Theory of Electronic Structures and Lattice Distortions in Polyacetylene and Itinerant Peierls Systems. II: Coulomb Interaction Dependences of the HF Ground State, Lattice Dimerization and 1Bu Excited State in Regular Trans-Polyacetylene

We study the Coulomb interaction dependences of the HF ground state, lattice dimerization and 1Bu excited state in regular trans-polyacetylene using the PPP hamiltonian model developed in a previous paper. The nature of the HF ground state is determined by the relative magnitudes of the on site and nearest neighbour parts and the screening of the longer range part of the effective Coulomb potential. The Coulomb interaction with relatively large nearest neighbour part and not too strongly screened longer range part induces lattice dimerization. The driving force of the Coulomb induced dimerization is the nearest neighbour exchange interaction. The lattice dimerization in polyacetylene is due to the Coulomb mechanism. The SSH model is implicitly taking into account the nearest neighbour exchange interaction. The Franck-Condon band gap is mostly determined by the nearest neighbour exchange interaction. The 1Bu excited state is excitonic. The exciton binding energy is estimated for the effective Coulomb potential with the screened long range part. It is not large owing to very small effective mass of electron and hole. To explain the observed 1Bu excitation energy, the short range part of the effective Coulomb potential must be screened by about half compared to the one in small conjugate molecules. The condition for splitting of the exciton into a zwitter-ionic pair of charged solitons is discussed.