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