In this paper we report first-principles calculations on the ground-state electronic structure of two infinite one-dimensional systems: ͑a͒ a chain of carbon atoms and ͑b͒ a chain of alternating boron and nitrogen atoms. Meanfield results were obtained using the restricted Hartree-Fock approach, while the many-body effects were taken into account by second-order Mo "ller-Plesset perturbation theory and the coupled-cluster approach. The calculations were performed using 6-31G** basis sets, including the d-type polarization functions. Both at the Hartree-Fock ͑HF͒ and the correlated levels, we find that the infinite carbon chain exhibits bond alternation with alternating single and triple bonds, while the boron-nitrogen chain exhibits equidistant bonds. In addition, we also performed density-functional-theory-based local-density-approximation ͑LDA͒ calculations on the infinite carbon chain using the same basis set. Our LDA results, in contradiction to our HF and correlated results, predict a very small bond alternation. Based upon our LDA results for the carbon chain, which are in agreement with an earlier LDA calculation ͓E.J. Bylaska, J.H. Weare, and R. Kawai, Phys. Rev. B 58, R7488 ͑1998͔͒, we conclude that the LDA significantly underestimates Peierls distortion. This emphasizes that the inclusion of many-particle effects is very important for the correct description of Peierls distortion in onedimensional systems.