Electronic structure of 3d-transition-metal oxide clusters with partially filled d shells from GW calculations

The GW approximation using atom-centered localized basis sets is an emerging method for studying the excited properties of confined systems. However, G₀W₀@PBE, which is typically used for simple extended systems, fails to accurately describe the electronic excitations in 3d-transition-metal oxide clusters due to dimensionality and correlation effects, and suffers from exhibiting multiple solutions of the quasiparticle equation due to complex self-energy poles. G₀W₀ on top of exact exchange (EXX) is one way to overcome these problems, but the predictions depend on the amount of EXX and the method suffers from convergence errors in open-shell systems (e.g. due to spin contamination). In our previous work on early and late 3d transition metal oxide clusters, we showed that G_nW₀@PBE addresses all the above issues, and thus is an accurate and efficient GW method for these systems. In this work, we investigate various flavors of the GW method (one-shot, partially self-consistent, quasiparticle self-consistent) with different starting points for 3d transition metal oxide clusters, VO^-, CrO^-, MnO^-, FeO^-, CoO^-, and NiO^-, which display a number of high multiplicity states and exhibit moderate electronic correlation.