¹ College of Chemistry, Peking University, Beijing, China

²Fritz-Haber-Institut der MPG, Berlin, Germany

The accurate first-principles description of d- and f-electron systems is currently regarded as one of the great challenges in condensed matter physics. These systems are characterized by the simultaneous presence of itinerant (delocalized) and highly localized states and interactions between them. Density-functional theory (DFT) in the local-density or generalized gradient approximation (LDA or GGA, respectively) proves to be inadequate for d/f-electron systems due to the severe delocalization (or self-interaction) error, leading to qualitatively incorrect metallic ground states for many wide-gap insulating systems. This difficulty can be partly overcome by introducing a local Hubbard-like correction (LDA+U), but itinerant states are still treated on the LDA level. Many-body perturbation theory in the GW approach offers both a quasi-particle perspective (appropriate for itinerant states) and an exact treatment of exchange (appropriate for localized states). The combination of GW with LDA+U (GW@LDA+U) is therefore promising for d/f-electron systems.

In this talk, we first apply the GW@LDA+U method to lanthanide oxides (CeO₂ and Ln₂O₃ (Ln=lanthanide series)) [1]. These compounds have important technological applications, in particular in catalysis and microelectronics. Good agreement between the GW density of states and experimental spectra is observed for CeO₂ and Ce₂O₃. Unlike the LDA+U method GW@LDA+U exhibits only a weak dependence on U in a physically meaningful range of U values. Our GW@LDA+U calculations provide a quantitative and qualitative understanding of the general trend observed for the band gaps of the Ln₂O₃ series in terms of the relative positions of the occupied and unoccupied f-states and reproduce the characteristic features of the series.

We further investigate the GW@LDA+U method in a set of prototypical d-electron systems including 1) ZnS with semicore d-states, 2) ScN and TiO₂ with empty d-states and 3) late transition metal oxides (MnO, FeO, CoO and NiO) with partially occupied d-states. It is found that for ZnS, ScN and TiO₂, the GW _ band gap only weakly depends on U, but for the late transition metal oxides the dependence on U is as strong as in LDA+U. These different trends can be understood in terms of changes in the hybridization and screening.

Our work demonstrates that GW@LDA+U with “physical” values of U provides a balanced and accurate description of both localized and itinerant states in d/f-electron systems.

[1] H. Jiang, R. I. Gomez-Abal, P. Rinke and M. Scheffler, Phys. Rev. Lett. 102, 126403 (2009).