Recent advances in the theory of conjugated polymers

1-13This article discusses the importance of some of the recent theoretical developments in the field of conjugated polymers. In the theoretical design of conjugated organic polymers with small band gaps, donor-acceptor polymers having a regular alternation of conjugated donor- and acceptor-like moieties along the conjugated backbone are the novel promising candidates. These polymers which are a one-dimensional analogue of inorganic n-i-p-i superlattice structures owe their low band gap values to the bending of their valence and conduction bands by the space-charge effects. Some of the recent results of novel donor-acceptor polymers are reviewed and their low band gap values rationalised on the basis of their π-bond order data and the patterns of the frontier orbitals. As the second significant development, the fundamental question of design of low band gap polymers from the monomers with low HOMO-LUMO separation (ΔE) is discussed. Taking the examples of polythiophene and polythienothiadiazole, it is shown that though the low Δ E of thiophene oligomers is carried over to its polymer, that of thienothiadiazole oligomers is not. The reasons for these differences are discussed in terms of the orbital interactions and the role of non-bonding molecular orbitals in the oligomers and the reduced π-conjugation and the enhanced intercell interactions in the polymers. From the methodological side, a brief review is given of the methods for the treatment of electron correlation in periodic 1D and 2D polymers and non-periodic 1D polymers. These methods include not only the correlation correction of the total energy per unit cell but also of the recalculation of the band structures themselves in the periodic case as well as the density of states (DOS) for non-periodic 1D-chains. Finally, a new method to take into account the simultaneous effect of a static and periodic time-dependent electric field on the one-electron wave functions and on the total electronic energy of a periodic polymer is briefly reviewed. It is shown how one can calculate the non-linear optical properties of conjugated polymers with the help of the derivatives of the quasi-energies. according to the different-field (both static and time-dependent) components