We present a method for calculating the self-energy in the $\mathrm{GW}$ approximation that can be applied to systems containing $3d$ and $4f$ electrons. The method is applied to NiO and a gap of $\sim 5.5$ eV is obtained, which is in reasonable agreement with the experimental value of 4.0 eV. The local density O $p$ band is also improved. The high binding energy satellite at 8 eV, however, is not obtained and there is no substantial increase of O $p$ character at the top of he valence band compared to the local density result. Based on our results, we discuss to which extent the $\mathrm{GW}$ approximation is capable of describing highly correlated systems such as NiO.

• Received 31 August 1994

DOI:https://doi.org/10.1103/PhysRevLett.74.3221