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For weakly-correlated compounds, encompassing simple metals, insulators and semiconductors, implementations of density functional theory (DFT) performs extremely well. DFT is a workhorse of the materials science community, providing efficient and accurate computations of the total energy and distribution of electrons of a compound, requiring only the coordinates of the atoms in its crystal lattice as input. From the total energy, one can obtain lattice constants, equations of state and the spectrum of lattice vibrations. Furthermore, one can obtain electronic properties such as band gaps, electric polarization and topological numbers, which are by no means trivial for these "simple" compounds.   It starts with  the Kohn-Sham formulation~\cite{kohn_sham} formulation~\cite{Kohn_1965}  of density functional theory. It states the existence of a potential $V_{KS}(r)$, which is itself a functional   of the density. One should write $V_{KS}(\vec{r})[\{ \rho(\vec{r}') \}]$ to indicate this dependence, but  we omit this in the following. The exact (but unknown) functional is such that the solution