Band theory applied to polymers

If we regard each molecule for the moment as a 1-dimensional lattice we can make the following initial assumptions  

In the case of a polymer with a saturated chemical structure, such as polyethylene, the strength of a-bonding is such that the band gap will be comparable to that in diamond. However, for a polymer with a conjugated structure, such as polyacetylene, the chemical binding of the re-electrons is much weaker and a gap of a few eV, comparable to those in inorganic semiconductors, is anticipated. 

There are a number of different theoretical approaches to the calculation of the band structures of polymers. These are extensions of the methods employed to calculate the electronic states of molecules, which obtain molecular orbitals from a linear combination of atomic orbitals. In this case the states in question are those of an infinitely long molecule, which is approximated by a finite length system with cyclic boundary conditions, i.e. the right-hand end of the chain is, in effect, joined to the left-hand end of the chain. This is the method used for band 

The ab initio approach includes all a- and 71-electrons and seeks to use either analytical or numerical solutions to the integrals that occur in the quantum mechanical problem. This procedure was initially carried out within the framework of the one electron HF-SCF method using the basis sets described above. Subsequently it has been implemented using density functional theory (DFT). If the electron density in the ground state of the system is known, then in principle this knowledge can be used to determine the physical properties of the system. For instance, the locations of the nuclei are revealed by discontinuities in the electron density gradient, while the integral of the density is directly related to the number of electrons present. Ab initio methods are obviously computationally intensive. 

An important defect of all the single electron calculations is the neglect of electron correlation. Various methods have been employed to rectify this problem. Its inclusion using second order perturbation theory has been found to provide much better agreement between theory and experiment in some instances. The inclusion of electron correlation has a profound effect since the electrons and holes in the first excited state are bound by their Coulomb interaction to form a localised state, an exciton. This state is separated from the conduction band by the exciton binding energy. That this model 

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