  A two-dimensional carbon allotrope, Stone-Wales graphene, is identified in
stochastic group and graph constrained searches and systematically investigated
by first-principles calculations. Stone-Wales graphene consists of
well-arranged Stone-Wales defects, and it can be constructed through a
90$^\circ$ bond-rotation in a $\sqrt{8}$$\times$$\sqrt{8}$ super-cell of
graphene. Its calculated energy relative to graphene, +149 meV/atom, makes it
more stable than the most competitive previously suggested graphene allotropes.
We find that Stone-Wales graphene based on a $\sqrt{8}$ super-cell is more
stable than those based on $\sqrt{9} \times \sqrt{9}$, $\sqrt{12} \times
\sqrt{12}$ and $\sqrt{13} \times \sqrt{13}$ super-cells, and is a "magic size"
that can be further understood through a simple "energy splitting and
inversion" model. The calculated vibrational properties and molecular dynamics
of SW-graphene confirm that it is dynamically stable. The electronic structure
shows SW-graphene is a semimetal with distorted, strongly anisotropic Dirac
cones.
