  Using the density functional theory we investigate a quasi-two dimensional
carbon allotrope, ZzC, formed by square carbon lattice buckled in zigzag
manner. By analyzing the Kohn-Sham energy and phonon dispersion obtained by
lattice dynamical calculations we show that ZzC is stable with binding energy
of 7.46 eV per atom. To examine the possible route of formation we find out
reaction pathway from ZzC to graphene using nudge elastic band method,
generalized for solid state calculations. The reaction pathway shows the
formation of carbyne as the intermediate state. Such a pathway is seen to
exhibit two transitions states with reaction barriers of 0.21 eV/atom from ZzC
to carbyne, and of 1.19 eV/atom from graphene to carbyne. Although ZzC is
stable, upon hydrogenation it dissociates and prefers the carbyne-like
structure by forming chains of polyacetylene.
