correction with orbital dependence in LSDA+U and this implies that one should include dynamical correlation effects.

GW approximation was applied and the resultant band gap still remains very small (0.2). [@re:NiO-GW-Ferdi; @re:NiO-GW-Nohara] Quasiparticle self-consistent GW (QPscGW) approximation [@re:NiO-GW-Kotani] was also applied and a system becomes charge-transfer insulator. However, the resultant band gap is overestimated (4.8) and the bonding states of nickel ${\mbox{e}_{g}}$ bands are observed at around $6~{\mbox{eV}}$ below the Fermi energy. These fact implies that the dynamical electron correlation should play a more crucial role in NiO than treated by RPA in GW approximation.

LDA+DMFT was applied to paramagnetic NiO [@re:Kunes-NiO-DMFT; @re:Ren-NiO-DMFT] and the resultant band gap is in good agreement with experimentally observed XPS result. [@re:NiO-expt] and the system becomes charge-transfer insulator. However, the top of valence bands mainly consists of nickel 3d bands, while the cluster-model CI calculation [@re:NiO-fujimori2; @re:NiO-vanElp] and oxygen x-ray absorption of Li$_x$Ni$_{1-x}$O [@re:NiO-Kuiper-expt] show that the top of valence bands is mainly based on oxygen 2p bands. This difference comes from that these LDA+DMFT calculations use projected effective Hamiltonian constructed by Wannier-like functions with fixing the hybridization mixing. Moreover, no calculation has been carried out for antiferromagnetic NiO by LDA+DMFT.

The target of 