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The dream of materials design is to leverage our theories of electronic structure, rather than ignoring them, and combine them with our increasing computational and storage abilities to discover new materials. Beyond its technological implications, the challenge of materials design is also one of great intellectual depth. In principle, we know all the fundamental equations needed to model the behavior of electrons and nuclei. Solving these equations is another matter.  For a large class of materials called 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 the charge  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, as a byproduct of these calculations  one can obtain estimates for  electronic properties such as band energy  gaps, electric polarization and topological numbers, which are by no means trivial for these "simple" compounds. Using DFT, several groups have been constructing databases spanning large swaths of the space of known compounds, containing these computed properties which can then be data mined for specific properties. Successes include the prediction of multiferroics~\cite{Fennie_2008}, intermetallic semiconductors\cite{Gautier_2015} and even heavy fermion materials\cite{Fredeman_2011}. It starts with  the The  Kohn-Sham formulation~\cite{kohn_sham} of density functional theory.   It theory  states the existence of a potential $V_{KS}(r)$, which is itself a functional of the density. One density and which added a single particle Hamiltonian can reproduce the exact density of a compound by solving   %One  should write $V_{KS}(\vec{r})[\{ \rho(\vec{r}') \}]$ to indicate this dependence, but we %we  omit this in the following. The exact (but unknown) functional is such that the solution of the set of a  self-consistent equations, equations:  \begin{equation}  \left[-\nabla^{2}+V_{KS}\left(\vec{r}\right)\right]\psi_{\vec{k}j}\left(\vec{r}\right)=\epsilon_{\vec{k}j}\psi_{\vec{k}j}\left(\vec{r}\right).  \label{Kohn-Sham}