrum of Nitric Oxide
• Exceptions to the infrared ΔJ ≠ 0 selection rule are found for some diatomic molecules such as NO.
Q-branch
P-branch
R-branch
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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
• Selection rule for Raman transitions in diatomic molecules is ΔJ = 0, ±2.
B4B4
B12
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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.