Towards a unified description of ground and excited state properties: \textit{GW} vs RPA and beyond

Fabio Caruso, Patrick Rinke, Xinguo Ren +2 more

Sohrab Ismail‐Beigi

Fabio Caruso, Patrick Rinke, Xinguo Ren +2 more

Fully self-consistent GW (sc-GW) – based on the iterative solution of Dyson’s equation – incorporates many-body correlation effects in the electronic ground-state, providing a recipe to consistently describe ground- and excited-states on an equal footing. We have implemented sc-GW in the localized basis all-electron code FHIaims [1]. We show that, for finite systems, the ground-state properties as well as the excitation spectrum of the sc-GW Green’s function are unique and are not affected by different initialization of the sc-GW loop, curing the pathological dependence on the starting point of one-shot GW (G0W0). In addition, self-consistency systematically improves ionization energies and Galitskii-Migdal total energies of closed shell systems compared to G0W0 based on Hartree-Fock and density-functional theory in local and semilocal approximations. Since our implementation is based on interacting Green’s functions (unlike all G0W0 implementations) it is also a first step towards going beyond the GW approach.

P.J. Ellis

Assa Auerbach

Thomas Olsen, Kristian Sommer Thygesen

We investigate various approximations to the correlation energy of a H2 molecule in the dissociation limit, where the ground state is poorly described by a single Slater determinant. The correlation energies are derived from the density response function and it is shown that response functions derived from Hedin's equations (Random Phase Approximation (RPA), Time-dependent Hartree-Fock (TDHF), Bethe-Salpeter equation (BSE), and Time-Dependent GW) all reproduce the correct dissociation limit. We also show that the BSE improves the correlation energies obtained within RPA and TDHF significantly for intermediate binding distances. A Hubbard model for the dimer allows us to obtain exact analytical results for the various approximations, which is readily compared with the exact diagonalization of the model. Moreover, the model is shown to reproduce all the qualitative results from the ab initio calculations and confirms that BSE greatly improves the RPA and TDHF results despite the fact that the BSE excitation spectrum breaks down in the dissociation limit. In contrast, second order screened exchange gives a poor description of the dissociation limit, which can be attributed to the fact that it cannot be derived from an irreducible response function.