1. Chapter 8. Molecular Motion and Spectroscopy
Translation
Rotation
Vibration
Review from Chap. 2
Energy levels
Degrees of Freedom
microwave
infrared
UV/vis
Rotational Spectroscopy
Vibrational Spectroscopy
Electronic Transitions

2. Ch 8. Molecular Motion and Spectroscopy
• Study of Interaction of Matter and Light (Photon)
• Molecular Spectroscopy
 Information about molecules such as geometry and energy levels are obtained by the interaction of molecules and photons
• Molecular motions: Translation, Rotation, Vibration
 determines the energy levels for the absorption or emission of photons

3. Spectroscopy In Ch 2, spectroscopy of atoms:
transition between energy levels

4. 8.1 Degrees of Freedom: Translation, Rotation, and Vibration4
8.1 Degrees of Freedom: Translation, Rotation, and Vibration
Consider a single Ar atom moving in 3-D space:
- Moving motion is referred to as Translation
To analyze the translation of an Ar, we need to know position (x, y, z) and momentum (px, py, pz)
Where it is Where it is headed
Each coordinate-momentum pair [for example, (x,px)] is referred to as a Degree of Freedom (DF)
An Ar atom moving through 3-D space has three DFs
N argon atoms possesses 3N DFs:
All translational DFs

5. 5
Internal Motions
- A collection of N atoms possesses 3N DFs - If N atoms happen to be bonded together into an N-atom molecule, the number of DFs is still 3N. - But, atoms in a molecule cannot translate independently of each other No 3N translational DFs Contribution of DFs to Internal Motions - Two types: Rotation and Vibration

6. Center of Mass (Balanced Point)6
Center of Mass (Balanced Point)
- A point mass that can represent the molecule - Motion of the center of mass requires 3 DFs to describe it - In general, regardless of its size or complexity, a molecule has 3 translational DFs - Thus, (3N – 3) DFs for the internal motions of rotation and vibration

7. Figure 8.1

8. Figure 8.2

9. Rotational and vibrational DFs9
Rotational and vibrational DFs
N atomic
Linear Molecule
Non-Linear Molecule
Rotation
2 DFs
3 DFs
Vibration
3N – 5
3N - 6

10. Table 8.1

11. Etotal = Enuclear + Eelectron
= Etrans + Evib + Erot + Eelectron
= Etrans + Einternal

12. Electronic, Vibrational, and Rotational Energy Levels of a Diatomic Molecule
Exercise: Indicate the molecular state in which it is electronically in the ground state, vibrationally in the first excited state, and rotationally in the ground state.

14. 8.2 Rotational Motion: Defining a Molecular Day
re = rA + rB
Rotational Kinetic Energy (Erot)
where ω is angular velocity, dθ/dt

15. Rotational Kinetic Energy (Erot)
reduced mass
moment of inertia
(compare this with )
Using angular moment
(compare this with )
the rotational kinetic
energy becomes
(compare this with )

16. Rotational period For Krot = kBT
For a typical molecule at room temperature
(one picosecond)

17. Quantization of Rotational Energy
V = 0
cyclic boundary condition: Ψ(2π + θ) = Ψ(θ)
By solving Schrodinger equation for rotational motion,
the rotational energy levels are
Rotational energy levels in wavenumber (cm-1)

18. Spacing between adjacent rotational levels j and j-1,

19. Rotational Spectroscopy
(1) Bohr postulate
(2) Selection Rule

20. The molecule should have a permanent electric dipole moment
Requirements for a molecule to show a pure rotational spectrum (absorption or emission):
The molecule should have a permanent electric dipole moment
Review from Ch 6
• The electric dipole moment,
μ = q r distance between charges
magnitude of the charge separation

21. far-infrared to the microwave spectral regions
(microwave spectroscopy)

23. 8.3 Vibrational Motion: Molecular Calisthenics
Harmonic oscillator
A molecule vibrates ~50 times during a molecular day (one rotation)

24. Quantization of Vibrational Energy
By solving Schrodinger equation for vibrational motion,
Vibrational energy level
where is a vibrational quantum number
Zero point energy
Spacing between adjacent vibrational sates

25. Department of Chemistry, KAIST

27. Infrared spectral region

28. Vibrational Spectroscopy
Vibrational selection rule

29. Department of Chemistry, KAIST

32. 8.4 Electronic Transitions in Molecules
Molecular Orbital (MO) Theory
for C2H4 molecule,
UV or Visible spectral region

33. Department of Chemistry, KAIST

35. Department of Chemistry, KAIST
Fate of Excited Electronic States
Department of Chemistry, KAIST

36. We will skip Photoelectron Spectroscopy !!