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.

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

θ = 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 > IA Prolate symmetric top

4. IC > IB = IA Oblate symmetric top

5. IC > IB > IA Asymmetric top

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Linear Molecules

IC = IB , IA = 0

Linear molecules

Other examples:

• HCl

• CO2

• H–C≡C–H

• H–C≡C–C≡C–C≡C–H

• LiF

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Spherical Top Molecules

IC = IB = IA

Spherical top

Other examples:

• CH4

• CCl4

• Generally, molecules with Oh, Td, or Ih point groups are considered spherical top molecules.

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Prolate Symmetric Top Molecules

IC = IB > IA

Prolate symmetric top

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Oblate Symmetric Top Molecules

IC > IB = IA

Oblate symmetric top

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Asymmetric Top Molecules

IC > IB > IA

Asymmetric top

Most of the molecules are 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