Electron hopping interaction effects

Here the 7r-system is treated with a very simple, but still quantum mechanical method e.g. by the Hiickel Hamiltonian and MO LCAO approximation (which in the particular case of the Hiickel Hamiltonian gives the exact answer). No explicit interaction, i.e. junction, between the subsystems was assumed at that time however, the effects of the geometry of the classically moving nuclei were very naturally reproduced by a linear dependence of the one-electron hopping matrix elements of the bond length ... 

In Ae small polaron picture, on the other hand, the electron-phonon interaction, compounded by the localization effects introduced by the disorder, leads to the formation of small polarons. The polaron binding energy is then the largest energy in the problem, and charge transport involves multiphonon-assisted hopping of small polarons (Emin, 1984). 

The four-spin interaction as discussed in Chap 3 (Sect. 3.4.2) is the effective matrix element between the determinants matrix element of the electronic Hamiltonian between them is zero (there are more than two different columns in the determinants), there must be other, indirect interactions that account for the non-zero value of this interaction. In analogy to the normal two-center magnetic interaction, we will review the role of the ionic determinants in the effective matrix elements. Figure 5.14 shows one of the pathways that connects ionic states. In the first step an electron hops from site A to B to form the ionic determinant [Pg.166]

In amorphous semiconductors, electron-electron interactions are important only when two electrons of opposite spin occupy the same localized state or for Mott hopping at the Fermi level at very low temperature. Electron-phonon interactions are always present and more important in disordered than ordered semiconductors. The electron-phonon (e-p) interaction has two kinds of effects, elastic or static and... 

However, on the one hand, low ESR signals alone are a weak argument for the assumption of hole bipolarons. On the other hand, several experimental results are in contradiction of this model. For example, (a) the electrical conductivity of boron carbide is maximum at the minimum concentration of BnC icosahedra in the homogeneity range (b) polaron-type effects are restricted to one electron per icosahedron and no corresponding electron-phonon interaction with holes, in particular not with hole pairs in icosahedra, has been proved experimentally (c) the distortion of the icosahedra in boron carbide depends to only a small degree on electron-phonon interaction and (d) the electronic transport in boron-rich solids is due to classical band-type conduction and hopping processes side by side. Hence, the hole bipolaron theory for boron-rich solids can hardly be maintained. 

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