Radiationless Transitions within a Molecule

Empirically, the singlet-state energy is best determined from the intersection between normalised absorption and fluorescence spectra. The same principle could be applied to the triplet energy, but this is not usually feasible because the singlet-to-triplet absorption is very difficult to observe. Alternatively, the triplet energy is estimated from the origin of the phosphorescence spectmm. Non-spectroscopic techniques, such as photoacoustic calorimetry, often provide a better estimate of the triplet energies. 

The first calculation of Franck-Condon factors in terms of nuclear tunnelling preceded this formal demonstration [13]. Using the WKB approximation for tunnelling through intersecting parabolas, the tunnelling rate can be expressed as 

Clearly, for benzene eq. (15.72) is identical to eq. (15.71), but for the other aromatic hydrocarbons, the relative number of CH modes is somewhat lower and the rate is reduced. 

The minima of the CH bonds represented in this figure in their Sq and Sj states are displaced because each CH bond contracts by Ar 0.01 A upon electronic excitation. This contraction directs the crossing of the curves to their repulsive side. McCoy and Ross [17] expressed the electronic transitions in polycyclic aromatic hydrocarbons in terms of a bond-length displacement coordinate A/ , 

Internal conversion and inter-system crossing rates exhibit a free-energy dependence which is remarkably different from those of the reactions discussed in the previous chapters. As the exothermicity of the internal conversion increases, its rate becomes smaller. This is known as the energy-gap law of radiationless transitions [22]. 

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