Physical Chemistry Third Edition

974 23 Optical Spectroscopy and Photochemistry

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EBO

Figure 23.11 An Electronic Transition According to the Franck–Condon Principle.

In the case of this figure, a transition from thev1 state of the lower electronic state most

likely will lead to thev2 state of the upper electronic state.

typical electronic transition. The line segment is vertical, corresponding to the Franck–

Condon principle. One factor in the integrand of the transition dipole moment is the

product of the vibrational wave functions in the initial and final states. Integration

over the vibrational coordinate gives an overlap integral for the two vibrational states

that is called theFranck–Condon factor. The value of the Franck–Condon factor will

be small unless there is a range of internuclear distance over which both vibrational

wave functions are appreciably different from zero. For a highly probable transition

the vertical line segment in Figure 23.11 must connect one of the regions of relatively

large value of one vibrational wave function to a region of relatively large value of

the other vibrational wave function. Since the equilibrium internuclear distance of

the upper electronic state in Figure 23.11 is somewhat larger than that of the lower

state, the most probable transitions will take place from the ground vibrational state

of the lower electronic state to excited vibrational states of the upper electronic state.

Figure 23.12 shows the electronic band spectrum of nitrogen, which exhibits bands

corresponding to various vibrational transitions occurring with the electronic transition

and sets of lines within each band corresponding to different initial and final rotational

states.

If the electronic wave functions are represented by orbital approximations, an elec-

tronic transition corresponding to the transition of a single electron from one orbital to

another can be characterized by specifying the initial orbital and the final orbital. For

example, if an electron makes a transition from a pi bonding orbital to a pi antibonding

orbital, the transition is called aπ→π∗(pi to pi-star ) transition. If an electron goes

from a nonbonding orbital to a pi antibonding orbital, the transition is said to be an

n→π∗(nto pi-star) transition.

6787

6126

4861.3 (H)

4666

4434

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Dv 522

Dv 521

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Figure 23.12 The Electronic

Band Spectrum of Diatomic

Nitrogen.