Molecules and Radiation

An Introduction to Modern Molecular Spectroscopy. Second Edition

Jeffrey I. Steinfeld

• Publisher: Dover Publications
• Year: 2012
• Print ISBN: 9780486441528
• eBook ISBN: 9780486137544
• Topic: Physical Sciences
• Subtopic: Physical & Theoretical Chemistry

This unified treatment introduces upper-level undergraduates and graduate students to the concepts and methods of modern molecular spectroscopy and their applications to quantum electronics, lasers, and related optical phenomena.
Starting with a review of the prerequisite quantum mechanical background, the text examines atomic spectra and diatomic molecules, including the rotation and vibration of diatomic molecules and their electronic spectra. A discussion of rudimentary group theory advances to considerations of the rotational spectra of polyatomic molecules and their vibrational and electronic spectra; molecular beams, masers, and lasers; and a variety of forms of spectroscopy, including optical resonance spectroscopy, coherent transient spectroscopy, multiple-photon spectroscopy, and spectroscopy beyond molecular constants. The text concludes with a series of useful appendixes.

1

Review of the Quantum Mechanical Background

1 State Vector Notation

If one were to ask for a definition of the basic operation in spectroscopy, the answer would probably be in terms of carrying out a measurement on a molecule, using electromagnetic radiation as a measuring tool. The essence of the quantum mechanical behavior of systems as small as atoms and molecules is that carrying out a measurement on such a system forces it to take on a sharp value of the one or more observables being measured. In spectroscopic measurements, this observable is almost always the total energy of the system. The measured quantity is the set of differences between the possible energy levels, which is related to an observed set of resonances in the electromagnetic radiation spectrum by the Bohr-Einstein law,

where v is the frequency of the radiation, in hertz (the term cycles per second, or sec ^{– 1}, is no longer officially used); λ is the wavelength of the radiation in centimeters;

is the wave number of the radiation in reciprocal centimeters, or cm ^{– 1}.

Energy and frequency are related by Planck’s constant h = 6.62617₄ x 10 ^{– 27} erg sec, while frequency and wavelength are related by the speed of light in vacuum, c = 2.99792458 x 10¹⁰ cm/sec.²

Since the concept of measurement is a key aspect of the whole, it seems appropriate to introduce the use of a quantum mechanical notation known as measurement algebra at this point. The primary advantage of this notation, as we shall see, is that it provides a very compact and handy way of expressing the matrix elements, and relations between them, in terms of which spectroscopic theory is formulated. It is well to remember that merely using a new notation, while it may be convenient, does not introduce any more content than was expressed by the more familiar language of wave functions and eigenvalues. Several classic quantum mechanics textbooks employ this notation, and the reader is encouraged to look at these as an aid in becoming familiar with this algebra. Especially recommended are the texts by Messiah, Gottfried, and Feynman, Leighton, and Sands (references 1-3).

Figure 1.1

Schematic representation of a Stern-Gerlach experiment. A beam in a j = 1 state enters from the left through a magnetic field inhomogeneous in the z direction. It is split into three j_z components; the +1 component is selected and sent through a magnetic field inhomogeneous in the x direction, whereupon it splits up into three j_x components. If one of these components is then sent through another z magnet, it will again split up into three j_z components, despite the earlier z measurement.

The basic object of this algebra is the state of a system, which is given the symbol |n〉. This state may correspond to an energy level E_n, or to an an...

Table of contents

• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Preface to the Second Edition
• Preface to the First Edition
• 1 - Review of the Quantum Mechanical Background
• 2 - Atomic Spectra
• 3 - Diatomic Molecules
• 4 - Rotation and Vibration of Diatomic Molecules
• 5 - Electronic Spectra of Diatomic Molecules
• 6 - Rudimentary Group Theory
• 7 - Rotational Spectra of Polyatomic Molecules
• 8 - Vibrational Spectra of Polyatomic Molecules
• 9 - Electronic Spectra of Polyatomic Molecules
• 10 - From Molecular Beams to Masers to Lasers
• 11 - Optical Resonance Spectroscopy
• 12 - Coherent Transient Spectroscopy
• 13 - Multiple-Photon Spectroscopy
• 14 - Spectroscopy beyond Molecular Constants
• Appendix A Direct Product Tables
• Appendix B Lagrangian Mechanics
• Appendix D Dipole Correlation and Spectral Density Functions
• Appendix E The Literature of Spectroscopy
• Index