Optimized geometries and electronic structures of graphyne and its family

TLDR

These carbon allotropes consist of hexagons connected by linear carbon chains. The optimized geometries and electronic band structures of graphyne, graphdiyne, graphyne‑3, and graphyne‑4 were calculated using a full‑potential linear combination of atomic orbitals method within the local‑density approximation. The calculations show that graphyne and graphdiyne have slightly longer hexagon bonds, binding energies of 7.95 eV/atom and 7.78 eV/atom, lattice constants of 6.86 Å and 9.44 Å, are semiconductors with moderate band gaps located at the M or Γ point depending on the number of acetylenic linkages, and possess very small effective masses for both conduction and valence bands.

Abstract

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.