Franck-Condon vibronic coupling

A much more interesting example of the intermediate case is encountered when the density of states is rather small but the vibronic coupling elements are large (due to favorable Franck-Condon vibrational overlap factors). The consequences of this type of intramolecular vibronic coupling are seen in the anomalously long radiative lifetimes of the first singlet states of N02, S02, and CS2 86-99 and in the many extra unexpected lines in the spectra of these molecules. 

Although the presented numerical approach to the coupled master equations has shown that a turnover feature can be seen in vibronic dynamics appearing in the calculated pump-probe stimulated emission spectra as a function of the energy gap between the two relevant vibronic states. It is found that vibronic quantum beats cannot be observed when the energy gap becomes larger in which situation it leads to smaller Franck-Condon overlaps between the energy conserved levels. 

In the crude Born-Oppenheimer approximations, the oscillator strength of the 0-n vibronic transition is proportional to (FJ)2. Furthermore, the Franck-Condon factor is analytically calculated in the harmonic approximation. From the hamiltonian (2.15), it is clear that the exciton coupling to the field of vibrations finds its origin in the fact that we use the same vibration operators in the ground and the excited electronic states. By a new definition of the operators, it becomes possible to eliminate the terms B B(b + b ), BfB(b + hf)2. For that, we apply to the operators the following canonical transformation ... 

The sum of these factors equals 1, so that the vibronic series is assimilated to the first five vibronic levels.) The quadratic couplings are negligible, so that the above Franck-Condon factors correspond roughly to a linear coupling with 2 1. 

Two paradigms have been widely used in the past decade to describe the ultrafast relaxation of optically excited tttt states in purine molecules, through internal conversions [69], One of them relies on the existence of a conical intersection (Cl) between the excited state and the ground state, accessible on the excited state surface from the Franck-Condon region [69, 70], The second one, Lim s proximity effect , stems from vibronic coupling between the tttt state and nearby mr states found in these heteroatomic molecules [71]. Excited state quantum calculations have therefore focused recently on a precise characterisation of the strong perturbations and interactions undergone by these tttt or nit states. 

The vibronic theory of the RR effect distinguishes two major intensity enhancement mechanisms that play a dominant role in the RR spectra (i) Franck-Condon (FC) principle and (ii) Herzberg-Teller (FIT) vibronic coupling, which have quite different properties. The FC scattering mechanism involves displacement of the potential minima of the ground and excited electronic states along a vibrational normal... 

The other enhancement method is to use molecular electronic resonances [19, 22, 23]. A most interesting topic in this enhancement method is so-called molecular near-held effect reported by Kano et al. [34]. This effect, explained by intermolecular vibronic coupling, makes HRS spectroscopy highly sensitive to intermolecular interactions one can observe HRS modes of solvent molecules adjacent to the solute dye molecules via the intensity borrowing from the dye molecules. That is, solvent-solute interactions are selectively observed without impairment from signals of the bulk solvent. It is almost impossible to observe a similar effect in resonance RS spectroscopy because of the unavoidable contribution from Franck-Condon type resonance. 

The conditions for photoinduced charge separation and recombination in solvent-free molecules have recently been analyzed theoretically by Jortner et al. [103]. The important factors that could lead to intramolecular ET are (i) sufficiently large electronic coupling V and significant Franck-Condon vibrational overlap factors between the excited state (D-A) and the vibronic state of the CT (D+-A ) manifold (Figure 6) and (ii) a large density of effectively coupled vibronic levels... 

Fig. 2 Representative cuts through the potential energy surfaces of Bz+ (upperpanel or a) and its mono fluoro derivative, F-Bz+ (lowerpanel or b). The upper panel shows the results for the linear vibronic coupling model, while in the lower one the quadratic coupling terms are also included. In both panels the effective coordinate connects the centre of the Franck-Condon zone to the minimum of the intersection seam between the A and C states of F-Bz" ", and between the X and B states of the parent cation (within the subspace of JT active coordinates)...

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