1. Vibrational Spectroscopy I
CHEM 515 Spectroscopy
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
1330 cm-1
667 cm-1 V V R R
Dissociatve
Non-dissociatve

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
Vibrational spectrum of HCl is based on the harmonic oscillator model with ωe = 2989 cm-1. v
ν (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 non-zero 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. Birge-Sponer Diagram

21. Birge-Sponer Diagram

22. Vibration-Rotation Spectra
Energy increases

23. Vibration-Rotation Spectra
Infrared spectrum
ΔJ = ±1
Raman spectrum
ΔJ = 0 , ±2

24. Vibration-Rotation Infrared Spectrum of HCl
νvib is different for H35Cl and H37Cl molecules due to the slight difference in their reduced masses. au

25. 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.

26. Vibration-Rotation Infrared Spectrum of HCl
Band center
H35Cl
Band center
H37Cl

27. 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.

28. 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.

29. Vibration-Rotation Infrared Spectrum of HCl
Approximation of B values

30. Vib-Rot Infrared Spectrum of Nitric Oxide
R-branch
P-branch
Q-branch
Exceptions to the infrared ΔJ ≠ 0 selection rule are found for some diatomic molecules such as NO.

31. 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 = cm-1
B1 = cm-1

32. Raman Stokes and Anti-Stokes Transitionsv v v

33. Rot-Vib Raman Spectrum of Carbon Oxide
Selection rule for Raman transitions in diatomic molecules is ΔJ = 0, ±2.

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.