Franck-Condon effects approximation

The most serious obstacle to extracting useful information from the low-resolution DF spectrum is the progressively more severe spectral overlap between separate polyad features as Vjb increases. This is due to two effects the density of Franck-Condon bright ZOBSs increases (approximately as anc width of each polyad increases (owing to the i>4 scaling of the dominant anharmonic resonance experienced by the ZOBS). 

The possibility of the anomalous isotope effect for electron tunneling reactions was first noted by Ulstrup and Jortner [7]. This effect becomes possible when the reorganization energy is approximately equal to the reaction exothermicity. If, in this case, for example, the relationship Er - J + a) — 0 is satisfied, where co is the vibrational frequency for a heavy isotope, then from the viewpoint of the activation energy [see eqn. (42)1, the transition (0 - 1) is optimal for the heavy isotope. Compared with this transition for the heavy isotope, both the transitions (0 - 0)and(0 - 1) for the light isotope contain the additional activation multiplier. In this situation the anomalous isotope effect will be observed, provided that the Franck Condon factor for the transition (0 -> 1) of the heavy isotope is not too small compared with that of the light isotope. An example of the electron tunneling reaction for which the anomalous isotope effect is observed experimentally will be considered in Chap. 7, Sect. 4. 

The solvent effects on spectroscopic properties i.e., electronic excitation, leading to absorption spectra in the ultraviolet and/or visible range, of solutes in solution are due to differences in the solvation of the ground and the excited states of the solute. Such differences take place when there is an appreciable difference in the charge distribution in the two states, often accompanied by a profound change in the dipole moments. The excited state, in distinction with the transition state discussed above, is not in equilibrium with the surrounding solvent, since the time scale for electronic excitation is too short for the re-adjustment of the positions of the atoms of the solute (the Franck-Condon principle) or of the orientation and position of the solvent shell around it. The consideration of the solvation of the excited state as if it were an equilibrium state of the system is therefore an approximation, which, however, is commonly implicitly made. 

This is only an approximate relation correlating the cross-section to quencher properties since it ignores Franck-Condon and other effects. Nonetheless, a plot of In (ag) versns In agpj g) is fonnd to be reasonably linear. ... 

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. 

Abstract The transition between electronic energy surfaces of molecules is usually described in the Franck-Condon approximation where the spatial variation of the coupling matrix elements is neglected. In this work we go beyond this approximation and explore the effects of such a variation using a simply parameterized interaction instead of the usually poorly known realistic variations. Moreover, we propose a model that allows us to steer molecular transitions by shaping the space-dependence of the coupling. 

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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