GW reduced density matrix from iterated linearized Dyson equation

Iterating the Dyson equation with the static part of the self-energy leads to a concise and possibly improved expression of the one-body reduced density matrix from any self-energy approximation. Here, we apply the procedure to Hedin's GW approximation. The non-iterated GW-based density matrix was already known to yield accurate density matrices for molecular systems. We show that the Dyson-equation-based procedure is equivalent to the so-called variational Z-vector approach applied to the random-phase approximation energy functional, but only in the case of a Hartree-Fock mean-field starting point. When a generalized Kohn-Sham scheme is employed instead, the two approaches differ. By comparing the density matrix for a benchmark set of 34 small molecules to coupled-cluster reference values, we conclude that the iterated Dyson equation indeed produces improved density matrices for molecular systems. Interestingly, we observe that the excitation rank of the reference coupled-cluster matters much and that the inclusion of triple excitations quantitatively changes the conclusions of the benchmark compared to single and double excitations coupled-cluster.