Optimized geometries and electronic structures of graphyne and its family

The optimized geometries of carbon allotropes related to graphite, called graphyne, graphdiyne, graphyne-3, and graphyne-4, as well as their electronic band structures were calculated using a full-potential linear combination of atomic orbitals method in the local-density approximation. These carbon allotropes consist of hexagons connected by linear carbon chains. The bond length of a hexagon is a little longer than that of the bond that links a hexagon to the outside carbon. Furthermore, part of the linear carbon chain is composed of acetylenic linkages (---C\ensuremath{\equiv}C---) rather than cumulative linkages (=C=C=). The binding energies are 7.95 eV/atom for graphyne and 7.78 eV/atom for graphdiyne, and the optimized lattice lengths are 6.86 \AA{} for graphyne and 9.44 \AA{} for graphdiyne. These materials are semiconductors with moderate band gaps. The band gap occurs at the M point or \ensuremath{\Gamma} point depending on the number of acetylenic linkages that are contained between the nearest-neighboring hexagons. The effective masses are very small for both conduction and valence bands.