Localized excitons

It is possible to make elastic scattering corrections to the algorithm (24) in the case of an Einstein phonon spectrum and purely local exciton-phonon coupling. If we calculate the energy of the polaron state at the value E ss nuio only the matrix elements 5 " should be considered in Eqs.(16). In this case... 

The physical phenomenon of current generation in simple D/A systems can be thought of in terms of the six chemical steps depicted in Fig. 4. (1) The absorption of a photon leads to a localized exciton with energy oo on either the donor or... 

Compared with the momentum of impinging atoms or ions, we may safely neglect the momentum transferred by the absorbed photons and thus we can neglect direct knock-on effects in photochemistry. The strong interaction between photons and the electronic system of the crystal leads to an excitation of the electrons by photon absorption as the primary effect. This excitation causes either the formation of a localized exciton or an (e +h ) defect pair. Non-localized electron defects can be described by planar waves which may be scattered, trapped, etc. Their behavior has been explained with the electron theory of solids [A.H. Wilson (1953)]. Electrons which are trapped by their interaction with impurities or which are self-trapped by interaction with phonons may be localized for a long time (in terms of the reciprocal Debye frequency) before they leave their potential minimum in a hopping type of process activated by thermal fluctuations. 

In Fig. 3d shown with squares is the dependence of the localized exciton quantum well width on the parameter (x) obtained in accordance with Eq. (1) and experimental A/T (x) data. For convenience, we chose the thickness of the crystal layer as a unit of the exciton localization, while solid circles do that considering the localization in the QW. 

EfC = C2W20 = Franck-Condon energy, an energy stabilization of the localized exciton in the absence of transfer. 

As a consequence of the rapid variation of n(E) around the bottom of the excitonic band, one expects a stronger broadening in the upper energies, i.e. an asymetric lineshape. We must remark that (2.104) shows that the perturbations theory to second order does not give the high-temperature limit in Tm of (2.33), obtained using the localized-exciton model, which is better adapted for high-temperature cases. 

A — (2SkBT) 12, which measures53 at high temperatures (kBT hQs) the energy fluctuation of a localized exciton due to thermal fluctuations of the phonon bath. 

Last, we may estimate from (2. 130b) the stabilization S of the localized exciton, S = 150 cm"l. This value does not include the contribution from higher-energy phonons [which should not be very important—see (2.128)], but is still well consistent with the absence of self-trapping of the anthracene exciton S < B 200-250cm 1. 

Fig. 11. Total energy of an exciton in an anisotropic elastic continuum for different Pt-Pt distances Rm). The energy is calculated for Mg[Pt(CN)4] 7 H20 from Eq. (6). a(ai ct ) represents a localization parameter which describes a free exciton (FE) with a = 0 and a localized exciton (self-trapped exciton STE) with a = 1. The exciton binding energy EB is normalized to zero for different R-values...

The LCGTO-Xa approach described so far has been successfully applied to a large variety of systems, including main group molecules (50,52,53), transition metal compounds, e.g. carbonyl complexes (27,28,55,56) and ferrocene (57), and a number of transition metal dimers (47). Besides these investigations on ground state properties useful information has also been obtained for selected problems involving excited states (52), such as the photolysis of Ni(CO)4 (58,59) and localized excitons in alkali halides (60) and in other ionic crystals ( ). 

In situations where high concentrations of sensitizers exist the energy may be transferred to an activator ion. The excitation migrating on a lattice of sensitizers can be considered to be a localized exciton , sometimes referred to as a Frenkel or Davydov exciton i). Each energy transfer step between sensitizers can be treated by one of the ion-ion interaction mechanisms discussed previously. This may be either the same as or different from the mechanism of sensitizer-activator interaction. In characterizing this type of energy transfer it is important to describe both the dynamics of the... 

For computing the wavefunction of a localized exciton the adiabatic approximation (see (20), 28,29) can be used. The first step in this approximation consists of establishing the wavefunction x and the corresponding eigenenergy U for the electronic subsystem assuming that the positions of atomic nuclei are fixed. Thus, denoting by r the set of electronic coordinates and by R the set of nuclear coordinates, we have x = x(R), U = U(R), i.e. the wavefunction x and the energy U depend on R treated as parameters in this approximation. 

Finally we remark that within the same excitonic band, if its width is sufficiently large, one can find both states, for which the exciton-phonon interaction is strong, and states where it is weak so that these states can be computed by means of perturbation theory (for a more detailed discussion of this problem see Ref. (18)). Only in the limit of very narrow excitonic bands do the excitonic states show the character of localized excitons, on which we have concentrated our attention. In all references which we have mentioned above the variational method was used, which gives only the lowest states in the excitonic band. 

The problem of the kinematic interaction between two paulions is similar to the problem of localized states of an exciton in the presence of a vacancy (98). Indeed, the kinematic interaction governing the relative motion of two Pauli particles is formally analogous to the one-particle potential created by a vacancy, which cannot be occupied by an exciton. In this case the equation determining the localized exciton state energy E is... 

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