Physical Chemistry , 1st ed.

the American physicist Edward U. Condon. Franck shared a 1925 Nobel Prize

for his work on the interactions between electrons and atoms. Among other

things, Condon worked on the Manhattan Project to develop the nuclear

bomb.) The law of conservation of momentum can be used to justify the

Franck-Condon principle. Since momentum equals mv, the velocity of the

atoms must be very close in both states in order for a transition to occur (since

masses of the atoms are constant). Molecules whose atoms are moving very

quickly will experience transitions to (vibrational) states in which the atoms

are also moving quickly. Molecules whose atoms are almost at rest (like at the

turning point of a vibration) will experience transitions to higher vibrational

states in which atoms in the excited state are also almost at rest.

A second consideration in electronic spectra is the recognition that elec-

tronic states, usually separated by a relatively large amount of energy, have

within each of them a vibrational manifold of states. High-resolution elec-

tronic spectra such as the one shown in Figure 15.13 reveal a set of lines su-

perimposed on the transition. These lines represent different initial and final

vibrationalstates of the molecules within the initial and final electronic states.

Such transitions are referred to as vibrational-electronic, or vibronic,transi-

tions. In vibronic spectra, the selection rules for the electronic transition are

given in equations 15.18 to 15.22 (for diatomic molecules). However, there are

no specific selection rules for what vibrational states can participate in the

vibronic transition. This is because the vibrational selection rule, v1, is

applicable only for harmonic-oscillator vibrations within a singleelectronic

state. It is not applicable to vibrational wavefunctions from differing electronic

states.Anyvibrational transitions can participate in a combined vibrational-

electronic transition.

However, not all of them will, and it is the Franck-Condon principle that

justifies the participation of various vibrational levels in a vibronic spectrum.

The Franck-Condon principle requires that an electronic transition be repre-

sented by a verticalmove in a diagram such as Figure 15.14. In order for such

a transition to be considered likely, not only must the two particular vibra-

tional states overlap each other vertically, but the overlap must include parts of

the vibrational wavefunctions that have similar probability. Figure 15.14 shows

540 CHAPTER 15 Introduction to Electronic Spectroscopy and Structure

34,300

Wavenumber (cm^1 )

35,100

Relative intensity

34,500 34,700 34,900

Figure 15.13 A high-resolution electronic spectrum of methylaniline, showing a pattern of

lines that is attributable to different vibrational energy levels involved in the electronic transition.

Source:B. Ballesteros and N. Santos,Spectrochim. Acta, Part A,2002, 58: 1074.

Figure 15.14 Two examples of electronic tran-
sitions that have different probabilities due to the
Franck-Condon principle. The transition labeled
A has a low probability, because it is going from
a maximum probability in the ground-state
vibrational wavefunction to a minimum proba-
bility in the excited-state vibrational wavefunc-
tion. The transition labeled B has a higher prob-
ability, because it involves two vibrations of more
similar probability at that particular internuclear
separation.

Internuclear separation

AB

Energy