Reduced density-matrix from the GW approximation

The GW approximation is well known for the calculation of high-quality ionization potentials and electron affinities in solids and molecules. However, the Green's function contains much more information than the mere quasiparticle energies. In particular, the instantaneous Green's function G(r, r', t-t'=0^-) is nothing else but the celebrated one-body reduced density-matrix. The density-matrix gives a direct access to many physical observables: electronic density, kinetic, Hartree and exchange energies, etc.

In this talk, we will benchmark the quality of this approach for the electronic density of molecules [1,2]. We will also show how the GW reduced density-matrix readily contains the correlated part of the kinetic energy and produces one-shot total energies that well approximate the fully self-consistent GW total energies [3]. Finally, we will address the extension of this approximation to solids [4].