This is a review of our papers, PRB 78, 125116 (2008) and PRB 79, 241312(R) (2009), and a report on further developments. Our method is based on Slater’s transition state idea and Janak’s theorem. With those tools we were able to define a self-energy, not the self-energy of GW but that of elementary Electrostatic, and find a way to calculate it for the electronic elementary excitations in a crystal. Our point of view is that the elementary excitations are in localized wavefunctions, not Bloch functions, and that is why they have sizable self-energies. The inclusion of the selfenergy is made by means of a “self-energy potential” defined in the atoms of the crystal. Thus the procedure is very simple and fast. The new band gap results are as good as, or perhaps even better than, the published results. Originally we adapted our method to the codes VASP and SIESTA (for programs and instructions see www.gf1901.net). Lately we adapted the method to WIEN2k, with which we calculated CdTe, CdSe, MnO, and NiO. In the case of the last oxide, we diverged

from Professor Blaha’s paper [PRL 102, 226401 (2009)], with whom we would welcome a friendly discussion.