A theoretical study of π-conjugated materials

Conducting polymers and fullerenes are π-conjugated materials. In these materials, sp2 hybridized orbits provide the framework structure, and 2pz electrons are delocalized and fill the π-electron band partially. Even though the π-band is partially filled, undoped conducting polymers and fullerenes are insulators or semiconductors at best. Actually they have a considerable gap in the π-band because of either electron-photon 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 π-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