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ESPITE THE FACT THAT WE TREATED vibrational and rotational

spectroscopy first, the astute student will recognize that one of the mys-

teries of classical mechanics involved electronic spectroscopy. The inability to

explain the (electronic) spectrum of the hydrogen atom was a major reason for

the development of quantum mechanics. Yet, we have put off a detailed dis-

cussion of it until after considering rotational and vibrational spectra.

The reason for the delay is that a detailed discussion is slightly more com-

plicated for electronic spectra than for rotations or vibrations. Some new ideas

will have to be developed in order to begin to understand the electronic spec-

tra and structures of many-electron systems. (We should recognize that the

electronic spectrum of hydrogen, even in the formalism of quantum mechan-

ics, will be relatively simple.) However, as with rotational and vibrational spec-

troscopy, our treatment of electronic spectroscopy in this chapter is limited by

necessity. Entire books are written on the subject, and we can only introduce

some basic ideas here.

15.1 Synopsis

We will start by considering the selection rules for electronic transitions. Then,

we will consider the electronic spectrum of the hydrogen atom in terms of the

selection rules and quantum mechanics. There will be few if any surprises here,

since the positions of the lines of the hydrogen atom’s spectrum were at least

known (but not completely understood) over a hundred years ago. The elec-

tronic spectrum of helium, the simplest multielectron system, is not so easy

to model mathematically. This is expected, since quantum mechanics cannot

determine analytic expressions for the wavefunctions for the helium atom. An

electronic spectrum, which shows changesin energies, is equally nonanalytic.

However, for helium and larger atoms (and molecules), we will find that cer-

tain regularities in the spectrum can be traced back to the angular momentum

of the electrons in the atom or molecule. Ultimately, the angular momen-

tum—which was central to Bohr’s theory of hydrogen—will have a central role

in our understanding of electronic spectra. We will see how it is utilized in

atomic, diatomic, and (briefly) molecular electronic spectra.

15.1 Synopsis

15.2 Selection Rules

15.3 The Hydrogen Atom

15.4 Angular Momenta: Orbital
and Spin

15.5 Multiple Electrons:
Term Symbols and
Russell-Saunders Coupling

15.6 Electronic Spectra of
Diatomic Molecules

15.7 Vibrational Structure and
the Franck-Condon Principle

15.8 Electronic Spectra of
Polyatomic Molecules

15.9 Electronic Spectra of
Electron Systems:
Hückel Approximations

15.10 Benzene and Aromaticity

15.11 Fluorescence and
Phosphorescence

15.12 Lasers

15.13 Summary

Introduction to Electronic

Spectroscopy and Structure