Rotational Spectra and Molecular Structure - 1st Edition - ISBN: 9781483167374, 9781483194851

Rotational Spectra and Molecular Structure

1st Edition

Physical Chemistry: A Series of Monographs

Authors: James E. Wollrab
Editors: Ernest M. Loebl
eBook ISBN: 9781483194851
Imprint: Academic Press
Published Date: 1st January 1967
Page Count: 484
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Physical Chemistry, A Series of Monographs: Rotational Spectra and Molecular Structure covers the energy levels and rotational transitions. This book is divided into nine chapters that evaluate the rigid asymmetric top molecules and the nuclear spin statistics for asymmetric tops. Some of the topics covered in the book are the asymmetric rotor functions; rotational transition intensities; classes of molecules; nuclear spin statistics for linear molecules and symmetric tops; and classical appearance of centrifugal and coriolis forces. Other chapters deal with the energy levels and effects of centrifugal distortion, as well as the internuclear distance and moments of inertia. The discussion then shifts to the coriolis coupling effects on rotational constants and the perturbation treatment of vibration-rotational Hamiltonian. The last chapter is devoted to the examination of origin of the quadrupole interaction.
The book can provide useful information to chemists, physicists, electrical engineers, students, and researchers.

Table of Contents


Chapter 1 Rotational Spectra

1-1. Energy Levels and Rotational Transitions

1-2. Information Contained in Rotational Spectra

Chapter 2 Rigid Rotor

2-1. Introduction

2-2. Molecular Parameters

2-3. Classes of Molecules

2-4a. Rigid Linear Molecules

2-4b. Spectrum and Selection Rules

2-5a. Rigid Symmetric Top Molecules

2-5b. Spectrum and Selection Rules

2-6a. Rigid Asymmetric Top Molecules

2-6b. Matrix Elements of E(κ)

2-6c. Asymmetric Rotor Functions

2-6d. Selection Rules

2-6e. K Doubling in an Asymmetric Rotor

2-6f. Graphical Methods for Determining κ and (A — C)/2

2-7. Rotational Transition Intensities

2-8. Statistical Weights

2-9. Nuclear Spin Statistics for Linear Molecules

2-10a. Nuclear Spin Statistics for Symmetric Tops

2-10b. Rotational Wave Functions

2-10c. Spin Wave Functions

2-1la. Nuclear Spin Statistics for Asymmetric Tops

2-11b. Rotational Wave Functions

2-11c. Spin Wave Functions

2-12a. Dipole Matrix Elements

2-12b. Dipole Matrix Elements for a Linear Molecule

2-12c. Dipole Matrix Elements for a Symmetric Rotor

2-12d. Dipole Matrix Elements for an Asymmetric Rotor

2-13. Transition Strengths and Approximate Wave Functions for Near Symmetric Tops

Chapter 3 Centrifugal Distortion, Coriolis Coupling, and Fermi Resonance

3-1. Introduction

3-2. Classical Appearance of Centrifugal and Coriolis Forces

3-3. Centrifugal Distortion in a Linear Molecule

3-4. Centrifugal Distortion in Symmetric Top Molecules

3-5. The Coriolis Coupling Constant

3-6a. l-Type Doubling in Linear Molecules

3-6b. Direct l-Type Transitions

3-7a. Degenerate Coriolis Splitting

3-7b. l-Type Doubling in Symmetric Top Molecules

3-7c. Energy Levels and Effects of Centrifugal Distortion

3-8. Dipole Matrix Elements and Selection Rules for l-Doubling

3-9. Fermi Resonance in Linear Molecules

3-10a. Nonrigid Effects in Asymmetric Rotors

3-10b. Perturbation Treatment of Vibration-Rotation Hamiltonian

3-10c. Interactions for Near Degeneracies

3-11. Coriolis Coupling Effects on Rotational Constants

3-12. Centrifugal Distortion in Asymmetric Tops

3-13. Fermi Resonance in Nonlinear Molecules

Chapter 4 Molecular Structure

4-1. Internuclear Distances and Moments of Inertia

4-2. r0 Structure

4-3. rs Structure

4-4a. Linear Molecules

4-4b. Comparison of r0 and rs Structures for Linear Molecules

4-5. Off-Axis Substitution in a Symmetric Top

4-6a. Planar Asymmetric Tops

4-6b. Nonplanar Asymmetric Tops

4-7. Structure Determinations When All Atoms are Not Isotopically Substituted

4-8a. Determination of Coordinates near Principal Axes:Linear Molecules

4-8b. Near Axis Coordinates in Asymmetric Tops

4-8c. Coordinates of Atoms near the COM in an Asymmetric Top with a Plane of Symmetry

4-9a. The Inertia Defect

4-9b. Planar Molecules

4-9c. Inertia Defect and Molecular Structure of Planar Molecules

4-9d. Inertia Defect in Nonplanar Molecules

4-10. Variation of Bond Length with Isotopic Substitution

4-11. Values and Limitations of the Average Structure

Chapter 5 Nuclear Quadrupole Coupling

5-1. Quadrupole Nuclei in Molecules

5-2. Origin of the Quadrupole Interaction

5-3. Matrix Elements of HQ

5-4. First-Order Quadrupole Energy

5-5. Second-Order Quadrupole Energy

5-6. Molecules with Two Quadrupole Nuclei

5-7. Molecules with Three Quadrupole Nuclei

5-8. Quadrupole Hyperfine Structure in Excited Vibrational States

5-9. Relative Intensities of Quadrupole Components

Chapter 6 Internal Rotation

6-1a. Introduction

6-1b. Physical Models

6-1c. Potential Energy and Hindered Rotation

6-2. High Potential Barriers

6-3a. Energy Levels, Selection Rules, and Intensities for a High Barrier

6-3b. A Single Internal Rotor

6-3c. Two Equivalent Internal Rotors

6-4. The PAM for a Symmetric Top Molecule

6-5. The IAM for a Symmetric Top Molecule

6-7. IAM for Asymmetric Top Molecules

6-8. Low Barriers

6-9. Completely Asymmetric Molecules

6-10. Internal Rotation Barriers from Intensities

6-11. Internal Barriers from Vibration-Rotation Interactions

6-12. Excited Torsional States 185

6-13a. Coriolis Interactions and Internal Rotation in Symmetric Top Molecules

6-13b. Coriolis Interactions in Excited Torsional States of Asymmetric Rotors

6-14. V6 Contributions to the Torsional Barrier

6-15. Internal Rotation and Nuclear Quadrupole Coupling

6-16a. Molecules with Two Equivalent Methyl Groups

6-16b. Kinetic Energy

6-17. Symmetric Tops with Three Methyl Groups

6-18. Rotational Isomerism

6-19. Barriers Determined from Rotational Spectra

Chapter 7 Inversion

7-1. Characteristics of the Inversion Motion

7-2. Properties of the Inversion Wave Functions

7-3. Inversion in Symmetric Top Molecules

7-4a. Some Potential Functions for the Twofold Inversion Barrier

7-4b. Morse-Stuckelberg Potential

7-4c. Dennison-Uhlenbeck Potential

7-4d. Rosen-Morse Potential

7-4e. Manning Potential

7-4f. Wall-Glocker Potential

7-4g. Newton-Thomas Potential

7-4h. Sutherland-Costain Potential

7-4i. Harmonic Oscillator Perturbed by a Gaussian Barrier

7-4j. Quartic Oscillator

7-4k. Mixed Harmonic-Quartic Potential

7-5. Inversion-Vibration Interactions

7-6. Reduced Mass for NH3-like Symmetric Tops

7-7. Rotational Dependence of Inversion Splittings in Symmetric Tops

7-8. Inversion Transitions in Ammonia

7-9a. Inversion in Asymmetric Tops

7-9b. Selection Rules for Asymmetric Tops

7-9c. Types of Barriers

7-9d. Application of Symmetric Top Potential Functions to Asymmetric Tops

7-9e. Reduced Mass for Inversion in an Asymmetric Top

7-9f. Rotational Dependence of the Inversion Splittings in an Asymmetric Rotor

7-10. Inversion-Inversion Coupling

7-11. Inversion and Internal Rotation—The Methyl Amines

7-12a. Inversion in Near-Planar Molecules

7-12b. Inertial Defect

7-12c. Satellites and Intensities

7-12d. Stark Effect

7-12e. Far Infrared Spectrum

7-12f. Variation of Rotational Constants with Vibrational State

7-13. Vibration-Rotation Interactions

Chapter 8 Stark Effect

8-1. Introduction

8-2. General Properties of the Stark Effect

8-3. Matrix Elements of Ht

8-4. First-Order Stark Effect

8-5. Second-Order Stark Effect

8-6. High Field Stark Effect and Higher-Order Perturbation Terms

8-7. Stark Effect for Near Degeneracies

8-8a. Stark Effect and Quadrupole Hyperfine Structure

8-8b. Weak Field with a Single Quadrupole Nucleus (με << eqQ)

8-8c. Strong Field with a Single Quadrupole Nucleus (με >> eqQ)

8-8d. Intermediate Case (με ≈ eqQ)

8-8e. Near Degeneracies

8-9. Polarizability

8-10a. Stark Splittings and Relative Intensities

8-10b. ΔM = 0 Transitions

8-10c. ΔM = ± 1 Transitions

8-10d. Intensities in the Presence of Hyperfine Structure

8-11a. Stark Effect in a Linear Molecule—OCS

8-11b. Stark Effect for an l-Type Doublet

8-11c. Stark Effect in a Symmetric Top Molecule—CH3F

8-11d. Stark Effect in an Asymmetric Rotor—CH3CHF2

8-11e. Stark Effect in a Ð Electronic State—NO

8-12. Stark Effect and Hindered Internal Motions

8-13. Dipole Moment Measurement Techniques

8-14. Stark Effects in Rapidly Varying Fields

8-15. Variation of μ with Isotopic Substitution and with Vibrational State

Chapter 9 Instrumentation

9-1. Spectroscopy in the Microwave Region

9-2. General Qualities of the Spectrometer

9-3a. Characteristics of Microwave Spectrometers

9-3b. Radiation Sources

9-3c. Source Stabilization

9-3d. Waveguide Stark Cell

9-3e. Modulation, Detection, and Display

9-3f. Frequency Measurements

9-3g. Millimeter and Submillimeter Techniques

9-4. Relative Intensity and Line Width Measurement

9-5. Parallel Plate Spectrometers

9-6. High Temperature and Molecular Beam Spectroscopy

9-7. Applications of Double-Resonance and Beam-Maser Spectrometers

9-8. Study of Free Radicals and Unstable Species

9-9. Zeeman Effect Spectrometers

Appendix 1 References

Appendix 2 Short Table of Physical Constants, Conversion Factors, and Waveguide Nomenclature

Appendix 3 Evaluation of E(κ)

Appendix 4 Derivation of the Hamiltonian for Treating the Vibration-Rotation Interaction Problem

Appendix 5 Derivation of the Inertial Defect

Appendix 6 Coupling of Angular Momentum Vectors

Appendix 7 The Van Vleck Transformation

Appendix 8 Internal Rotation Splittings for the IAM

Appendix 9 Barriers to Internal Rotation Determined by Microwave Spectroscopy

Appendix 10 Vanishing of Odd-Orde'r Nondegenerate Stark Corrections

Appendix 11 Mathieu's Equation

Appendix 12 Perturbation Coefficients for the Internal Rotation Problem

Appendix 13 Molecular Zeeman Effect

Appendix 14 Stark Corrections for a Linear Molecule

Author Index

Subject Index


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© Academic Press 1967
Academic Press
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About the Author

James E. Wollrab

About the Editor

Ernest M. Loebl

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