CHEM 515 Spectroscopy

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CHEM 515Spectroscopy

• Microwave Spectroscopy II

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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.

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Moment of Inertia
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Moments of Inertia for a Water Molecule

• Given
• r 0.958 Å
• ? 104.5
• mH 1.00 atomic mass unit (u)
• mO 16.00 atomic mass unit (u)
• Results in
• f 0.7575 Å
• g 0.5213 Å
• h 0.0652 Å

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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 gt IA Prolate symmetric top
4. IC gt IB IA Oblate symmetric top
5. IC gt IB gt IA Asymmetric top
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Linear Molecules

• Other examples
• HCl
• CO2
• HCCH
• HCCCCCCH
• LiF

• IC IB , IA 0
• Linear molecules

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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

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Prolate Symmetric Top Molecules

• IC IB gt IA
• Prolate symmetric top

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Oblate Symmetric Top Molecules

• IC gt IB IA
• Oblate symmetric top

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Asymmetric Top Molecules
Most of the molecules are asymmetric top.

• IC gt IB gt IA
• Asymmetric top

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Line Intensities in Rotational Spectra
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Line Intensities in Rotational Spectra
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Centrifugal Distortion
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Splitting Due to Stark Effect
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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).

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Nuclear Hyperfine Splitting
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Nuclear Hyperfine Splitting
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Symmetric Top Molecules
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Energy Levels for Symmetric Top Molecules
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Energy Levels for Symmetric Top Molecules
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Selection Rules for Symmetric Top Molecules
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Rotational Spectra of Symmetric Top Molecules
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Rotational Spectra of Symmetric Top Molecules
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Asymmetric Rotor Rotational Levels
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Asymmetric Rotor Rotational Levels
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Asymmetric Rotor Rotational Levels
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Selection Rules for Asymmetric Rotor