Density functional theory (DFT) is in principle an exact method to describe any many-electron systm, from a single atom or a molecule to a complex crystalline solid. The accuracy of the method hinges on reliable approximations to the unknown exchange-correlation (xc) potential, which is responsible to describe all the quantum interactions between the electrons in the system. The most popular approximations usually lack features of the exact xc potential that are important for an accurate prediction of the fundamental gap and the distribution of charge in complex systems. Two principal features in this regard are the spatially uniform shift in the potential, as the number of electrons infinitesimally surpasses an integer, and the spatial steps that form, e.g., between the atoms of stretched molecules. Although both aforementioned concepts are well-known, the exact relationship between them remained unclear. In this talk, we establish this relationship and introduce a new concept: the charge-transfer derivative discontinuity, Δ_CT. By numerically solving the many-electron Schrödinger equation, we extract the exact Kohn-Sham potential and directly observe its features, particularly the spatial interatomic steps. For the first time, spatial steps in the exact xc potential of a full configuration-interaction (FCI) calculation of a molecule are presented in three dimensions [1].

[1] M.J.P. Hodgson, E. Kraisler, A. Schild, E.K.U. Gross, "How Interatomic Steps in the Exact Kohn–Sham Potential Relate to Derivative Discontinuities of the Energy", J. Phys. Chem. Lett. 8, 5974 (2017)