Ab InitioCalculations of the Quasiparticle and Absorption Spectra of Clusters: The Sodium Tetramer

We report the first ab initio quasiparticle calculation in a real cluster ${\mathrm{Na}}_4$ within Hedin's $\mathrm{GW}$ approximation for the valence electron self-energy. Our approach avoids the summations over empty states, and also eliminates the problem of residual interactions between the periodic images. Self-energy corrections open the local density approximation gap by more than 2 eV; finite-size effects on screening are shown to play an important role. The absorption spectrum calculated by including excitonic effects using our ab initio screened interaction gives a good account of the experimental photodepletion data.