Linear polyenes and trans-polyacetylene

The many unusual properties of trans-polyacetylene have already been described in this book in the context of understanding the roles of electron-electron and electron-lattice interactions in 7r-electron models. These have been described in Chapters 4 and 7, in particular. In this chapter we describe some experimental observations and show how these are explained within a framework of correlated electrons with strong electron-lattice coupling. The chemical structure of trans-polyacetylene is illustrated in Fig. 1.1. 

The realization that electronic interactions play a significant role in polyenes came via the experimental observations by Hudson and Kohler (1972) that the dipole-forbidden 2 Ag state lies below the dipole-allowed PS state. Further extensive studies of polyene oligomers by Kohler confirm the hypothesis that the relaxed energy of the 2 Ag state lies below the relaxed energy of the state. An analysis of oligomer spectroscopy from 6 to 16 carbon atoms suggests the empirical relation (Kohler 1988), 

The existence of the 2 Ag state below the PBu state in polyacetylene thin films was suggested by a number of experiments. Third harmonic generation (THG) and two-photon absorption by Halvorson and Heeger (1993) indicates that a Ag state lies below 1.1 eV in energy, while hnear absorption, which locates the state, typically rises at 1.8 eV and peaks at 2.0 eV (Vardeny 1993), as illustrated in Fig. 10.1. Peaks at 0.6 and 0.89 eV were observed in the THG spectrum by Farm et al. (1989). From the discussion of THG in Chapter 8, we know that this data implies some combination of Ag states at twice the photon energy (namely 1.2 and 1.8 eV), and states at three times the photon energy (namely 1.8 and 2.7 eV). Fann et al. interpreted the experiments as indicating the Ag and states virtually coincident at 1.8 eV. 

As we will describe in this Chapter, theoretical modelling indicates that the 2 A+ state, unhke the PB state, imdergoes considerable lattice relaxation. A reasonable interpretation of these experiments is therefore that the relaxed 

89 eV discussed above). Whether the correct interpretation of the 2.5 eV feature is that it is the n = 2 Mott-Hubbard exciton or the particle-hole continuum, it seems reasonable to assume that 0.5 eV is a lower boimd on the binding energy 

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