Infinite polyene limit

Extrapolation ofS and S, Sq Transition Energies to Long Carotenoids The Infinite Polyene Limit... 

Table 1. Extrapolations of carotenoid/Iinear polyene transition energies to the infinite polyene limit...

In the SSH model, both neutral and charged solitons will show an absorption peak at half the energy gap between HOMO and LUMO. Experimentally, both charged solitons and neutral solitons are claimed to be photogenerated and they show absorption features which are distinct and at two different frequencies [174, 175]. This feature is believed to be due to electron-electron interactions. It is by now well established that electron correlations remove the notion of a mid-gap state in the neutral odd-polyene compounds this is demonstrated by the fact that in undistorted finite polyenes, the optical gap of both odd and even polyenes plotted as inverse chain length, fall on the same straight line in the PPP and the Hubbard models [176] and extrapolate to the same infinite chain value. In the dimerized case, while the odd and even chains extrapolate differently [177], the optical gap in the infinite chain limit are quite close in value. However, in the SSH model, the odd and even car-... 

All carbon-carbon bonds in the skeleton have 50% double bond character. This fact was later confirmed by X-ray diffraction studies. A simple free-electron model calculation shows that there is no energy gap between the valence and conduction bands and that the limit of the first UV-visible transition for an infinite chain is zero. Thus a simple free-electron model correctly reproduces the first UV transition with a metallic extrapolation for the infinite system. Conversely, in the polyene series, CH2=CH-(CH=CH) -CH=CH2, he had to disturb the constant potential using a sinusoidal potential in order to cover the experimental trends. The role of the sinusoidal potential is to take into account the structural bond alternation between bond lengths of single- and double-bond character. When applied to the infinite system, in this type of disturbed free-electron model or Hiickel-type theory, a non-zero energy gap is obtained (about 1.90 eV in Kuhn s calculation), as illustrated in Fig. 36.9. 

Hiickel analysis of /-PA with 5 = 0.18 matches E]b 1.8 eV and suffices for most aspects of e-ph coupling in Section III, where analytical results for the infinite chain are particularly important. Smaller 5 - 0.07 occurs in PPP models of polyenes or PA, since V R) also contributes to fie, and yields comparable but less precise X- for vibrations on extrapolating to the polymer (Fig. 6.8). Different 77-electron models are therefore suitable for different applications. Wider applications place more restrictions on the form and parameters of He - The inherently approximate nature of models, however, limits quantitative comparisons even if parameters are readjusted for each polymer, as is often done in solid-state discussions, and leaves open the range of optical, vibrational, NLO, or other spectra described by More detailed analyses and novel applications are certain in view of the generality of alternating chains and the flexibility of models. 

Figure 2. Results of calculations for conjugated polyenes. (Left) Results of full calculations, where the dashed line (la) gives the normalized r-energies for linear polyenes and the solid line (Ila) gives the energies for cyclic polyenes. The line at 2.14 eV represents the limit for an infinite chain. (Right) Results of calculations in which the antisymmetry principle was not included. The energies for the linear polyenes and the 4n + 2 cyclic polyenes are unchanged, but the An cyclic polyenes are calculated to be too stable. (Reprinted with permission from ref 124a. Copyright 1996 Elsevier Science.)...

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