Rotational Structure in Molecular Infrared Spectra - 1st Edition - ISBN: 9780124077713, 9780124078932

Rotational Structure in Molecular Infrared Spectra

1st Edition

Authors: Carlo di Lauro
Hardcover ISBN: 9780124077713
eBook ISBN: 9780124078932
Imprint: Elsevier
Published Date: 13th May 2013
Page Count: 344
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Recent advances in infrared molecular spectroscopy have resulted in sophisticated theoretical and laboratory methods that are difficult to grasp without a solid understanding of the basic principles and underlying theory of vibration-rotation absorption spectroscopy. Rotational Structure in Molecular Infrared Spectra fills the gap between these recent, complex topics and the most elementary methods in the field of rotational structure in the infrared spectra of gaseous molecules. There is an increasing need for people with the skills and knowledge to interpret vibration-rotation spectra in many scientific disciplines, including applications in atmospheric and planetary research. Consequently, the basic principles of vibration-rotation absorption spectroscopy are addressed for contemporary applications. In addition to covering operational quantum mechanical methods, spherical tensor algebra, and group theoretical methods applied to molecular symmetry, attention is also given to phase conventions and their effects on the values of matrix elements. Designed for researchers and PhD students involved in the interpretation of vibration-rotation spectra, the book intentionally separates basic theoretical arguments (in the appendices), allowing readers who are mainly concerned with applications to skip the principles while at the same time providing a sound theoretical basis for readers who are looking for more foundational information.

Key Features

  • Reviews basic theory and contemporary methods of vibration rotation absorption spectroscopy, including operational quantum mechanical methods, spherical tensor algebra, and group theoretical methods applied to molecular symmetry
  • Covers sophisticated mathematical topics in simple, easy-to-read language
  • Discusses methods and applications separately from basic theoretical arguments for quick reference


Physical and theoretical chemists, analytical and biochemists, physicists, astronomers, atmosphericists, astrophysicists, and graduate-level/post-doctoral students in these disciplines

Table of Contents



1. The Vibration-Rotation Problem

1.1 Classical Kinetic Energy

1.2 The Quantum Mechanical Hamiltonian


2. Interaction of Matter and Light

2.1 Time-Dependent Perturbations

2.2 A Charge in an Electromagnetic Field

2.3 A System of Charged Particles in a Radiation Field

2.4 More on Electric Dipole Transitions

2.5 Spontaneous Emission


3. Molecular Symmetry and Spectroscopy

3.1 Molecular Symmetry and Molecular Point Groups

3.2 Rotational Energy and Rotational Hamiltonian of Rigid Rotors

3.3 Rotational Symmetry and Rotational Groups

3.4 Molecular Deformations and Molecular Symmetry Groups

3.5 The Inversion Operation E* and Parity

3.6 The Complete Nuclear Permutation and Permutation-Inversion Groups

3.7 Feasible Operations and Molecular Symmetry Groups

3.8 The Extension of Molecular Symmetry Groups

3.9 Time Reversal

3.10 A First Glance to Transition Selection Rules: Parity


4. Symmetry of Wavefunctions in Vibration-Rotation Spectroscopy

4.1 Rotational Coordinates

4.2 Rotational Operators and Wavefunctions

4.3 Molecular Vibrations

4.4 Vibration-Rotation Wavefunctions

4.5 Linear Molecules

4.6 Asymmetric Top Molecules

4.7 Spherical Top Molecules


5. Nuclear Spin Statistical Weights

5.1 Symmetries of Nuclear Spin, Rovibronic, and Total Wavefunctions

5.2 Linear Molecules


6. Expansion and Transformations of the Vibration-Rotation Hamiltonian

6.1 Expansion of the Vibration-Rotation Hamiltonian

6.2 The Expanded Vibration-Rotation Hamiltonian

6.3 An Isolated Vibrational State


7. Effects of Centrifugal Distortions

7.1 Linear Molecules

7.2 Symmetric Top Molecules

7.3 Spherical Top Molecules

7.4 Asymmetric Top Molecules


8. Spectra of Symmetric Top and Linear Molecules

8.1 Molecular Degrees of Freedom

8.2 The Harmonic Oscillator-Rigid Rotor Approximation

8.3 Semirigid Symmetric Top Molecules

8.4 Overtones and Combinations

8.5 Linear Molecules

8.6 Vibration-Rotation Selection Rules: Line Intensities and Line Strengths

8.7 Parallel and Perpendicular Line Strengths

8.8 Line Strengths with Perturbed Upper States

8.9 Line Shapes

8.10 Main Spectral Features in Symmetric Tops and Linear Molecules

8.11 Lower and Upper State Combinations Differences

8.12 Hot and Difference Bands

8.13 Phase Conventions

8.14 Anharmonic Interactions

8.15 Coriolis Interactions

8.16 l-Type Interactions and Doublings

8.17 Higher Order Perturbations

8.18 Isolated Vibrational Levels and Polyads


9. Spectra of Asymmetric Top Molecules

9.1 Rotational Energy

9.2 Orthorhombic Molecules

9.3 Vibration-Rotation Transitions

9.4 Hybrid Bands

9.5 Near-Symmetric Tops

9.6 Anharmonic and Coriolis Interactions

9.7 Intensity Calculation


10. Spectra of Spherical Top Molecules

10.1 General Considerations

10.2 Fundamental Vibrational States

10.3 Overtones and Combinations of F-Modes

10.4 Coriolis Coupling in Overtones and Combinations of F-Modes

10.5 Selection Rules and Intensities

10.6 Effects of Anharmonicity

10.7 Centrifugal Distortion Effects

10.8 Remarks

10.9 Cubic Symmetry


11. Floppy Molecules

11.1 Molecular Inversion

11.2 Internal Rotation

11.3 Effects of Torsional Coriolis Coupling


Appendix 1. Phases of Wavefunctions

Appendix 2. Eigenfunctions of Commuting Operators

Appendix 3. Coupling of Angular Momenta

A3.1 Internal and Rotational Angular Momenta

A3.2 Separation of Rotation and Vibration

A3.3 Coupling of J with the Nuclear Spin

A3.4 Phases and Clebsch-Gordan Coefficients

Appendix 4. Angular Momentum Matrix Elements

A4.1 Rotational Angular Momenta in a Molecule-Fixed Frame

Appendix 5. The Full Rotation Group and Irreducible Spherical Tensors

A5.1 The Wigner-Eckart Theorem

A5.2 Reduced Matrix Elements in Uncoupled and Coupled Representations

A5.3 Products of Tensor Operators

A5.4 Contraction of Tensor Operators

A5.5 The Full Rotation-Reflection Group

Appendix 6. Direction Cosine Operators

Appendix 7. Harmonic Oscillators

A7.1 Monodimensional Harmonic Oscillator

A7.2 Two-Dimensional Isotropic Harmonic Oscillator

A7.3 Three-Dimensional Isotropic Harmonic Oscillator

Appendix 8. Vibrational Normal Modes and Coriolis Coefficients

A8.1 Vibrational Normal Modes

A8.2 Coriolis Coefficients

Appendix 9. Contact Transformation and Perturbation Methods

A9.1 Contact Transformations

A9.2 Van Vleck Perturbation Method



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About the Author

Carlo di Lauro

Carlo di Lauro obtained, with honor, the title of Doctor in Industrial Chemistry in 1963 and soon started his research activity. In 1965, he won an OCSE fellowship where he worked at the University of Reading, U.K., focusing on his interests in the theory and interpretation of vibration-rotation spectra of light molecules, working with Prof. I. M. Mills. He has been teaching since then, and has been at the University of Napoli, Federico II since 1984. In 1991 he was awarded the knighthood “Chevalier des Palmes Académiques” by the Ministère de l’Education Nationale of France. His research activity, in the field of the Molecular Spectroscopy of gases, has always covered both the theoretical aspects and the application to the interpretation of actual spectra. He is the author or co-author of more than 90 scientific articles in relevant international journals. Presently, Dr. di Lauro’s research activity is devoted to vibration-torsion interaction mechanisms in molecules with internal rotation, especially those like ethane. His achievements in the fields of Interactions of Molecular Vibrations and Rotation, Electron Spin Structure in Ro-vibronic Spectra of Molecules in Multiple States, Phases in the Wavefunctions in Molecular Spectroscopy, and Internal Rotation in Floppy Molecules are widely known in the scientific community. In particular, he has shown that torsional Coriolis interactions (coupling of vibrational modes with the internal rotation or large amplitude torsion) can have drastic predictable effects on the magnitude of torsional line splitting. He is consultant of the Jet Propulsion Laboratory of Pasadena, California, since 2007, on a Nasa project for the study of the atmosphere of Titan. He is still working in the detailed interpretation of high resolution infrared spectra of ethane, and this activity has earned for him an international reputation in the community of planetary astronomers. Beyond his scientific activity, Dr. di Lauro is passionate about classical and opera music and is an amateur flute player.

Affiliations and Expertise

University of Napoli Federico II, Italy


"Lauro offers a bridge between recent research on advanced aspects of molecular spectroscopy and elementary basic methods in the field of the rotational structure in the infrared spectra of gaseous molecules, an area that has not been studied much during the past few decades.", April 2014