  By using of the first-principles calculations based on density functional
theory, a novel monolayer planar structure named C64-graphyne is predicted.
Tetratomic and hexatomic rings, as well as C-C triple bonds exist in this new
stable structure with the lattice parameter of 9.291 {\AA}. The carbon
hexatomic ring in C64-graphyne contains two quite distinct C-C bonds, which is
known as cyclohexatriene. Its electronic band structures show a semiconductor
nature with a narrow direct band gap of 0.35 eV. Interestingly, by substituting
one nitrogen atom for a carbon atom in the hexatomic ring or a sp hybridized
carbon atom on the carbon chain of C64-graphyne, two stable planar structures
are obtained. Such doping with nitrogen atom induced metal properties in this
monolayer structure. Further investigation shows that the alternating
substitution of boron and nitrogen atoms for all carbon atoms in C64-graphyne
also induced a new stable structure, the (BN)64 structure. The electronic
studies proved its insulator property with the band gap of 4.08 eV.
