Frenkel exciton spectrum

Historically, the first conflicted picture to be resolved was whether the photogeneration of carriers proceeded as a result of a direct transition from the valence band to the conduction band (band-to-band, BB) (2, p. 470). In anthracene, it was known that the absorption spectrum was essentially explicable in terms of transitions to bound, neutral, Frenkel exciton states the BB transition would thus have to be weak since the final states would be buried in the Frenkel exciton spectrum. An alternative hypothesis was that carrier generation requires the excitation of a Frenkel exciton that could dissociate if its energy was degenerate with that of a pair of uncorrelated carriers. 

On the other hand, molecular crystals are characterized by the existence of strongly bound (Frenkel type) excitons, and it has been shown that the lower-energy part of the absorption spectrum (say, the first 2 eV) is completely dominated by these excitons [168], even to the extent that the absorption corresponding to electron-hole pair generation is completely hidden in the exciton spectrum [128] and is revealed only by such methods as modulated electrorefletance [169]. The only states in the exciton bands that are accessible by photon absorption are those at the center of the Brillouin zone, so the absorption is not a continuous band as for semiconductors, but a sharp line. The existence of this sharp line therefore does not mean that the exciton band is narrow (i.e., that its dispersion relation in the Brillouin zone is flat). On the contrary, since that dispersion is caused by dipolar interactions, exciton bandwidths can be several eV [168,170] the total bandwidth is four times the coupling term. This will be particularly... 

Electro-absorption (EA) spectroscopy, where optical absorption is observed under the application of an electric field to the sample, is another method that can distinguish between localised and inter-band excitations. The electric field produces a Stark shift of allowed optical absorptions and renders forbidden transitions allowed by mixing the wavefunctions of the excited states. Excitons show a quadratic Stark (Kerr) effect with a spectral profile that is the first derivative of the absorption spectrum for localised (Frenkel) excitons and the second derivative for charge transfer excitons, i.e. 

In the analysis of the lowest electronic excitations in quasi-one-dimensional crystals, it is natural to take into account not only Frenkel excitons, but also one-dimensional charge-transfer (CT) excitons. We will show below that the spectrum of excited states in the molecular chain is strongly sensistive to the mixing of Frenkel and CT states. 

In the following 20 years, a group of physicists in the Ukraine [2] studied a series of other aromatic crystals spectroscopically. It developed that there are also very characteristic differences from the spectra of free molecules. In the year 1948, A. S. Davydov [3] formulated the basic theoretical explanation for the observable interaction processes in the crystal spectra, between the molecules in electronically excited states within the crystal. He made use of the model of Frenkel excitons [4] and was able in particular to give a quantitative explanation of a characteristic line splitting, the Davydov splitting, as a fundamental property of organic molecular crystals. Fig. 6.1 shows as an example the splitting of the 0,0-transition in the Ti So absorption spectrum of anthracene at room temperature. 

The lowest excited triplet state Ti of this crystal belongs, in contrast, only to the anthracene molecule and corresponds to triplet Frenkel excitons with no polar character, as we described in Sect. 6.5. This follows from the energetic position (not shown here) and the vibronic structure of the phosphorescence spectrum [36]. 

The spectrum depends on the solvent. The solvent may be a crystal, in which case there is a small red-shift (to longer wavelengths) of the absorption compared to the free molecule. Furthermore, there is a formation of excitons. Local excitons are referred to as Frenkel excitons. Excitons extended over the whole crystal have been studied in great detail by Davydov and are called Davydov excitons. The lowest exciton state is further red-shifted compared to the free molecule absorption. Local excitons polarize themselves and the medium (Figure 18.3). As usual, when the reorganization energy is less than the coupling, the excitons are delocalized. 

The Frenkel exciton Hamiltonian formalism with energies calculated with MBE schemes was recently applied to investigate the electronic absorption spectrum of liquid HCN [34], water [35], and liquid and supercritical CO2 [36]. 

It should be noted that the above classification of the electroabsorption spectrum is valid only approximately, because first of all eqn (11.11) is correct only in the case of weak absorption and, second, the Frenkel and CT exciton states usually mix. We finally mention that the change of the refractive index Sn is of the same order as 5k new experimental techniques are required to measure this change, however. Good candidates for such methods have been proposed by War-man and coworkers (18). The success of such measurements could be the basis of electrorefraction spectroscopy, complementary to the existing electroabsorption spectroscopy. 

However, even in perfect ID structures, the mixing of Frenkel and CT excitons destroys this simple picture. Below, following (43), we show that this mixing is responsible for the appearance of new excitonic states, which are localized at the ends of a one-dimensional crystal chain and which are analogous to Tamm surface states of electrons. Their energy can be blue- or red-shifted in comparison with the bulk states. In the case of red-shift, these states can determine the fluorescence spectrum of a molecular chain. They can also play an important role in quantum confinement of the states in the molecular chain. For the description... 

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