Exciton delocalisation

The first mechanism, called exciton delocalisation, occurs when the inter-chromophore separation is about 1-2 nm, and is dependent on the inverse cube (i.e. r ) of that separation. What happens is that when the chromophore molecules are held rigidly together (as they would be, more or less, in the chloroplast membrane) at about 1-2 nm, their excited states become perturbed enough to form a new set of excited states that are delocalised over the whole array of chromophores. Thus, as soon as an electron is excited, it is delocalised over all the pigment molecules (Figure 3.39). 

The B850 ring forms a densely packed excitonically coupled aggregate. Shortly after the structure of the LH2 became available, the question of the extent of exciton delocalisation in B850 became a hot research subject. Different experimental techniques and theoretical methods lead... 

Fig. 2. Time evolution of three different numerical characteristies of exciton delocalisation length in B850. For more detailed description of the characteristics see ref. 24.

The mechanism of control with multipulse excitation is likely due to dynamics of the carotenoid donor. The presumably incoherent EET process [1] would not support the observed dependence on the carrier phase via the parameter c. Furthermore, the control effect does not suffer from annihilation at higher excitation intensities [2], as would be characteristic for the delocalised excitons in the B850 ring [1], However, it is well known that femtosecond pulses populate higher ground state vibrational levels by impulsive Raman scattering (IRS) [4], and that the periodic phase modulation (Eq. 1) makes IRS selective for specific vibrations... 

Excitation of the polymer creates one electron and a hole on the chain. This effect is particularly important when the electron-hole interactions are strong. Coulomb attraction keeps them together and we consider the two opposite charges as a bound electron-hole pair. An exciton (Fig. 1.11) is named according to its delocalisation. If it is localised, it is called a Frenkel exciton and, if it is delocalised, i.e., it extends over many molecular units, it is a Mott-Wannier type of exciton. ... 

One idea was that conduction should be looked for in materials based on organic unsaturated molecules, where electrons and holes are more easily excited into delocalised states. Little proposed that, in these materials, carriers created by such excitonic excitations could couple into electrons and holes plasmons, as later indeed observed in classical semiconductors under light, and thus produce a conductive state hopefully a superconductor state could develop under the same electron-electron interactions, leading possibly to high T<. s. The search for such excitonic conduction had been initiated shortly before as a porposal by W. Kohn for normal covalent semiconductors it had been carried out notably by D. Jerome, when he came to Orsay after on year s stay with Kohn in La Jolla various mineral semiconductors were studied, with small gaps and often low dimensionally. 

Scheme 2. In this photophysical scheme it was proposed that M, and D interact by the generally accepted exciton diffusion mechanism. M was considered to be an isolated naphthalene chromophore wliich can transfer energy into M with a transfer rate characterized by the rate coefficient kt- Reverse transfer from M to M was considered unimportant for the following reason. Exciton diffusion is expected to be very efficient within sequences of naphthalene chrcmiophoies within the chain comprising the M sites. In view of the reduced lifetime of M relative to M and of the delocalised nature of the energy within extended chromc hore sequences which increases the effective sqiaiation of M and M, M to M enei transfer by Foster or Dexter mechanisms is dimini ed relative to the to Mf process.

More generally, there are two kinds of exciton when the electron and hole are completely delocalised from any specific atomic site and form bound states, one has a Wannier-Mott exciton. When both the electron and hole are localised on or near a specific atomic site in the solid, so that the exciton is formed from atomic or molecular states perturbed by the crystalline environment, one has a FVenkel-Peierls exciton 102. ... 

The AC Stark effect is relevant, not only in atomic spectroscopy, but also in solid state physics. The biexciton state (or excitonic molecule), where two Wannier excitons are bound by the exchange interaction between electrons, occurs in various semiconductors (see section 2.22). Various experiments on the AC Stark effect of excitons have been reported, but the clearest example to date is probably the observation of the Rabi splitting of the biexciton line in CuC reported by Shimano and Kuwata-Gonokami [477]. It is very interesting to consider how Bloch states in solids, which themselves are delocalised and periodic, are dressed or modified by the electromagnetic field, since their properties are rather different from those of purely atomic states, which are by definition completely localised. 

In the spectroscopy of solids, questions of localisation or delocalisation of particles with respect to each other or else with respect to individual sites play a crucial role. Thus, for example, one distinguishes between two types of luminescence, viz. excitonic type and electron-hole type, depending on whether the electron and hole are bound together to form an exciton, or whether they are essentially independent. In the former case, the yield increases with incident energy, while in the latter it is essentially constant. 

A broadening of the terms from discrete terms in the molecule, bands are formed in the crystal, the excitonic bands E(k), since the excitation energy in the periodic potential of the ideal crystal is delocalised over all the molecules. 

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. 

Equation (6.12) describes an exciton whose excitation energy is delocalised over the whole crystal, but is limited to a set of translationally-equivalent molecules a. This one-site wavefunction thus holds for linear crystals or for crystals with only one molecule in the unit ceU. Quasi-one-dimensional excitons can for example be... 

The dissociation of an exciton in a polymer/fullerene BHJ does occur within tens of fs. This may allow both the presence of hot excitons and for electron transfer to a distribution of electron-hole distances. The subsequent transport of the free holes delocalised on polymer chains is also very fast and has two contributions. The initial hole mobility is comparable to the polymer intrinsic mobility and is assigned to hot holes. These cool down at a fast rate of (1/180) fs and are trapped at an initial rate of (1/860) fs [69]. At longer times, the conductivity decreases and represents the equilibrium population of mobile and trapped charge carriers. 

When the electronic interaction between the chromophores along a polymer chain is so strong that the electrons may be delocalised over several cbromophores, the exciton may also be similarly delocalised. Such a delocalised exciton is called a Frenkel exciton. Frenkel excitons have been observed in conjugated polymers such as polyphenylacetylene (Figure 13.10). 

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