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GW calculations with fully self-consistent G and W -- based on the iterativesolution of the Dyson equation -- provide an approach for consistentlydescribing ground and excited states on the same quantum mechanical level. Weshow that for the systems considered here self-consistent GW reaches the samefinal Green function regardless of the initial reference state.Self-consistency systematically improves ionization energies and total energiesof closed shell systems compared to G_0W_0 based on Hartree-Fock and(semi)local density-functional theory. These improvements also translate to theelectron density as exemplified by an improved description of dipole momentsand permit us to assess the quality of ground state properties such as bondlengths and vibrational frequencies.

Unified description of ground and excited states of finite systems: the self-consistent GW approach