Ab initio GW quasiparticle energies of small sodium clusters by an all-electron mixed-basis approach

A state-of-the-art GW calculation is carried out for small sodium clusters, Na₂, Na₄, Na₆, and Na₈. The quasiparticle energies are evaluated by employing an ab initio GW code based on an all-electron mixed-basis approach, which uses both plane waves and atomic orbitals as basis functions. The calculated ionization potential and the electron affinity are in excellent agreement with available experimental data. The exchange and correlation parts to the electron self-energy within the GW approximation are presented from the viewpoint of their size dependence. In addition, the effect of the off-diagonal elements of the self-energy corrections to the local-density-approximation exchange-correlation potential is discussed. Na₂ and Na₈ have a larger energy gap than Na₄ and Na₆, consistent with the fact that they are magic number clusters.