Franck-Condon responses

In spectroscopy we may distinguish two types of process, adiabatic and vertical. Adiabatic excitation energies are by definition thermodynamic ones, and they are usually further defined to refer to at 0° K. In practice, at least for electronic spectroscopy, one is more likely to observe vertical processes, because of the Franck-Condon principle. The simplest principle for understandings solvation effects on vertical electronic transitions is the two-response-time model in which the solvent is assumed to have a fast response time associated with electronic polarization and a slow response time associated with translational, librational, and vibrational motions of the nuclei.92 One assumes that electronic excitation is slow compared with electronic response but fast compared with nuclear response. The latter assumption is quite reasonable, but the former is questionable since the time scale of electronic excitation is quite comparable to solvent electronic polarization (consider, e.g., the excitation of a 4.5 eV n — n carbonyl transition in a solvent whose frequency response is centered at 10 eV the corresponding time scales are 10 15 s and 2 x 10 15 s respectively). A theory that takes account of the similarity of these time scales would be very difficult, involving explicit electron correlation between the solute and the macroscopic solvent. One can, however, treat the limit where the solvent electronic response is fast compared to solute electronic transitions this is called the direct reaction field (DRF). 49,93 The accurate answer must lie somewhere between the SCRF and DRF limits 94 nevertheless one can obtain very useful results with a two-time-scale version of the more manageable SCRF limit, as illustrated by a very successful recent treatment... 

It has been proposed (5) that in the case of the Ln + ions an excited state involving a metal d state is responsible for the absence of luminescence. It is then necessary that this state has a large Franck-Condon shift and is situated at energies not very much higher than those of the 4/-c.t. state. Whatever the solution of this problem may be, it is clear that either c.t. or 4f 5d states play an important role in the quenching process of the luminescence. The conclusion of all the material presented in this section is that this is true for all types of lanthanide luminescence. 

The goal of theory and computer simulation is to predict S i) and relate it to solvent and solute properties. In order to accomplish this, it is necessary to determine how the presence of the solvent affects the So —> Si electronic transition energy. The usual assmnption is that the chromophore undergoes a Franck-Condon transition, i.e., that the transition occurs essentially instantaneously on the time scale of nuclear motions. The time-evolution of the fluorescence Stokes shift is then due the solvent effects on the vertical energy gap between the So and Si solute states. In most models for SD, the time-evolution of the solute electronic stracture in response to the changes in solvent environment is not taken into accoimt and one focuses on the portion AE of the energy gap due to nuclear coordinates. 

Based on the expression for, a large increase in the useful NLO coefficient for a fixed wavelength is predicted in the case where the absorbance of the NLO dye lies between the fundamental and second harmonic. Residual absorption at the second harmonic is the limiting factor in the practical application of this technique, and has been addressed through the synthesis of new dyes. Improvement of lOx in reducing this absorbance has been achieved, and another factor of 5-lOx is estimated to be required before practical devices can be fabricated. Franck-Condon effects (vibronic structure) appear to be responsible for this residual absorption because small, rigid chromophores are often correlated with the lowest amounts of absorption. Chromophores based loosely on... 

If we limit our description to the initial step of the whole process, i.e. the vertical electronic transition (absorption and emission), we can safely assume a Franck-Condon like response of the solvent, exactly as for the solute molecule the nuclear motions inside and among the solvent molecules will not be able to follow immediately the fast changes in the solute electronic charge distribution and thus the corresponding part of the... 

Fig. 4.6 In the quantum mechanical version of the Franck-Condon principle, the molecule undergoes a transition to the upper vibrational state that most closely resembles the vibrational wavefunction of the vibrational ground state of the lower electronic state. The wavefunctions with the greatest overlap integral of all the vibrational states are responsible for the strongest absorption...

Franck-Condon factors, rather than energy-level density, are primarily responsible for the variation in nonradiative rates. 

In calculating solvent effects on excitation energies one has to take into account that normally the excitation process is sufficiently rapid for the Franck-Condon principle to hold, which means that while the induced dipole of the solvent molecule can change in response to the change of solute dipole on excitation, the permanent dipoles cannot—that is, there is negligible dipole reorientation. Such reorientation can, however, occur in the time period between absorption and emission and lead to a large Stokes shift in the emission. (Cf. Section 5.3.1.)... 

The term solvatochromism is used to describe the change of position, intensity and shape of the UV-Vis absorption band of the chromophore in solvents of different polarity [1, 2], This phenomenon can be explained on the basis of the theory of intermolecular solute-solvent Interactions in the ground g) and the Franck-Condon excited state e). We will consider only the effect of the solute-solvent interaction on the electronic absorption and nonlinear optical response of a dilute solution of the solute. This way we avoid the explicit discussion of the solute-solute interaction, which significantly obscures the picture of the solvatochromism phenomenon. 

Marcus theory is that the actual change in the electronic charge distribution of the ET system is fast relative to the nuclear motions underlying the static response, but is slow relative to the electronic motions which determine s. In other words the electron transfer occurs at constant nuclear polarization, or at fixed nuclear positions. This is an expression of the Franck-Condon principle in this continuum dielectric theoiy of electronic transitions. 

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