The exciton model

The exciton model is based on the fact that, in organic photoconductors, the light-induced transition of an electron to an excited state causes a pronounced polarization of the chromophoric group. Because of the relatively high stability of this state, it is considered to be an entity of special nature. This entity, called an exciton, is an excited state of quasi-particle character located above the valence band. It resembles a hydrogen-like system with a certain binding energy. 

Moreover, CT excitons are thought to be formed by intermolecular interaction in certain polymeric systems containing small molecules. A typical example is poly(N-vinyl carbazole) doped with trinitrofluorenone (TNF), a system which played a major role in early photoconductive studies on polymeric systems (see Chart 2.1). 

As regards the nature of the so-called dissociation sites referred to above, it may be noted that generally any kind of disorder-induced kink may play an activating 

Chart 2.1 Chemical structures of po y N -vinyl carbazole) and trinitrofluorenone. 

Chart 2.2 Chemical structures of solitons formed in tra s-polyacetylene. 

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Kasha, M., H.R. Rawls, and M. Ashraf El-Bayoumi. 1965. The exciton model in molecular spectroscopy. Pure Appl. Chem. 11 371-392. 

Packard, B. Z., Toptygin, D. D., Komoriya, A. and Brand, L. (1996). Profluorescent protease substrates intramolecular dimers described by the exciton model. Proc. Natl. Acad. Sci. USA. 93, 11640-11645. 

On the other hand in the exciton description occasionnally adopted by some authors to interpret the main absorption peak in the polydiacetylenes one finds x " negative and its values two orders of magnitude lower than expression 6 since electron correlation (28) is essential in the exciton model, the calculation of even the simplest optical properties becomes prohibitively complicated and the physical insight is obscured. 

Dimerization causes shifts of optical absorption and emission bands of the order of several hundred cm (cf. Table I). This suggests that the triplet EPR data must be interpreted in terms of exciton and charge transfer effects. In the case of ZnTCP the effect of dim.erization on zfs values can be accounted for on the basis of rapid triplet excitation transfer between essentially unperturbed porphyrin moieties. If the exciton model applies the principal components of the zfs tensor in the dimer (X, , Z ) can be related... 

In this expression 1, m, n denote the direction cosines specifying the relative orientations of the principal axes in the monomer and dimer. (The expressions defining the values D and E are D = -3/2 Z and E = 1/2 (Y - X).) For the face-to-face structure proposed for [ZnTCP]2 (14) exciton theory predicts that dimerization should not affect the out-of-plane component (Z) of the tensor. The in-plane component, and therefore E, depends on the angle of rotation of one porphyrin plane relative to the other. According to the exciton model the observed reduction in E (cf. Table II) corresponds to an angle of rotation of about 23. This is reasonably close to the value predicted by molecular models (14). 

The exciton model of polyene spectra assumes that each excited state of the polyene may be described by a linear combination of basis states, each having only one (singly) excited ethylenic unit. Only states with neighboring excited ethylenic units can interact. 

Xmax is shifted to 410 nm in 44 (c and g annelation) it is shifted to 422 nm. The explanation of this effect is quite straight forward. Benzo-annelation across a double bond substitutes a bond with half double bond character for a double bond. In terms of the exciton model this decreases both the length of the interacting system and the strength of the interaction. 

We mentioned the main models for generation, transfer, and recombination of the charge carriers in polymers. Very often, these models are interwoven. For example, the photogeneration can be considered in the frame of the exciton model and transport in the frame of the hopping one. The concrete nature of the impurity centers, deep and shallow traps, intermediate neutral and charged states are specific for different types of polymers. We will try to take into account these perculiarities for different classes of the macro-molecules materials in the next sections. 

During this study, we found that the exciton model underestimates the splitting between the coupled states by about a factor of four, indicating that interactions other than dipole-dipole coupling act between adjacent carbonyl groups. These interactions are most likely straightforward vibrational coupling terms, as discussed at the end of Section 3. 

The first observation of VCD in small model DNA molecules, and in large deoxynucleic acid models, was reported by us in 1989 [18]. The VCD signals in the 1550 to 1750 cm"1 spectral region were found to be similar to those observed for the RNA reported earlier. In addition, our first report on DNA models also contained the observation of B and Z form DNA, along with the DECO equations and model calculations of the helical polymers. Subsequently, VCD was reported for poly(dG-dC) poly(dG-dC), poly(dG) poly(dC), poly(dA-dT) poly(dA-dT) and poly(dA) poly(dT) in the B-conformation in buffered, aqueous solution [22]. Differences were observed for DNA models, depending on the base composition and sequence, and the observed results were quantitatively interpreted in terms of the exciton model for coupled carbonyl stretching vibrational states. 

Data from a CD detector can be used to successfully confirm the absolute stereochemistries of the eluted enantiomers and the elution order. This important application has been introduced by Salvadori and co-workers [23], More recently it was demonstrated that an on-line detection system can be made which measures the CD spectrum of the eluate by trapping and holding it in the HPLC cell. By comparing the spectrum with data in a CD spectral library, absolute configurations can be confirmed. Where spectra are unavailable, absolute configurations might be obtained by means of either empirical and semiempirical approach or by using nonempirical methods such as the exciton model or the DeVoe approach [22, 23]. 

These fits, although excellent, do not mle out the alternative exciton model. To judge which better describes the data, one needs a similar critical comparison between theory and experiment based on the exciton model. When such a quantitative comparison is made, one finds a fundamental discrepancy between the exciton model and the experimental results The exciton model predicts a symmetric absorption lineshape for oriented materials in which the conjugated polymer is chain aligned and chain extended. 

On the contrary, in the PPVs, the onset of photoconductivity coincides with the onset of absorption. In the PPVs, mobile charge carriers are photogenerated (see Fig. VD-1). The data in Fig. IVD-1 are consistent with a weak exciton binding energy, less than approximately 0.1 eV. In the exciton model, however, this coincidental onset of photoconductivity and absorption must be explained as an accident excitons are photogenerated as a first step with subsequent dissociation as a result of secondary processes. 

Thus, the relevant question is whether the photoconductive response in PPV results principally from secondary processes following the photogeneration of neutral geminate pairs, in agreement with the exciton model, or from separated, mobile, positive and negative charged polarons. 

The exciton model of linear aggregates was used to explain the evolution of the electronic state parameters with stepwise incorporation of additional monomer units [64,408,409]. In this model, the transition dipole moments have only one component directed along the main molecular axis. Thus, the amplitude of the transition dipole moment is expressed by Eq. (47) for nc< 12. 

Deviations from OGM were recognized early on spectroscopic properties of molecular crystals Davydov shifts and splittings of absorption bands in molecular crystals are clear deviations from OGM and were rationalized based on the excitonic model (EM) [10, 14, 15, 16, 17]. This same model proved extremely successful to describe the complex and technologically relevant spectroscopy of molecular aggregates, i.e. of clusters of molecules that spontaneously self-assemble in solution or in condensed phases [IS]. Much as it occurs in molecular crystals, due to intermolecular electrostatic interactions the local bound electron-hole pair created upon photoexcitation travels in the lattice and the corresponding wave function describes an extended delocalized object called an exciton. We explicitly remark that the Frenkel picture of the exciton, as a bound electron-hole pair, both residing on the same molecule, survives, or better is the basis for the excitonic picture. The delocalization of the exciton refers to the fact that the relevant wave function describes a Frenkel exciton (a bound e-h pair) that travels in the lattice, and this is of course possible even when electrons and/or holes are, separately, totally localized. In other terms, the EM describes localized charges, but delocalized excitations. 

The paper is organized as follows. Section 2 shortly introduces the exciton model and its approximations. Section 3 reviews calculations of ground state properties (mainly the polarization and polarizability) paying special attention to the mean-field approximation. Push-pull chromophores, the special family of polar and polarizable molecules studied in this contribution, are presented in Section 4, with a brief discussion of their properties in solution and of relevant models. In Section 5 we present a model for interacting push-pull chromophores that will be the basis for the discussion of collective and cooperative effects in relevant materials. Static susceptibilities of clusters of push-pull chromophores are discussed in Section 6, focusing attention on cooperative effects in tlie ground state. Excited state properties are addressed in Section 7, with special emphasis to systems where intermolecular interactions lead to extreme consequences. Section 8 finally summarizes main results. 

Sum-over-state (SOS) expressions [35] relate static susceptibilities to optical excitations. Of course (hyper)polarizabilities obtained as field derivatives of P coincide with SOS results, provided that the calculations refer to the same Hamiltonian. In this respect it is particularly interesting to discuss the merit of the excitonic approximation in the calculation of susceptibilities. Our best excitonic approximation to the Hamiltonian for interacting molecules in Eq. (10) defines the vacuum states for the excitonic model as the mf gs, i.e. adopts as gs the best uncorrelated solution of the total Hamiltonian. Therefore exactly the same OGM and mf-OGM susceptibilities discussed above can be obtained also in the liM approach from the derivatives or the relevant gs polarization. As a matter of fact mf-OGM results can also be obtained from a SOS calculation, summing over the excited states of the cluster described by the mf Hamiltonian in Eq. (15), or, equivalently, by summing up the SOS susceptibilities calculated for the chromophores in their mf gs. Instead, susceptibilities obtained by summing over the excited states calculated in the excitonic approximation (i.e. by diagonalizing H j- + are different, and... 

Junction parameter within the excitonic model Excitonic perturbation matrix element Transition oscillator strength Two-photon absorption transition strength N,N-Diethyl-4-(2-nitroethenyl)phenylamine Oligomer consisting of N monomers V-shape molecule with N monomers on branches g-generation dendrimer with N monomers on branches fluorene-fluorene junction... 

THE EXCITON MODEL OF SUPERCONDUCTIVITY IN LINEAR CHAINS - REVISITED... 

A microscopic model for the exciton in the undoped Cu-oxides has been proposed earlier [8.39] in which a quantitative agreement between theoretical calculations and experimental EELS results is presented. Here, we shall only briefly sketch some basic aspects of the theory. The exciton model is illustrated in Fig. 8.13. The ground state of the undoped Cu-oxides is antiferromagnetic... 

Molecular assemblies of dyes often show hypsochromic or bathochromic shifts of the main absorption bands if the n systems are touching each other ( 4 A) or if the distance is less than 6-7 A. This shift can be explained by the exciton model, which assumes resonance interaction between the dipoles of excited states. The most simple case is the interaction between two such dipoles of excited state of linear dyes, e.g., carotenoids. The interaction of two stacked chro-mophores then leads to a short wavelength shift (stack or H aggregate) of the monomer absorption bands the interaction of two chromophores in lateral position (Scheibe or Jelly or J aggregate) leads to a long-wavelength shift (Fig. 1.5.15). 

This new theory of the non-equilibrium thermodynamics of multiphase polymer systems offers a better explanation of the conductivity breakthrough in polymer blends than the percolation theory, and the mesoscopic metal concept explains conductivity on the molecular level better than the exciton model based on semiconductors. It can also be used to explain other complex phenomena, such as the improvement in the impact strength of polymers due to dispersion of rubber particles, the increase in the viscosity of filled systems, or the formation of gels in colloids or microemulsions. It is thus possible to draw valuable conclusions and make forecasts for the industrial application of such systems. 

Kasha, M., Rawls, H. R., and Ashraf EI-Bayoumi, M. The Exciton Model in Molecular Spectroscopy. Pure Appl. Chem. 11, 371 (1965). 

Fluorescence emission data of the diporphyrins also are given in Table I the Q(0,0) band is red shifted and fluorescence yield is decreased. Although some reduction in is predicted by the exciton model (9), the extent of quenching found in the diporphyrins is certainly impressive. It is likely that the enormous red tail of the Soret band further enhances the self quenching of the dimer fluorescence yield. 

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