Exciton level

With tlie development of femtosecond laser teclmology it has become possible to observe in resonance energy transfer some apparent manifestations of tire coupling between nuclear and electronic motions. For example in photosyntlietic preparations such as light-harvesting antennae and reaction centres [32, 46, 47 and 49] such observations are believed to result eitlier from oscillations between tire coupled excitonic levels of dimers (generally multimers), or tire nuclear motions of tire cliromophores. This is a subject tliat is still very much open to debate, and for extensive discussion we refer tire reader for example to [46, 47, 50, 51 and 55]. A simplified view of tire subject can nonetlieless be obtained from tire following semiclassical picture. 

Fig. 24. The dispersion curves for USb energy plotted against wave-vector transfer Q (in units of 2 3t/a). The dashed lines represent the phonon dispersion and are based on the measured open points as well as on knowledge of phonons in NaCl structures. The magnetic modes are represented by solid squares (the collective excitation) and the hatched area (excitonic level). (Lander and Stirling )...

The explanation of this peak is as follows. Suppose that the number of conduction electrons is small, so that the Coulomb field is not screened out and that a hole in the X-ray level creates an exciton level below the bottom of the conduction band. The levels are shown in Fig. 2.13. Then an exciton absorption line should be possible. But the sudden change in field will produce excitations of electrons at the Fermi level, so that the exciton line is broadened as shown in Fig. 2.14(a). Also, we do not expect a sharp increase in absorption when the electron jumps to the Fermi level, leaving the exciton level A in Fig. 2.13 unoccupied, because of the very large Auger broadening due to transitions from the Fermi level into this unoccupied state. 

The question of whether the carriers screen the hole and so prevent the formation of any exciton level has not been discussed recently (see Cauchois and Mott 1949). Gearly this is a qualitative rather than an exact question, for the... 

Although all the exciton levels are not equally allowed, they are important for energy migration or exciton delocalization. Using time dependent perturbation equation, time period for transfer tw is given as... 

Consider, now, radiationless transitions in pure molecular crystals of aromatic molecules. At the very outset we must realize that crystal field effects may lead to the inversion of the order of the triplet and singlet exciton levels relative to the ordering of the corresponding molecular states.12 The Davydov tight binding formulation of exciton theory leads to the following representation for the manifold of optically accessible (k = 0) energy levels in a pure molecular crystal 138... 

Fig. 9 Adiabatic exciton levels of P4 (introduced in Section 2.5) versus time. Upper panel neglect of the electrostatic CC solvent coupling, lower panel inclusion of the...

Fig. 10 Room temperature absorption spectra of P4 (upper two panels), P8 (two central panels), and Pi6 (bottom panels) estimated according to Eq. (66) and in using adiabatic exciton energies and oscillator strengths. The overall spectrum (thick line) follows as the sum of single exciton level contributions (thin lines). The left column of figures shows spectra without including the modulation of the chromophore excitation energy by a coupling to the solvent. The right column of figures shows spectra where this effect is inciuded.

This was defensible in the inert-gas solids (though we noted that the gap was slightly reduced in those solids), but in the ionic crystal the nonmctallic ion electronic levels are greatly raised and the important excited levels (for exciton levels as well as for lower conduction-band levels) are dominated by the states on metallic ions see Fig. 14-1. Pantelides noted in fact that a critical study of the analysis of experiments in terms of the independent-ion model did not support the model. The model appeared to work for the alkali halides, but this was by fitting 16 experimental numbers with 8 adjustable parameters and the systematic variation made this fitting possible. Little success was had with other compounds. 

H.-M. Wu, N.R.S. Reddy, G. J. Small, Direct observation and hole burning of the lowest exciton level (B870) of the LH2 antenna complex of Rhodopseudomonas acidophila (strain 10050). J. Phys. Chem. B 101, 651-656 (1997b)... 

Absorption of radiation in the far ultraviolet by an insulator, may be sufficient to promote an electron from the full VB to the empty CB, wherein it is free to migrate. This is observed as photoconductivity. At slightly lower energies, the electron may be promoted to an exciton level (e.g. the first unoccupied level of the metal atom)... 

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