Generalized electronic polaron model

In the actual calculation the complicated side chains R were substituted by an H atom. For the first step (calculation of the HF band structures) a 6-3IG basis set (double C + polarization function on both the carbon and hydrogen atoms) was applied. The valence and conduction bands obtained in this way were then corrected using the generalized electronic polaron model [quasi-particle (QP) band structures see Section 5.3]. The lowest sin et-exciton enei es (at K = 0) were then calculated using the QP one-electron levels and performing the three steps described in the previous section after equation (8.22). Table 8.1 shows the results obtained in this way for both PTS and TCDU. ... 

One can define a generalized Koopmans theorem if, by calculating quantity (8.27), one takes into account correlation effects and determines a quasi-particle (QP) band structure based on the generalized electronic polaron model (see Section 5.3). One can then write for a polymer... 

There are some (Heinze, 1996) to whom the polaron explanation of the ionic introduction of electronic conductivity in organic compounds is specious The roughness factor of 400 would limit the degree of penetration of ions into the interstices of the polymer. However, Li+ or even CIOJ is of course much smaller than the test molecules (large dye molecules) which are generally used to probe the real area. Thus, one might conceive of a model of the polymer that is all fibers, the intercalation being all pervasive. It is obvious that an Li+ ion adsorbed on the surface of a fiber will promote an electron that may indeed be free to move under a field, i.e., to conduct. 

The prominence of these quantum dynamical models is also exemplified by the abundance of theoretical pictures based on the spin-boson model—a two (more generally a few) level system coupled to one or many harmonic oscillators. Simple examples are an atom (well characterized at room temperature by its ground and first excited states, that is, a two-level system) interacting with the radiation field (a collection of harmonic modes) or an electron spin interacting with the phonon modes of a surrounding lattice, however this model has found many other applications in a variety of physical and chemical phenomena (and their extensions into the biological world) such as atoms and molecules interacting with the radiation field, polaron formation and dynamics in condensed environments. 

The new states can either be interpreted in the band picture as polarons and/or bipolarons which occur due to electron-phonon coupling after ionization (see below) (electron-electron interaction is neglected) or as the new HOMO and LUMO states in charged particles if localized molecular orbitals are assumed (electron-electron correlation is taken into account, electron-phonon coupling neglected). Both models will be discussed in parallel in the following subsections. However, in general discussions the band stmeture terms will be used as they are more common in literature. 

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