Band Structure And Long-range Correlation Energies Calculations Of One-dimensional Organic Polymer

As a new kind of organic functional materials, the organic macromolecule polymers have received more and more people's attention recently. After the unceasing research, in 1977, the scientists discovered that by doping, the conductivity of polyacetylene can add several or even dozens of orders of magnitude, turned into a good conductor. Form them on, the scientists began to study the properties of organic conjugated polymers. As the organic polymers have many advantages, such as ease of processing, flexibility and low in price, in addition to organic polymers also have the electronic properties of metals and semiconductors, and so on. The study of organic polymers will lead to great interest in scientists, and has become a hotspot research in recent years. Especially in recent years, the organic macromolecule polymers have made great development. After a few years of development, many of the organic optoelectronic devices have been interested from a simple experiment into a new practical technologies. At present, scientists have developed a variety of organic optoelectronic devices, such as organic light-emitting diodes, field effect transistor, photovoltaic batteries, and so on.On the experimental study and theoretical analysis,the W. P. Su, Schriefferh and Heeger established SSH model. This model has an important effect on the development of polymer. Recently, scientists have found new phenomena. For example, the electron correlations have been a very important issue in investigating the electronic structures of various electron systems. Especially the electron correlations have a strong influence on the bonding properties of atoms, semiconductor band gap. The local density approximation (LDA) raised by Kohn and Sham and later the density functional theory established by Hohhenberg and Kohn made a contribution to the exchange-correlation energy. A formula for correlation energy Ec is obtained by Zhao. In reference [59], authors studied the correlation energies of polyethylene(CH2)x(PE) using the local ansatz. In reference [60], authors used the Gutzwiller ansatz as the variational ground state and studied correlatin energy of polyacetylene(PA). In reference [61], auther used a variational method to study the correlation of PA where both Hubbard term and the long-range Coulomb internaaction were included. People have realized the importance of the correlation energy from the long-range Coulomb interaction. Therefore, study of the correlation effect due to the lonng-range Coulomb interaction in the conjugated polymers becomes significant.With a tight-bounding SSH model and the expansion of the Hubbard model,we studied the band energy structure and long-range correlation energy (the nearest-neighbor interaction in this study) of PA. In the third chapter, the long-range correlation energies of polyacetylene (PA) chain have been calculated by the formula for correlation energy Ec in HF approximation with taking the electron- electron interaction into account (containing periodic boundary conditions and natural boundary conditions). We compare our results with those by other methods and find that they are consistent with each other very well. We also discuss the influence of the long-range correlation energies on the length and the band energy gap.In the forth chapter, we use another method. We also discuss the band energy gap and long-range correlation energy of PA with the e-e interaction and correlation Hamiltonian into account. And we compare results with last chapter.