Physical Chemistry Third Edition

978 23 Optical Spectroscopy and Photochemistry

Exercise 23.8

One of the normal modes of the benzene molecule is the “breathing mode,” in which the entire

molecule alternately expands and contracts. Will this mode be infrared active?

Electronic Spectra of Polyatomic Molecules

As with diatomic molecules, vibrational and rotational transitions in polyatomic mole-

cules take place along with electronic transitions. The Franck–Condon principle applies,

so that the final state will usually be an excited vibrational state as well as an excited

electronic state. Since there are several normal modes in any polyatomic molecule

the simultaneous electronic, vibrational, and rotational transitions can give very com-

plicated spectra. The most important selection rule is the same for all molecules and

atoms: The total spin quantum number is the same for the final as for the initial state:

∆S 0 (23.5-2)

The selection rules for the space part of the electronic wave function can be derived

using group theory to investigate the effects of wave function symmetry.^20 We state

only the most important rule:

The symmetry of the electronic wave function must change

For example, a transition from a u state to a g state is ordinarily allowed (and vice

versa), whereas a transition from a g state to another g state or from a u state to another

u state is not allowed. The other selection rules are more complicated, and we will not

discuss them.

The molecular electronic selection rules are not exact because they are derived with

approximate wave functions. “Forbidden” transitions are often observed but usually

have smaller probabilities. For example, a transition from an excited singlet state to a

singlet ground state with emission of a photon is allowed and will generally occur with

a mean lifetime of the excited state of a microsecond to a millisecond. Such a transition

is calledfluorescence. A transition from an excited triplet state to a singlet ground state

with emission of a photon is forbidden, and if it occurs it will have a smaller intensity

and a longer mean lifetime of the excited state (sometimes as long as 10 seconds). Such

a transition is calledphosphorescence.

If orbital wave functions are used for a polyatomic molecule the electronic transitions

can be classified by specifying the initial and final orbitals. If an absorption corresponds

to a transition from a nonbonding orbital to an antibondingπorbital, we call it annto

π∗(n→π∗) transition, and similarly for aπtoπ∗(π→π∗) transition. In many cases

a whole class of compounds will exhibit similar spectral lines that can be attributed

to a functional group or other group of atoms within a molecule. Such a group that

exhibits a characteristic absorption is called achromophore. For example, most organic

compounds containing a carbonyl group have an absorption near 200 nm corresponding

to aπ→π∗transition and another absorption near 300 nm corresponding to ann→π∗

transition.

(^20) B. S. Tsukerblat,Group Theory in Chemistry and Spectroscopy, Academic Press, San Diego, 1994,
p. 223ff.