Electron polaron

The combination of a hole polaron and an electron polaron, with binding energies Ep+ and Ep-, respectively, results in the formation of an exciton. Their difference corresponds to Et and is also referred to as the single particle energy gap Egsp -... 

The critical densities for the formation of the electronic polaronic crystals depend on the effective volume occupied by the doped charge carriers. The anisotropic interactions between the doped charge carriers produce the stripe or checkboard phases [15-16],... 

If the valence band is completely filled in a polymer (or in a molecular crystal) we can subdivide the ground-state correlation into a long range and a short range part. For the long range correlation the electronic polaron model33 can be used. It has been applied already to the periodic DNA model polycytosine (polyC),34... 

Besides the mentioned aperiodicity problem the treatment of correlation in the ground state of a polymer presents the most formidable problem. If one has a polymer with completely filled valence and conduction bands, one can Fourier transform the delocalized Bloch orbitals into localized Wannier functions and use these (instead of the MO-s of the polymer units) for a quantum chemical treatment of the short range correlation in a subunit taking only excitations in the subunit or between the reference unit and a few neighbouring units. With the aid of the Wannier functions then one can perform a Moeller-Plesset perturbation theory (PX), or for instance, a coupled electron pair approximation (CEPA) (1 ), or a coupled cluster expansion (19) calculation. The long range correlation then can be approximated with the help of the already mentioned electronic polaron model (11). 

Figure 4.8-1 Electronic structure and chemical structure of hole and electron polarons (a), hole and electron bipolarons (b), and hole and electron solitons (c). Examples of chemical structures refer to poly(thiophene) and poly(acetylene), respectively.

A small proton polaron is different in some aspects from the electron polaron that is, the hydrogen atom is able to participate in the lattice vibrations in principle (in any case it is allowable for excited states see Section II.F), but the electron cannot. This means that one more mechanism of phonon influence on the proton polaron is quite feasible. That is, phonon fluctuations would directly influence wave functions of the protons and thereby contribute to the overlapping of their wave functions. In other words, phonons can directly increase the overlap integral in concept. Such an approach allows one to describe the proton transfer without using the concept of transfer from site to site through an intermediate state. 

Figure 9. A cyclotron resonance spectrum obtained in a conventional EPR experiment (9.15 GHz) carried out at 10K on an annealed, dislocation-free sample of pure AgBr. The sample was continuously exposed at 425 nm. The dashed line is a fit to the experimental data which yields an electron polaron mass of 0.289m0 and a mobility (in units of cm2/Vs) of 3.02 x 105. (Courtesy of M. T. Olm and A. D. Kirkwood).

The situation is drastically different in organic materials. Here, the electronic polaron has long enough time to form, so the energy levels of a charged molecule are significantly shifted with respect to that of a neutral molecule, as shown in Figure... 

FIGURE 2.2.6 Energy scheme of the electronic polaron in a molecnlar crystal. VL is the vacnum level, EA the electronic affinity, and IP the ionization potential. P and P- are the polarization energy for positive and negative charge, respectively, and the transport hand gap. (From Silinish, E. A. and Capek, V., Organic molecular crystals Interaction, localization, and transport phenomena, AIP Press, New York, 1994.)... 

Fig. 8.7 Energy diagram of the anthracene crystal, taking into account lattice relaxation, a the neutral molecule b ionised states. EZ and Ei are the electronic polaron states, MZ and...

The advanced models elaborated for the low-amplitude potential perturbation of metal/conducting polymer fihn/solution systems also take into account the different mobilities of electronic (polarons) and ionic species within the uniform film. An important feature of this approach is that the difference in the electric and ionic mobilities (Dq A) leads to nonuniformity of the electric field inside the bulk fihn, which increases as the ratio A/A increases, and the electric field will vanish when A=A [190,192,193],... 

From a consideration of these results and of the optical absorption data, the following unified model may be proposed. When the metal atom is dissolved in ammonia, it dissociates and produces the metal ion and electron. Some of the electrons get trapped in a polaron state and some in clusters around the metal ion. In dilute solutions it is supposed that most of the electrons are present as polarons which accounts for the success of the polaron theory in explaining the value of H in dilute solutions. As the concentration increases, dimer clusters are produced by the association of monomer clusters. The two-electron polaron is probably unstable. As the concentration increases toward saturation, the monomers and dimers form a lattice-like arrangement and the unpaired electrons get delocalized as in a metal. In the next section it will be seen that this model explains satisfactorily the optical, electrical, and other properties listed in Section I. 

The current idea is to associate the infrared band with the transition of the electron in the cavity from the ground state to an excited state. Such an explanation was proposed by Fowles, McGregor, and Symons and supported quantitatively by the calculations of Jortner. Jortner demonstrated that the 2p state for a one-electron polaron inside the solntion was a bonnd state. From Table IV giving the valnes of and it is possible to get the transition energy hv defined by... 

It is conceivable that the optical maximum and the continuous absorption in the short-wave region arise out of transitions to these higher states from the ground state of the polaron and eventually to the continuum. However, if this were true one would expect that the intensities of the infrared and optical bands would depend in the same manner on concentration and temperature. The available experimental data, as pointed out in Part 1-B, show that this is not true. The optical band has therefore to be associated with a different center such as the two-electron polaron cavity if it were stable. Hutchison and Pastors observation that the progressive increase in prominence of the optical band with increasing concen-... 

For the cavity model, a careful analysis of the two-electron polaron is necessary to test the correctness of the conclusion that it is unstable. Also, for the one-electron polaron, the orthogonality of the unpaired electron wave function to the wave functions of the electrons on neighboring ammonia molecules has to be considered carefully for possible contributions to the observed and proton Knight shifts in N.M.R. measurements. 

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