Franck-Condon differential

Internal conversion refers to radiationless transition between states of the same multiplicity, whereas intersystem crossing refers to such transitions between states of different multiplicities. The difference between the electronic energies is vested as the vibrational energy of the lower state. In the liquid phase, the vibrational energy may be quickly degraded into heat by collision, and in any phase, the differential energy is shared in a polyatomic molecule among various modes of vibration. The theory of radiationless transitions developed by Robinson and Frosch (1963) stresses the Franck-Condon factor. Jortner et al. (1969) have extensively reviewed the situation from the photochemical viewpoint. 

As shown in Fig. 6, there is a correlation between absorption spectrum and emission spectrum. Taking into consideration the Franck-Condon principle, which states that there is no motion of the atoms during an electronic transition, one has to differentiate between the two following possibilities in the one the geometry of the excited state is similar to the one of the ground state (same interatomic distances),... 

Fig. 29. (a) A hypothetical absorption cross section which does not reflect any vibrational effects. A differential element dE is split up into a vibrational progression of frequency and Franck-Condon factor ratios 7 12 15 10 4 2 1. (b) The hypothetical cross section of Figure la as it would be modified by the active vibration illustrated there. 

Xv,j xe,j)2 is a differential Franck-Condon factor because the continuum function Xe,j is energy-normalized. It has the dimensionality of E x, whereas the usual Franck-Condon factor is dimensionless. Contrary to the slow variation of He with energy, the differential Franck-Condon factor often varies rapidly and in an oscillatory manner with energy. 

One need only consider the energy dependence of the differential Franck-Condon factor. For small He, this factorization may be justified in the same way as in the case of second-order energy shifts of bound states. The variation of T and 5E with v and J provides information about the initially unknown shape of the repulsive potential curve. 

If isotopic effects on the differential Franck-Condon factors are neglected, it is indeed found that the hydride is four times more strongly predissociated... 

The isotope effect on differential Franck-Condon factors has been investigated by Child (1974) (see Fig. 7.29), and it can be predicted that the absolute maximum value of T varies roughly as /x1/6. This dependence for the magnitude of T is weaker and in the opposite sense to the n 2 dependence for gyroscopic predissociations. The oscillation frequency of r(i ) versus E is also sensitive to the reduced mass. Since the phase difference, (f>(EVyj) [Eq. (7.6.10)] increases approximately in proportion to the area,... 

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