Investigation on the Line Group Theoretical Analysis of Quasi One-Dimensional Polymer or Crystal Molecular Column

In the present paper, according to the principle that the operators of a line group for a polymer make the chemical properties of atomic orbitals unchanged, we have divided the translational periodic orbital base set of polymer into base subsets with different chemical properties which are invariant under the symmetric operate of the line group. And then the base subsets are divided into smaller baes subsets in terms of the atomic orbital environment. All these base sets and subsets can characterize the energy bands equivalently, so that we can use the elementary base subsets to characterize bands with less effort than the base sets. As examples, the energy bands of polypyrrole and polythiophene have been characterised with some invariant base subsets. Furthermore, the charge carrier skeleton has been represented with the characterized results of the highest occupied bands.