Fundamentals of Molecular Symmetry

P.R. Bunker

• Publisher: CRC Press
• Year: 2018
• ISBN:
  9781351989855
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Physical & Theoretical Chemistry

Winner of a 2005 CHOICE Outstanding Academic Book Award

Molecular symmetry is an easily applied tool for understanding and predicting many of the properties of molecules. Traditionally, students are taught this subject using point groups derived from the equilibrium geometry of the molecule.

Fundamentals of Molecular Symmetry shows how to set up symmetry groups for molecules using the more general idea of energy invariance. It is no more difficult than using molecular geometry and one obtains molecular symmetry groups.

The book provides an introductory description of molecular spectroscopy and quantum mechanics as the foundation for understanding how molecular symmetry is defined and used. The approach taken gives a balanced account of using both point groups and molecular symmetry groups. Usually the point group is only useful for isolated, nonrotating molecules, executing small amplitude vibrations, with no tunneling, in isolated electronic states. However, for the chemical physicist or physical chemist who wishes to go beyond these limitations, the molecular symmetry group is almost always required.

PART 1

SPECTROSCOPY AND THE QUANTUM STATES OF MOLECULES

Chapter 1

Molecular spectroscopy

The study of the extent of the absorption, emission and scattering of electromagnetic radiation by matter, as a function of the wavelength of the radiation and of the nature of the matter, is the subject of spectroscopy. We concentrate on situations involving weak electromagnetic radiation¹ and gas phase molecular samples. In these circumstances, classical theory is used to describe the radiation and quantum mechanics to describe the molecules and their interaction with the radiation.

The classical theory of electromagnetic radiation is based on Maxwell’s 1860 theory of the electromagnetic field. Electromagnetic radiation consists of oscillating electric and magnetic fields by virtue of which it carries electric and magnetic energy from a source to a detector. The electric and magnetic fields that constitute the radiation oscillate at the same frequency v [in units of cycles s⁻¹ or hertz (Hz)]; these fields oscillate perpendicular to each other and to the direction of propagation of the radiation. In a vacuum, radiation propagates at the speed of light c (= 299 792 458 m s⁻¹) and the distance between adjacent field oscillation crests is the wavelength λ, where

$\text{λ}=c/v.$

(1.1)

1.1 Molecular spectra

Electromagnetic radiation emitted from a region of auroral activity in the upper atmosphereof Jupiter can be dispersed to yield an emission spectrum such as shown in figure 1.1. An emission spectrum is a plot of the intensity of the radiation emitted from a source as a function of its wavelength, frequency or wavenumber $\tilde{\nu }(\tilde{v}=1/\text{λ}$; invariably quoted in cm⁻¹ units). Figure 1.2 is part of the absorption spectrum of carbon monoxide (CO) at 300 K plotted as transmittance (see below) versu...