Excitons Frenkel

excitation spectroscopy shows its strength. One irradiates the sample with an extremely sharp laser line (down to 0.001 cm ). Detection is accompUshed via the integrated fluorescence, which can readily be separated from the excitation light using filters, as the absorption and the fluorescence do not overlap. The emission hes at a higher quantum energy. With this method, it is even possible to identify and distinguish the isotope C, present with its natural abundance of only 1.1%, at different positions within the molecules [21]. 

Even with simple UV-VIS spectroscopy, the exchange interaction In of a naphthalene dimer in naphthalene, i.e. in a mini-exciton, could be detected as a spUtting of the 0,0 transition in the phosphorescence spectrum, yielding 1.2 0.2cm [18]. 

We now wish to extend the dimer model to encompass an infinitely large three-dimensional crystal lattice this is very similar to the transition from the covalent bonding of two atoms to the band structure of a metal or a semiconductor with delocalised states. Starting from the more or less sharp energy levels in the two-body system, we arrive at a band of energy states whose width depends on the interactions of the individual molecules or the overlap of the molecular orbitals in the lattice. We must then take the interaction of an excited molecule with aU the other molecules in the crystal and with the periodic lattice potential into account The levels and E in the dimer model of Fig. 6.7 are transformed into a more or less broad band of energy levels. These are the excitonic bands of the crystal, which we shall treat in this section. 

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Bittner ER (2007) Frenkel exciton model of ultrafast excited state dynamics in AT DNA double helices. J Photochem Photobiol A 190 328-334... 

Excited-state relaxation, in photochemical technology, 19 109-111 Excitons. See also Frenkel exciton in double heterostructure OLEDs, 22 217... 

Figure 4.13 The schemes of (a) a weakly bound (Mott-Wannier) exciton and (b) a tightly bound (Frenkel) exciton.

These two types of exciton are schematically illustrated in Figure 4.13. The Mott-Wannier excitons have a large radius in comparison to the interatomic distances (Figure 4.13(a)) and so they correspond to delocalized states. These excitons can move freely throughout the crystal. On the other hand, the Frenkel excitons are localized in the vicinity of an atomic site, and have a much smaller radius than the Mott-Wannier excitons. We will now describe the main characteristics of these two types of exciton separately. 

Table 4.4 The gap Eg) and binding (Ej) energies of (Mott-Wannier and Frenkel) excitons in different materials...

Crystal (Mott-Wannier excitons) Eg (eV) Eg (meV) Crystal (Frenkel excitons) Eg (eV) Ei (meV)... 

In tightly bound (Frenkel) excitons, the observed peaks do not respond to the hy-drogenic equation (4.39), because the excitation is localized in the close proximity of a single atom. Thus, the exciton radius is comparable to the interatomic spacing and, consequently, we cannot consider a continuous medium with a relative dielectric constant as we did in the case of Mott-Wannier excitons. 

Frenkel excitons are also observed in many organic crystals and in noble gas crystals (Ne, Ar, Kr, and Xe). However, for the latter crystals the band gap lies out... 

It should be noted that, besides free electrons and holes, the role of the free valencies in the crystal may be played by the so-called Frenkel excitons. The latter are, roughly speaking, excited atoms or ions of the lattice which can transfer their state of excitation to similar neighboring atoms or ions. As an example, we may take again the CU2O lattice in which a Frenkel exciton (in the same rough model) is represented by an excited Cu+ ion with the following electronic structure ... 

Free valencies of such an exciton nature may be significant in semiconductors, one component of which is a transition metal possessing an unfilled inner electron shell or a shell that can easily give up an electron. This may, perhaps, explain certain specific catalytic properties of such semiconductors. However, the role of Frenkel excitons in the phenomena of chemisorption and catalysis has been as yet investigated to a very small extent, and in the following we shall not consider free valencies of such an exciton origin. 

There are some recent application of a mixed quantum classical description to investigate quantum dynamics in large CC. The absorbance of a photosynthetic light harvesting complex caused by electronic Frenkel-exciton formation has been considered in Ref. [23], and Refs. [24,25] focused on excitation energy transfer in a DNA double helix strand. In both cases, however, the considerations have been restricted to an approximate description based on the use of... 

The paper is organized as follows. The next section quotes details of the Frenkel exciton model necessary for the later discussion. Comments on a full quantum dynamical description of all those quantities which are of interest in the mixed description are shortly introduced in Section 3. The used mixed quantum classical methodology is introduced in Section 4. Its application to EET processes is given in 5, to the computation of linear absorbance in Section 3.2, and to the determination of emission spectra in Section 7. The paper ends with some concluding remarks in Section 8. 

An important issue in the nature of the excited states in stacks of DNA bases is whether or not the states extended over a number of the bases are neutral Frenkel excitons or if they carry some degree of charge transfer character (exciplex or excimer).3 [2-4] A purely excitonic model neglects configurations... 

The simplest Frenkel exciton model consists of diagonal energies en representing the exciton energies of the individual bases with off-diagonal elements corresponding to the Coulomb coupling between exciton states, J... 

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