Electronic spectra Franck-Condon principle

Section 6.13.2 and illustrated in Figure 6.5. The possible inaccuracies of the method were made clear and it was stressed that these are reduced by obtaining term values near to the dissociation limit. Whether this can be done depends very much on the relative dispositions of the various potential curves in a particular molecule and whether electronic transitions between them are allowed. How many ground state vibrational term values can be obtained from an emission spectrum is determined by the Franck-Condon principle. If r c r" then progressions in emission are very short and few term values result but if r is very different from r", as in the A U — system of carbon monoxide discussed in Section 7.2.5.4, long progressions are observed in emission and a more accurate value of Dq can be obtained. 

Certain features of light emission processes have been alluded to in Sect. 4.4.1. Fluorescence is light emission between states of the same multiplicity, whereas phosphorescence refers to emission between states of different multiplicities. The Franck-Condon principle governs the emission processes, as it does the absorption process. Vibrational overlap determines the relative intensities of different subbands. In the upper electronic state, one expects a quick relaxation and, therefore, a thermal population distribution, in the liquid phase and in gases at not too low a pressure. Because of the combination of the Franck-Condon principle and fast vibrational relaxation, the emission spectrum is always red-shifted. Therefore, oscillator strengths obtained from absorption are not too useful in determining the emission intensity. The theoretical radiative lifetime in terms of the Einstein coefficient, r = A-1, or (EA,)-1 if several lower states are involved,... 

As shown in Fig. 6, there is a correlation between absorption spectrum and emission spectrum. Taking into consideration the Franck-Condon principle, which states that there is no motion of the atoms during an electronic transition, one has to differentiate between the two following possibilities in the one the geometry of the excited state is similar to the one of the ground state (same interatomic distances),... 

Radiative transitions may be considered as vertical transitions and may therefore be explained in terms of the Franck-Condon principle. The intensity of any vibrational fine structure associated with such transitions will, therefore, be related to the overlap between the square of the wavefunctions of the vibronic levels of the excited state and ground state. This overlap is maximised for the most probable electronic transition (the most intense band in the fluorescence spectrum). Figure... 

The most probable transitions, according to the Franck-Condon principle are the vertical ones. They correspond to the maxima of electron groups in the kinetic spectrum. The upper limits in the kinetic energies for each group correspond to the adiabatic ionization potentials. Thus from the difference of these energy values one can get the difference Ip between the vertical and adiabatic potentials (Table IV). 

To include the upper-state potential curve on the same graph, it is necessary to know r e, which can be estimated from the observed intensities of the absorption spectrum in the following way. According to the Franck-Condon principle, the intensity of an electronic transition is related to the overlap of the vibrational wavefunctions of the two states by... 

If the internuclear equilibrium distance of the excited electronic state (r s) shifts by the value A from the internuclear equilibrium distance of the ground state ( e). the Franck-Condon principle allows transitions to many excited vibrational levels. The shapes of the harmonic potentials also have an effect on the magnitude of the Franck-Condon integral. In this case, the theoretical intensities have been calculated as a function of A and B. The parameters B and A were varied until the theoretical intensities showed the closest match to the experimental intensities. In Fig. 21, the best fit for the progression obtained from the photoluminescence spectrum for the anchored vanadium oxidc/Si02 catalyst and theoretical Franck-Condon analysis is represented (725). 

A PE spectrum, therefore, displays the energy levels of the molecular ion as a series of bands. The bands may show vibrational structure. The spectral transition is governed by the Franck-Condon principle. Ionization of an electron takes place on a much faster timescale than molecular vibrations, so the nuclei are frozen during the transition. If the ion has a different ground-state geometry from the molecule, it is most probable that it is formed in a vibrationally... 

The intensity derived from Afoi(so) will appear in the absorption spectrum distributed over the electronic origin and totally symmetric vibronic bands according to the Franck-Condon principle. This follows from the fact that a rigid molecular framework is assumed in the mixing... 

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