### Abstract

We report a self-consistent linear-combination-of-Gaussian-orbitals study of the electronic states and ground-state geometry of an undoped and doped single, infinite chain of *trans*-polyacetylene using the density-functional theory in the local-density approximation. We find a dimerized ground state for an undoped chain with a dimerization amplitude of about 0.01 Å, which is lower than the experimental value of 0.023–0.03 Å. A pure Hartree calculation neglecting all exchange and correlation gives a much smaller dimerization amplitude of less than 0.005 Å. The local exchange-correlation energy thus significantly favors the dimerization although its effect is not strong enough. In the calculations of the doped chains, the dopant ions were approximated by a uniform background charge. We find that the undimerized state becomes energetically more favorable than any uniformly dimerized state at a critical doping level of about 0.04 (0.03) extra holes (electrons) per CH unit. The band structures and total energies of polaron and soliton lattices at a higher doping level of 0.2 holes per CH unit are calculated and compared with those of the uniformly dimerized and undimerized lattices, and possible models of the metallic state of *trans*-polyacetylene are discussed. According to our study, the bonds become increasingly similar with increasing doping. The undimerized chain model seems to be a good approximation for the metallic state of *trans*-polyacetylene at high doping levels although the possibility for a marginal soliton lattice cannot be fully excluded.

Original language | English |
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Pages (from-to) | 16948-16964 |

Number of pages | 17 |

Journal | Physical Review B: Condensed Matter |

Volume | 48 |

Issue number | 23 |

DOIs | |

Publication status | Published - 1993 |

MoE publication type | A1 Journal article-refereed |

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### Cite this

*trans*-polyacetylene.

*Physical Review B: Condensed Matter*,

*48*(23), 16948-16964. https://doi.org/10.1103/PhysRevB.48.16948