1. Microwave Spectroscopy II
CHEM 515 Spectroscopy
Microwave Spectroscopy II

2. Moment of Inertia
Moment of inertia (I), also called mass moment of inertia or the angular mass, is a measure of an object's resistance to changes in its rotation rate. It is the rotational analog of mass.
The moment of inertia of an object about a given axis describes how difficult it is to change its angular motion about that axis.

3. Moment of Inertia

4. Moments of Inertia for a Water Molecule
Given:
r = Å
θ = 104.5°
mH = 1.00 atomic mass unit (u)
mO = atomic mass unit (u)
Results in:
f = Å
g = Å
h = Å

5. Classes of Rotating Molecules
Molecules can be classified into five main groups depending on their moments of inertia. 1.
IC = IB , IA = 0
Linear molecules 2.
IC = IB = IA
Spherical top 3.
IC = IB > IA
Prolate symmetric top 4.
IC > IB = IA
Oblate symmetric top 5.
IC > IB > IA
Asymmetric top

6. Linear Molecules Other examples: HCl CO2 H–C≡C–H H–C≡C–C≡C–C≡C–H LiF
IC = IB , IA = 0
Linear molecules

7. Spherical Top Molecules
Other examples:
CH4
CCl4
Generally, molecules with Oh, Td, or Ih point groups are considered spherical top molecules.
IC = IB = IA
Spherical top

8. Prolate Symmetric Top Molecules
IC = IB > IA
Prolate symmetric top

9. Oblate Symmetric Top Molecules
IC > IB = IA
Oblate symmetric top

10. Asymmetric Top Molecules
Most of the molecules are asymmetric top.
IC > IB > IA
Asymmetric top

11. Line Intensities in Rotational Spectra

12. Line Intensities in Rotational Spectra

13. Centrifugal Distortion

14. Splitting Due to Stark Effect

15. Nuclear Hyperfine Splitting
An atomic nucleus is a collection of protons and neutrons.
These particles are `spin-1/2' particles.
They have a spin quantum number of 1/2.
The nucleus itself has a total spin angular momentum formed by the coupling of the individual spin angular momenta of its constituent protons and nuclei (nucleons).

16. Nuclear Hyperfine Splitting

17. Nuclear Hyperfine Splitting

18. Symmetric Top Molecules

19. Energy Levels for Symmetric Top Molecules

20. Energy Levels for Symmetric Top Molecules

21. Selection Rules for Symmetric Top Molecules

22. Rotational Spectra of Symmetric Top Molecules

23. Rotational Spectra of Symmetric Top Molecules

24. Asymmetric Rotor Rotational Levels

25. Asymmetric Rotor Rotational Levels

26. Asymmetric Rotor Rotational Levels

27. Selection Rules for Asymmetric Rotor