  The two kinds of carbyne, i.e., cumulene and polyyne, are investigated by the
first principles, where the mechanical properties, electronic structure,
optical and phonon properties of the two carbynes are calculated. The results
on the crystal binding energy and the formation energy show that polyyne is
more stable and harder than cumulene, and both are difficult to be synthesized
from diamond or graphite. The tensile stiffness, bond stiffness and Young's
modulus of cumulene are 94.669 eV/{\AA}, 90.334GPa and 60.62GPa, respectively;
while the corresponding values of polyyne are 94.939eV/{\AA}, 101.42GPa and
60.06GPa, respectively. The supercell calculation shows that carbyne is the
most stable at N=5, where N is the supercell number. It indicates that the
carbon chain with 10 atoms is the most stable. The calculation on the
electronic band structure shows that cumulene is conductor, while polyyne is
semiconductor with a band gap as 0.37eV. The dielectric function of carbynes
varies in different direction, consistent with the one dimensional nature of
the carbon chains. In the phonon dispersion of cumulene there are imaginary
frequencies with the lowest value down to -3.817THz, which indicates that
cumulene could be unstable at room temperature and normal pressure.
