Microwave Spectroscopy II

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Presentation transcript:

Microwave Spectroscopy II CHEM 515 Spectroscopy Microwave Spectroscopy II

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.

Moment of Inertia

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

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

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

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

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

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

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

Line Intensities in Rotational Spectra

Line Intensities in Rotational Spectra

Centrifugal Distortion

Splitting Due to Stark Effect

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).

Nuclear Hyperfine Splitting

Nuclear Hyperfine Splitting

Symmetric Top Molecules

Energy Levels for Symmetric Top Molecules

Energy Levels for Symmetric Top Molecules

Selection Rules for Symmetric Top Molecules

Rotational Spectra of Symmetric Top Molecules

Rotational Spectra of Symmetric Top Molecules

Asymmetric Rotor Rotational Levels

Asymmetric Rotor Rotational Levels

Asymmetric Rotor Rotational Levels

Selection Rules for Asymmetric Rotor