Franck Condon spectral overlap

An example of an application to actual spectroscopy is shown in Figure 6.9. This shows the states computed in the range of the 0 —> 3 CH spectral transition. The intensities were computed as a Franck-Condon overlap of the optically bright CH overtone state (Holme and Levine, 1989 Levine and Berry, 1989) with the relevant eigenstate. 

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). 

This relation was first obtained by Forster and is usually called the Forster theory. Rather than expressing W,-. y in the spectral-overlap relation, lT, y can be expressed in terms of the Franck-Condon factors which can be calculated from the potential surfaces as was done for the photo-induced ET or radiationless transitions. 

Spectral overlap and the Franck-Condon density of states... 

The photophysical processes of semiconductor nanoclusters are discussed in this section. The absorption of a photon by a semiconductor cluster creates an electron-hole pair bounded by Coulomb interaction, generally referred to as an exciton. The peak of the exciton emission band should overlap with the peak of the absorption band, that is, the Franck-Condon shift should be small or absent. The exciton can decay either nonradiatively or radiative-ly. The excitation can also be trapped by various impurities states (Figure 10). If the impurity atom replaces one of the constituent atoms of the crystal and provides the crystal with additional electrons, then the impurity is a donor. If the impurity atom provides less electrons than the atom it replaces, it is an acceptor. When the impurity is lodged in an interstitial position, it acts as a donor. A missing atom in the crystal results in a vacancy which deprives the crystal of electrons and makes the vacancy an acceptor. In a nanocluster, there may be intrinsic surface states which can act as either donors or acceptors. Radiative transitions can occur from these impurity states, as shown in Figure 10. The spectral position of the defect-related emission band usually shows significant red-shift from the exciton absorption band. 

Due to their direct relation to the spectral overlap integral, see Eq. (9), the emission and absorption spectra of the dye molecules are of interest in the context of EET processes. The simplest way to model excitation spectra employs the calculation of vertical energy separations, i.e., the separation of the Bom-Oppenheimer potential energy surfaces of the initial state and the final state at the equilibrium structure of the initial state. This energy separation is expected to coincide with the absorption maximum, as rationalized by the Franck-Condon principle (see for example [135]). This assumption is not always appropriate, rylene dyes being a prominent example. These dyes feature a strong 0-0 transition and a pronounced vibronic progression that is even visible in solution at room temperature (see for example [137]). A detailed simulation of the vibrational substructure of the absorption and emission bands is necessary to understand the details of the spectram. 

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