XαApproach for the Determination of Electronic and Geometric Structure of Polyacetylene and Other Chain Polymers

The first self-consistent $X\alpha$ study of trans-polyacetylene, ${\left(\mathrm{CH}\right)}_x$, is reported. This study is carried out by application of a new linear-combination-of-atomic-orbitals method which determines both the electronic structure and geometry of periodic chain polymers variationally from the $X\alpha$ total-energy functional. The present trans-${\left(\mathrm{CH}\right)}_x$ results compare favorably with experiment and indicate that the present method will be useful in the study of both the electronic and geometric properties of other quasi one-dimensional systems.