  The interaction between substitutional nitrogen atoms in graphene is studied
by performing first principles calculations. The nearest neighbor interaction
between nitrogen dopants is highly repulsive because of the strong
electrostatic repulsion between nitrogen atoms, which prevents the full phase
separation in nitrogen doped graphene. Interestingly, there are two relatively
stable nitrogen-nitrogen pairs due to the anisotropy charge redistribution
induced by nitrogen doping. We reveal two stable semiconducting ordered N doped
graphene structures C3N and C12N through the cluster expansion technique and
particle swarm optimization method. In particular, C12N has a direct band gap
of 0.98 eV. The heterojunctions between C12N and graphene nanoribbons might be
promising organic solar cells.
