  Using first-principles method, we investigate the energetic stability,
dynamic stability and electronic properties of two three-dimensional (3D)
all-sp2 carbon allotropes, sp2-diamond and cubic-graphite. The cubic-graphite
was predicted by Michael O'Keeffe in 1992 (Phys. Rev. Lett., 68, 15, 1992.)
possessing space group of Pn-3m (224), whereas the sp2-diamond with the space
group Fd-3m (227) same as that of diamond has not been reported before. Our
results indicate that sp2-diamond is more stable than previously proposed
K4-carbon and T-carbon, and cubic-graphite is even more stable than superhard
M-carbon, W-carbon and Z-carbon.The calculations on vibrational properties show
that both structures are dynamically stable. Interestingly, both sp2-diamond
and cubic-graphite behave as semiconductors which are contrary to previously
proposed all-sp2 carbon allotropes. The sp2-diamond is a semiconductor with a
direct band gap of 1.66 eV, and cubic-graphite is an indirect semiconductor
with band gap of 2.89 eV. The very lower densities and entirely sp2 configures
of sp2-diamond and cubic-graphite can be potentially applied in
hydrogen-storage, photocatalysts and molecular sieves.
