First-principle prediction of the existence of C64-graphyne and its nitrogen and boron substitutions

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.