All-electron $GW$ calculations beginning with the local density approximation of the density functional theory are carried out for both small gallium arsenide clusters and gallium arsenide crystal in a consistent way by means of the all-electron mixed basis approach, in which both plane waves and atomic orbitals are used as a basis set. This approach has the merit of expressing both core electron states and empty free-electron-like states accurately with a rather small number of basis functions. The present all-electron $GW$ method enables us to treat both clusters and crystal without difficulty. First, we determined the most stable structures of gallium arsenide clusters, ${\mathrm{Ga}}_n{\mathrm{As}}_n$ with $n=2–4$. For these clusters, since the structural change in the ionization process is not so large compared to silicon or germanium clusters, there is no significant difference in the vertical and adiabatic electron affinities. For both clusters and crystal, our one-shot $GW$ results for quasiparticle energy spectra agree fairly well with available experimental photoemission and inverse photoemission data. The present results include the semirelativistic effect.

• Received 2 April 2007

DOI:https://doi.org/10.1103/PhysRevB.76.075325