a Theoretical Study of Pi-Conjugated Materials

Conducting polymers and fullerenes are pi-conjugated materials. In these materials, ^^2 hybridized orbits provide the framework structure, and 2p_{z} electrons are delocalized and fill the pi-electron band partially. Even though the pi-band is partially filled, undoped conducting polymers and fullerenes are insulators or semiconductors at best. Actually they have a considerable gap in the pi-band because of either electron -phonon coupling or the structure. At the same time, their bonds are dimerized in the ground state due to the electron -phonon coupling, which is well explained by the Su-Schrieffer -Heeger (SSH) model Hamiltonian. Besides the electron-phonon coupling, the electron-electron interaction cannot be neglected. Because of the huge dimension of Hilbert space, a complete treatment of electron-electron interaction is impossible. We developed a useful calculational scheme to combine these two effects for the electronic ground state and the lowest excited states. Since the pi-band is split and the HOMO-LUMO gap is wide (about 2 eV), the ground state and lowest optically excited states are dominated by the SSH ground state and singlet single excitation (SSE) configurations. In this dissertation, we use either SSH's independent electron model or SSE calculation to study the electronic properties of conducting polymers and fullerenes. In addition, we study the manifestation of quantum chaos due to the electron-electron interaction from a triplet exciton on a linear molecule.