First-principles calculation of the Peierls distorsion in an infinite linear carbon chain: the contribution of Raman spectroscopy

The modulation of the longitudinal optical (LO) phonon branch of a linear, infinite carbon chain (carbyne) by the degree of bond length alternation (BLA) is discussed in relation to the wavenumber dispersion of the strongest Raman line of oligoynes. Furthermore, the potential energy surface describing the Peierls distortion of the infinite 1D crystal has been determined theoretically through DFT calculations with periodic boundary conditions. A two-minima potential surface has been obtained as a function of BLA parameter, under the constraint that the diatomic unit cell keeps its translational period fixed to the optimized value. In this way, it has been possible to obtain the generalized harmonic force constant associated with the LO phonon at the Gamma point. The results obtained can be related to the observed behavior of the LO Raman line upon the temperature-driven phase transition towards a cumulenic structure.