Electronic structure of aperiodic polymers. I. The average-matrix method and the effect of a cluster of impurities on the band structure of a periodic system

To treat a compositionally disordered one-dimensional polymer with not very different constituent units, a method has been developed in an ab initio SCF LCAO (self-consistent-field linear-combination-of-atomic-orbitals) framework. Using the composition and the first neighbor's frequencies of the polymers, the method solves instead of the original problem a periodic problem with average unit cells and average interaction matrices. This procedure is correct in the first order of the deviations of the different units and their interactions from the average unit and the interactions between them. Further, to be able to treat a cluster of impurities and/or defects imbedded in a one-dimensional periodic polymer, a resolvent method has been developed in the Hartree-Fock level using an LCAO basis (ab initio SCF LCAO treatment).