| Conjugated organic polymers, due to their great potential for device applications, have been the subject of intensive investigation. Although a large body of theoretical work exists to describe the bonding, electronic structure and excitations of these polymers, there is still plenty of room for improvement. The present work has improved the existing theory in two ways: (1) we have extended the well known Su-Schreiffer-Heeger (SSH) model so that it can describe all isomers of polyacetylene (PA) and (2) we have developed a quantitative semi-empirical method for calculating the ground-state bonding properties and electronic structure of polymers containing carbon, nitrogen, sulfur and hydrogen.; The extended SSH model utilizes natural boundary conditions to describe finite PA chains and includes a third-neighbor interaction to allow the model to discern different isomers. This extended model yields the correct band gaps and ordering of cohesive energies of the trans, cis-transoid and trans-cisoid structures. Besides reproducing the SSH description of the soliton and polaron excitations in trans, the extended model also correctly describes bound bipolarons and excitons on doubly charged cis chains, which cannot be addressed in the original SSH model.; The semi-empirical method preserves the understanding and quantitative results of the SSH model but has the ability to describe more complex molecular configurations. Density functional theory in the local density approximation (LDA) method is used to first construct a Hamiltonian to which a small correction is then added to treat the {dollar}pi{dollar}-{dollar}pi{dollar} interactions. The parameters in the connection are determined using experimental data for several different known polymer systems. The Hamiltonian is then applied to a variety of polymers, including polyacetylene (PA), poly(p-phenylene) (PPP), poly(p-phenylene vinylene) (PPV), polythiophene (PT), polypyrrole (PPY), poly(p-phenylene sulfide) (PPS), poly(thiophene vinylene) (PTV), poly(isothianaphthalene) (PITN) and polyaniline (PAN). Calculated ground state bond lengths and band gaps have been found to be consistent with the best experimental and theoretical results. The method has the potential to provide a basis for a thorough theoretical analysis of conjugated polymers, and can be extended to calculate conductivity, dielectric constants, non-linear optical constants, optical absorption spectra and mechanical properties in the near future. |
