Vibrational Structure and the Franck-Condon Principle

Recall that, generally, electronic states are separated by more energy than are vibrational states (which are in turn separated by more energy than are rotational states). It is common to consider that every electronic state of a molecule has its own collection, or manifold, of vibrational states. The following discussion is easiest if one assumes a diatomic molecule (although the ideas are applicable to all molecules). 

FIGURE 15.12 Different electronic states have different minimum-energy internuclear distances as well as different vibrational energy manifolds within each. This complicates the electronic spectra of even the simplest, diatomic molecules. 

Unless otherwise noted, all art on this page is Cengage Learning 2014. 

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. 

Mathematically, the transition moment of a vibronic transition depends on an overlap integral in terms of the electronic and vibrational wavefunctions. The form of the transition moment is 

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