Helical polyacetylenes (CH)n are perspective materials for many novel technology areas. Two helical isomers of polyacetylene were considered in the framework of density functional theory (DFT) from the point of view of spontaneous symmetry breaking. It was shown that it is necessary to take into account not only the Peierls-type metal–insulator transition, but also the Mott-Hubbard transition responsible for the appearance of antiferromagnetic ordering. It was shown that for the cis-cisoid isomer of the polyacetylene (denoted in the text as [1]PA), the Peierls-type transition leads to a much larger decrease in energy than the Mott-Hubbard transition. In the case of the [2]PA isomer (see the text for the structure), the situation is reversed, and the appearance of antiferromagnetic ordering becomes more favorable. It was shown that the preference for one or another type of transition may depend on more subtle factors (in this case, on the rotation angle), which opens up the possibility of a fine tuning the properties of 1D nanosystems.