Polyacetylene Electron-Phonon Interactions

The synthesis and characterization of polyacetylene (PA) provided new incentive for understanding 7r-electronic spectra, electron-phonon interactions and electronic correlations[l, 2, 14]. The electrical conductivity of chemically doped PA rivals that of metals. Families in Fig. 2 such as polydiacetylenes (PDAs), poly thiophenes (PTs), cr-conjugated polysilane (PSs) and polyparaphenylene vinylene (PPVs), among... 

We start this investigation by treating the electronic degrees of freedom within the Born-Oppenheimer approximation, where the nuclear degrees of freedom are static, classical variables. The 7r-electron model that describes both electron-electron and electron-phonon interactions in the Born-Oppenheimer approximation is known as the Pariser-Parr-Pople-Peierls model. This is described and its predictions are analyzed in the following sections. Chapter 10 will deal with quantum phonons in an interacting electron model, specifically for trans-polyacetylene. 

The discussion in this section has so far been based on electron-phonon interaction, which leads to the Peierls transition, as demonstrated in Figure 1.11. For a more complete consideration, electron-electron interaction also has to be taken into account. In fact, both interactions are of about equal importance in polyacetylene one cannot be treated just as a small perturbation of the other. The Hamiltonian of the system with both interactions will appear as... 

The Coulomb interaction between the re-electrons is neglected. The standard tra/is-polyacetylene parameters are ta=2.5 eV for the hopping amplitude in the undimcrizcd chain, u-4. cV/A for the electron-phonon coupling, and K= 21 eV/A2 for the spring constant [1,4, 8]. 

The dimerized chain is the simplest model of semiconducting polymers, and is applied in particular to trans-polyacetylene. The noninteracting electronic structure of conjugated polymers with more complex unit cells, such as poly(para-phenylene), will be discussed in their relevant chapters. We emphasize that the noninteracting model is a simple model. It is not a realistic description of the electronic states of conjugated polymers, as it neglects two key physical phenomena electron-phonon coupling and electron-electron interactions. Despite these deficiencies it does provide a useful framework for the more complex descriptions to be described in later chapters. 

In spite of the clear evidence for the importance of Coulomb interactions, and their role in determining the properties of conjugate molecules, the SSH model and its continuum version [18] are widely used, particularly for the modelling of polyacetylene in its excited states with the various parameters (bandwidth, electron-phonon coupling etc.) chosen empirically. This approach has been remarkably successful, and we follow it in the present work for the modelling of the effects of disorder on the chain. 

For one-dimensional systems interactions between electrons and phonons are very important because the low dimensionality increases the probability of collisions. This leads to the non-linear behaviour of linear chains. The simple structure of polymers, especially, with conjugated double bonds and particularly the high symmetry of rran -polyacetylene confer on these substances much importance when discussing the utility of the soliton concept. 

---