Theory of Electronic Structures and Lattice Distortions in Polyacetylene and Itinerant Peierls Systems. I: UHF Transfer Matrix Method Adapted to the Long Range Coulomb Interaction and UHF States in Regular Bond Alternated Lattice

Abstract

We develop in this series a theory of itinerant Peierls systems that mainly aims to study polyacetylene. In order to investigate roles of the long range Coulomb interaction in electronic structures and lattice distortions in a Peierls system, we develop a transfer matrix technique adapted to the unrestricted Hartree-Fock (UHF) approximation. The method makes it possible to calculate UHF states and equilibrium lattice geometries in a lattice with any aperiodic structure due to the presence of solitons. Applying the method, we obtain the UHF states in the case of regular lattice that may become the HF ground state. There are at least eight such UHF states which are distinguished by the long range orders in the spin and charge densities and the bond orders. The nearest neighbour exchange interaction is responsible to produce such plentiful UHF states. We calculate the bond alternation potential and the band gap in trans polyacetylene using parametrizations of the Hamiltonian and the elastic potential that are able to well reproduce spectra and equilibrium geometries of small conjugated hydrocarbons. The bond alternation potential is very sensitive to the strength of the nearest neighbour Coulomb interaction. The Coulomb potential with fast damping prevents the bond alternation. The band gap is much larger than the energy 2 eV of the lowest absorption band as long as the Coulomb interaction in polyacetylene is similar to that in small conjugated hydrocarbons, suggesting the excitonic nature of the absorption band. We make also an illustrative calculation for an itinerant spin Peierls system with an antiferromagnetic spin order as well as a lattice dimerization.