Assessment of the Linearized GW Density Matrix for Molecules

The GW approximation is well-known for the calculation of high-quality ionization potentials and electron affinities in solids and molecules. Recently, it has been identified that the density matrix that is obtained from the contraction of the GW Green's function allows one to include Feynman diagrams that are significant for the ionization potentials. However, the Green's function contains much more information than the mere quasi-particle energies. Here, we test and assess the quality of this so-called linearized GW density matrix for several molecular properties. First of all, we extend the original formulation to perform the linearization starting from any self-consistent mean-field approximation, and not only from Hartree-Fock. We then demonstrate the reliability and the stability of the linearized GW density matrix to evaluate the total energy out of a non-self consistent GW calculation. Based on a comprehensive benchmark of 34 molecules, we compare the quality of the electronic density, Hartree energy, exchange energy, and the Fock operator expectation values against other well-established techniques. In particular, we show that the obtained linearized GW densities markedly differ from those calculated within the widespread quasi-particle self-consistent GW approximation.