Ab initio calculations of layered compounds consisting of sp$^3$ or sp+sp$^2$ hybridized carbon atoms

The density functional theory method was used to study new layered carbon nanostructures consisting of sp$^3$- and sp+sp$^2$-hybridized atoms. The nanostructures are theoretically built on the basis of graphene 5 – 7 layers. As a result of calculations, it is found that the structures of two diamond-like bilayers and twenty-one graphyne layers are stable. The diamond-like bilayers have a band gap of $\sim$1.8 eV, so their properties should be semiconducting. For fourteen graphyne layers, the band gap is zero and their properties are metallic. Seven graphyne layers have band gaps ranging from 0.05 to 0.2 eV.