Some molecules have electronic structures that are more easily described
than others. The electron system of aromatic molecules is an example, and
we will discuss it briefly—but in enough detail to understand exactly where the
important idea of aromaticity comes from. Fluorescence and phosphorescence
are two electronic phenomena that show how complex the interactions of elec-
tronic wavefunctions can get. Finally, we will introduce lasers. Although laser
action can be due to transitions among vibrational, rotational, chemical, or even
translational energy levels, the original lasers were dependent on electronic
transitions. Given the prevalence of lasers in modern society, it is perhaps only
fitting that we end the chapter with an introduction to these powerful light
sources.15.2 Selection Rules
As with rotational and vibrational transitions, there is a selection rule for elec-
tronic transitions dictating which electronic wavefunctions participate in al-
lowed transitions. Allowed electronic transitions must have a nonzero transi-
tion moment as given by the expressionM*finalˆinitiald (15.1)
where now initialand finalrefer to wavefunctions of the system of interest.
ˆis the electric dipole operator that defines the interaction between light and
matter. In rotational and vibrational spectroscopy, the selection rules we could
derive from equation 15.1 were relatively straightforward in terms of changes
in rotational and vibrational quantum numbers.
Unfortunately, for electronic transitions, gross selection rules are not as
straightforward to define. Therefore, we will consider the selection rules for
electronic transitions as they arise in the discussion of the material. The elec-
tronic spectrum of the hydrogen atom, for example, has a relatively simple se-
lection rule. The electronic spectrum of the benzene molecule, as a counter-
example, follows more complex rules.
There is one assurance with regard to electronic spectra. Recall that allowed
transitions for both rotational and vibrational spectra depend on the presence
of a dipole moment, either a permanent one or a changing one. Allowed elec-
tronic transitions always occur with a change in the electronic charge distri-
bution in an atom or molecule. (This change is sometimes referred to as a
“dipolar shift.”) This statement is easily justified. An electron whose state is
described by an initial wavefunction has probabilities of existing in certain
locations in an atomic or molecular system. When described by a different
wavefunction, the electron has different probabilities of existing in those loca-
tions. The electron probability distribution has changed.Allowed electronic
transitions are therefore intimately tied to the idea of a changing electronic
charge, just like allowed rotational and vibrational transitions.
Specific selection rules for atoms and molecules can also be determined us-
ing group-theoretical analyses of the functions in equation 15.1, exactly as we
did in the previous chapter for allowed IR and Raman vibrational transitions.15.3 The Hydrogen Atom
Recall that when an electric current is passed through a sample of hydrogen
gas, light is given off and this light has certain specific frequencies. The inter-520 CHAPTER 15 Introduction to Electronic Spectroscopy and Structure