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 isa 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=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 Angstrom for graphyne and 9.44 Angstrom for graphdiyne. These materials are semiconductors with moderate band gaps. The band gap occurs at the M point or 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. [S0163-1829(98)07939-9].