First-principles calculations of the three-dimensional structure and intrinsic defects intrans-polyacetylene

We report a first-principles, local-density-functional (LDA) calculation of the electronic structure of crystalline, three-dimensional (3D) trans-(CH${)}_{\mathit{x}}$. For the perfect crystal, we find a broken-symmetry ground state having P$2_1$/a space-group symmetry, corresponding to in-phase dimerization on neighboring chains within the unit cell. We show that in this structure the interchain couplings, although weak, lead to an asymmetry between the valence and conduction bands and, more importantly, give 3D character to the electronic band-edge states. We investigate several additional aspects of the electronic structure of the perfect crystal, including self-consistent optimization of the ions in the unit cell, spin polarization and electronic charge densities, interchain electron-phonon interactions, and the density of states. To study intrinsic defects in trans-(CH${)}_{\mathit{x}}$, we map our LDA results onto a multi-orbital, tight-binding model; this mapping preserves very accurately all the electronic-structure properties of the full calculation. Using a Koster-Slater Green-function technique, we are able to examine both (shallow) polaronlike and (deep) bipolaronlike lattice distortions corresponding to localized defects. We find that the 3D character of the electronic band-edge states strongly suppresses the formation of the self-trapped, localized defects characteristic of the 1D models, destabilizing polarons and possibly bipolarons as well in perfectly ordered 3D trans-(CH${)}_{\mathit{x}}$. To establish a connection with earlier work, we demonstrate that by artificially decreasing interchain effects and/or increasing the intrachain electron-phonon coupling we can cause polarons and bipolarons to form. We examine the agreement of our results for the idealized perfectly crystalline material with experimental results on real samples of trans-(CH${)}_{\mathit{x}}$ and conclude with suggestions for future work, both theoretical and experimental.