First-principles modeling of localizeddstates with theGW@LDA+Uapproach

Abstract

First-principles modeling of systems with localized d states is currently a great challenge in condensedmatter physics. Density-functional theory in the standard local-density approximation ͑LDA͒ proves to be problematic. This can be partly overcome by including local Hubbard U corrections ͑LDA+ U͒ but itinerant states are still treated on the LDA level. Many-body perturbation theory in the GW approach offers both a quasiparticle perspective ͑appropriate for itinerant states͒ and an exact treatment of exchange ͑appropriate for localized states͒, and is therefore promising for these systems. LDA+ U has previously been viewed as an approximate GW scheme. We present here a derivation that is simpler and more general, starting from the static Coulomb-hole and screened exchange approximation to the GW self-energy. Following our previous work for f-electron systems ͓H. Jiang, R. I. Gomez-Abal, P. Rinke, and M. Scheffler, Phys. Rev. Lett. 102, 126403 ͑2009͔͒ we conduct a systematic investigation of the GW method based on LDA+ U͑GW @LDA+U͒, as implemented in our recently developed all-electron GW code FHI-gap ͑Green's function with augmented plane waves͒ for a series of prototypical d-electron systems: ͑1͒ ScN with empty d states, ͑2͒ ZnS with semicore d states, and ͑3͒ late transition-metal oxides ͑MnO, FeO, CoO, and NiO͒ with partially occupied d states. We show that for ZnS and ScN, the GW band gaps only weakly depend on U but for the other 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.

DFT investigation of the effect of spin-orbit coupling on the NMR shifts in paramagnetic solids

“…In all cases the deviation from the free-electron g-value is found to decrease with increasing U eff (converging to a plateau at high U eff [80]). This is at first sight surprising, as it is known that the Fermi contact shift for the same systems [81] decreases with increasing U eff , due to a reduction of the spin delocalisation from the 3d orbitals to the nucleus of interest -which, in the study in Ref.…”

Accurate screened exchange band structures for the transition metal monoxides MnO, FeO, CoO and NiO

“…While these methods have been used on NiO and MnO, the predictions depend on basis set and underlying approximations [12][13][14][15][16]19,20,25 , which make it difficult to draw a conclusive picture. Despite their wide success, quasiparticle methods are difficult for a variety of reasons: The energy dependence of the electron-electron interaction makes GW calculations computationally costly and finding a proper way to achieve self-consistency is non-trivial.…”

Hubbard-Ucorrected Hamiltonians for non-self-consistent random-phase approximation total-energy calculations: A study of ZnS,TiO2, and NiO

“…One popular method is to supplement the LDA/GGA XC potential with orbital-dependent U terms, designed to more accurately describe the on-site correlation of the d electrons [7]. Such "Hubbard-U " corrections have been found to give an improved description of the properties of TMCs like NiO [7][8][9][10][11].…”