Absorption wavepacket picture

Explain why, in the semiclassical wavepacket picture, the width of an absorption band increases with the slope of the excited-state potential surface in the region of the Franck-Condon maximum, whereas the width of an emission band increases with the corresponding slope of the ground-state potential surface. 

Because of the superposition of three distinct types of periodic motion with different periods the wavepacket by itself does not reveal a clear picture in the present case, i.e., the classical skeleton is hardly visible through the quantum mechanical flesh . The perfect agreement between the recurrence times of the quantum mechanical wavepacket and the periods of the classical periodic orbits, however, provides convincing evidence that the structures in the absorption spectrum are ultimately the consequence of the three generic unstable periodic orbits. This correlation is... 

The great asset of the time-dependent picture rests on the fact that no reference is made to the (many) stationary continuum states in the excited electronic state. The propagation of a single wavepacket, which contains the entire history of the dynamics in the upper state, thus yields the absorption cross section, all Raman cross sections, and the final state distributions of the photofragments. 

As one would guess from this picture, a slight steepening of the slope in the direction of the product (I + GN) causes the wavepacket to miss altogether, resulting in a smooth absorption curve. 

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