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Finding an accurate ab initio approach for calculating the electronicproperties of transition metal oxides has been a problem for several decades.In this paper, we investigate the electronic structure of the transition metalmonoxides MnO, CoO, and NiO in their undistorted rock-salt structure within afully iterated quasiparticle self-consistent GW (QPscGW) scheme. We study theconvergence of the QPscGW method, i.e., how the quasiparticle energyeigenvalues and wavefunctions converge as a function of the QPscGW iterations,and we compare the converged outputs obtained from different startingwavefunctions. We find that the convergence is slow and that a one-shotG$_0$W$_0$ calculation does not significantly improve the initial eigenvaluesand states. It is important to notice that in some cases the "path" toconvergence may go through energy band reordering which cannot be captured bythe simple initial unperturbed Hamiltonian. When we reach a fully iteratedsolution, the converged density of states, band-gaps and magnetic moments ofthese oxides are found to be only weakly dependent on the choice of thestarting wavefunctions and in reasonably good agreement with the experiment.Finally, this approach provides a clear picture of the interplay between thevarious orbitals near the Fermi level of these simple transition metalmonoxides. The results of these accurate {\it ab initio} calculations canprovide input for models aiming at describing the low energy physics in thesematerials.

Convergence of quasiparticle self-consistent GW calculations of transition metal monoxides