Wavepacket Pictures of Spectroscopic Transitions

One fruitful application this approach is to relate the absorption spectrum to the spatial overlap of the wavepacket initially created by the excitation (X(0)) with the moving wavepacket at later times (X(t)). HeUer and coworkers [132-137] showed that the spectrum can be obtained by a Fourier transform of the time-dependent overlap integral (X(0)LT(0)  

A Fourier transform of this function gives a set of lines separated in frequency by v, with each line weighted by the Franck-Condon factor Xk e) xo(g)) 1 - This is just the result we obtained in Chap. 4 for the shape of an absorption spectrum. If we multiply (X(0)lAi 0) by the damping factor exp(-f/Tc) that is included on the right 

11 Pump-Probe Spectroscopy, Photon Echoes and Vibrational Wavepackets 

The fluorescence emission spectmm can be obtained in the same way as the absorption spectrum by considering the time dependence of a wavepacket in the grotmd electronic state following a transition from the excited state. The weighting factor on the left-hand side of Eq. (11.53) is simply replaced by u in accord with the Einstein coefficients (Chap. 5). 

The main utility of the wavepacket approach lies in the evaluation of spectroscopic properties of molecules with congested vibrational modes. As we discussed in Chap. 4, the ground-state vibrational wavefunctions Xa g for a molecule with multiple vibrational modes are products of the wavefunctions for all the individual modes =Xa g)Xa2 g)Xai g)— If the normal coordinates do not change signifi- 

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