  We proved earlier that in the strained monoatomic chains with Lennard-Jones
potential there can exist an equilibrium static bi-structure, which corresponds
to N - 1 equal short interatomic bonds and one long bond with inversion in its
center (N is the number of atoms of the chain). In the present work, we
investigate with the aid of the density functional theory (DFT modeling)
similar structures that can exist in the strained carbon chains. In contrast to
the Lennard-Jones model, the bi-structures in this case are inhomogeneous (they
have short bonds of different lengths) and appear abruptly when the strain
exceeds a certain critical value $\eta_c$ as a result of a hard bifurcation of
the equilibrium state (an analogue of the first-order phase transition). Such a
bifurcation is associated with two different parts of potential, in which the
Lennard-Jones forces can be quite small (this is the vicinity of the potential
minimum and the potential tail) and, therefore, the forces acting on the
particle between the long and short bonds can be equal. Since practically all
interatomic potentials possess such features, the above bifurcation is
universal, i.e. it must occur for any monoatomic chain. We have studied in
detail the properties of the above structures, in particular, the behavior of
their parameters with increasing N. With the help of DFT-modeling, the electron
density of the above structures near the bifurcation point is investigated.
