Condon approximation radiationless transitions

In 1976 TET was first applied to H abstractions [53]. One year later Suhnel [54] used TET to explain radiationless transitions in indigoid compounds, and Phillips [55] tested the harmonic approximation used by the theory in H abstractions. CT interactions [56] and substituent effects [57] in H abstractions were also addressed, as well as H abstractions by uranyl ion [58]. Support for TET also came from the demonstration [59] that in radiationless transitions theories, some Franck-Condon factors may be expressed by a nuclear tunneling formula like the TET one. 

Third, as a consequence of the foregoing, the use of IDs is suitable in investigating the dependence of the electronic matrix element for radiationless transition on the nuclear coordinates. This problem can be solved, as has been shown in Chapter 5, by considering the matrix element as one that of an operator that depends upon both electronic and nuclear displacements and by introducing a q-centroid approximation for the electronic factor. The latter is obtained as an average with DSWVO factor. The familiar Condon approximation can be so improved as to write the whole matrix element as a product of a vibrational overlap integral and an electronic factor, the latter being evaluated at some (j-centroid for the nuclear positions. 

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