The GW approximation is today widely used in electronic structure calculations in order to obtain quasiparticle energies for solids. However, despite its success to improve the description of the bandstructure, e.g. significantly correcting the bandgap in semiconductors and insulators over LDA, it has deciencies which need to be addressed. One example is that although GW improves the position of localized semicore states as compared to LDA, it still places the states too high in energy when comparing to experiments. Since HF, which lacks screening, instead predicts the energies to lie below the experimental values, GW seems to have an issue with overscreening.

A possible origin of this overscreening is self-screening, which GW is known to suffer from. It is readily seen in the hydrogen atom where GW predicts too high quasiparticle energies, due to a non-zero contribution from the correlation part of the self-energy [1]. As there is only one electron present, there should be no screening when removing the electron, and hence no correlation self-energy, indicating that the electron unphysically screens itself.

A scheme was proposed in 2012 by Aryasetiawan et. al. [2] to improve GW by going beyond RPA and remove the self-screening error. This is done by altering the polarization propagator used in RPA to calculate a unique screened interaction for each orbital, with the self-screening removed. I will present the theory, and model calculations on Hubbard dimers, showing improved agreement for the self-screening corrected results with the exact cases in some parameter ranges. Also some early results of ab initio calculations for semicore states in semiconductors using a version of the GW code SPEX, which has been modified to include the self-screening correction, will be presented.

[1] Nelson, W., Bokes, P., Rinke, P, Godby R. W., Self-interaction in Green's function theory of the hydrogen atom. Phys. Rev. A 75 032505 (2007).
[2] Aryasetiawan, F., Sakuma, R, Karlsson, K., GW approximation with self-screening correction. Phys. Rev. B 85 035106 (2012).