Electronic structure of three-dimensional graphyne

Graphyne is a hypothetical carbon allotrope with a layered structure. We calculated the optimized geometries and electronic structures of three-dimensional graphyne in some possible stacking arrangements from symmetry considerations. The optimized lattice constants and the binding energy of graphyne are given in comparison with graphite. The binding energy of graphyne is about 90% of that of graphite, and graphyne will be stable when it is synthesized. The electronic structures are classified into two types, metallic and semiconducting, according to the stacking arrangements. The most stable graphyne is expected to be a semiconductor with a moderate band gap.