  Nonlinear vibrations in strained monoatomic carbon chains are studied with
the aid of ab initio methods based on the density functional theory. An
unexpected phenomenon of structural transformation at the atomic level above a
certain value of the strain was revealed in cumulene chain (carbyne-{\beta}).
This phenomenon is a consequence of stability loss of the old equilibrium
atomic positions that occur at small strain, and appearance of two new stable
equilibrium positions near each of them. The aforementioned restructuring gives
rise to a softening of {\pi}-mode whose frequency tends to zero in a certain
region of amplitudes when carbon atoms begin to vibrate near new equilibrium
positions. This resembles the concept of soft mode whose "freezing" is
postulated in the theory of phase transitions in crystals to explain the
transitions of displacement type. The dynamical modeling of mass point chains
whose particles interact via Lennard-Jones potential can approximate our ab
initio results well enough. In particular, this study demonstrates an essential
role of dipole-dipole interactions between carbon atoms in formation of their
new equilibrium positions in the cumulene chain. We believe that computer
studying of Lennard-Jones chains enables to predict properties of various
dynamical objects in carbon chains (different nonlinear normal modes and their
bushes, discrete breathers etc.) which then can be verified by ab initio
methods.
