Ab-initio calculations of the quasi-particule and absorption spectra of clusters: the sodium tetramer

We report the first ab initio quasiparticle calculation in a real cluster Na-4 within Hedin\textquoterights 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.