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V

IRTUALLY EVERYTHING WE KNOW about matter comes from the

interaction of matter with electromagnetic radiation. In its most straight-

forward fashion, such interactions define spectroscopy.Spectroscopy had its

origin with Bunsen and Kirchhoff in the early 1860s, as recounted in Chapter

9. Spectroscopy was also an important factor in the development of quantum
   mechanics, as shown by the Rydberg equation for the spectrum of the hydro-
   gen atom as well as Bohr’s theory of hydrogen.
   Spectroscopy probes energy levels of atoms and molecules. Therefore, it is
   an application of quantum mechanics. We have already seen that quantum me-
   chanics provides exact answers for the energies of several ideal systems. What
   we will find is that many of these ideal systems are useful in understanding the
   spectroscopy—and therefore the energy levels—of atomic and molecular systems.
   Atoms and molecules have energies due to several types of motion. In part,
   the Born-Oppenheimer approximation from Chapter 12 will be applied: we
   will treat various motions of atoms and molecules, and the energies of those
   motions, separately. Electronic, nuclear, rotational, and vibrational energy
   levels can and will be treated separately for the most part, although in some
   cases we will have types of spectroscopy that involve combinations of these
   energy levels.
   Conveniently, the transitions that involve the different types of energy levels
   (electronic, vibrational, rotational) usually occur in different parts of the elec-
   tromagnetic spectrum. This makes it even easier to consider them separately.
   We begin our multichapter treatment of spectroscopy by considering rotations
   and vibrations of molecules. Such motions are considered first for a reason.
   Both types of motions can be understood in terms of relatively simple quan-
   tum mechanics. We will also introduce some tools that we can apply to other
   forms of spectroscopy.

14.1 Synopsis

First, we explore the idea of selection rules, which are quantum-mechanical

predictions for which energy levels of an atomic or molecular system will par-

ticipate in a spectral transition. We will see that symmetry considerations are

useful for predicting a transition from one energy level to another. Next, we

14.1 Synopsis

14.2 Selection Rules

14.3 The Electromagnetic
Spectrum

14.4 Rotations in Molecules

14.5 Selection Rules for
Rotational Spectroscopy

14.6 Rotational Spectroscopy

14.7 Centrifugal Distortions

14.8 Vibrations in Molecules

14.9 The Normal Modes
of Vibration

14.10 Quantum-Mechanical
Treatment of Vibrations

14.11 Selection Rules for
Vibrational Spectroscopy

14.12 Vibrational Spectroscopy
of Diatomic and
Linear Molecules

14.13 Symmetry Considerations
for Vibrations

14.14 Vibrational Spectroscopy of
Nonlinear Molecules

14.15 Nonallowed and
Nonfundamental
Vibrational Transitions

14.16 Fingerprint Regions

14.17 Rotational-Vibrational
Spectroscopy

14.18 Raman Spectroscopy

14.19 Summary

Rotational and Vibrational

Spectroscopy