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The ability to design new materials with a desired set of properties is crucial to the development of new technology. The design of silicon and lithium-ion based materials are well known examples which led to the proliferation of consumer hand-held devices today. However, materials discovery has historically proceeded via trial and error, with a mixture of serendipity and intuition being the most fruitful path. For example, all major classes of superconductors--from elemental mercury in 1911, to the heavy fermions, cuprates and most recently, the iron-based superconductors--have been discovered by chance~\cite{Greene_2012}.  The dream of materials design is to leverage leverage, rather than ignore,  our theories of electronic structure, rather than ignoring them, structure  and combine it them  with our increasing computational ability to discover new materials. Beyond its technological implications, the challenge of materials design is also one of great intellectual depth. In principle, we know the fundamental equation needed to model the behavior of a material: it is the Schr\"odinger equation, equation  describing electrons moving in the potential of a periodic lattice, mutually interacting via the Coulomb repulsion. Solving this equation is another matter. In a sense, we We can  distinguish classes of materials by how well we can solve its corresponding Schr\"odinger equation. equation in practice.  For weakly-correlated weakly correlated  materials, which encompass simple metals, insulators and semiconductors,  we have a well-developed theory of their excitation spectra, namely spectra called  Fermi liquid theory, and practical tools theory. Additionally, we have a theoretical framework which naturally lends itself to computational implementations  for modeling their properties. properties: density functional theory (DFT). 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.  These materials encompass 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.   % and most recently, hydrogen sulfide in late 2014--have been discovered by chance.  It starts with the 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 of the set of self-consistent 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} 
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\sum_{\vec{k}j} |\phi_{\vec{k}j}(\vec{r})|^2f(\epsilon_{\vec{k}j}) = \rho(\vec{r})  \label{KS2}  \end{equation}  reproduces the density of the solid. It is useful to divide the Kohn-Sham potential into several parts: $ V_{KS} = V_{Hartree}+V_{cryst} +V_{xc}$, where one lumps into $V_{xc}$ exchange and correlation effects beyond Hartree. The eigenvalues $\epsilon_{\vec{k}j} $ of the solution of the self-consistent set of Eq.~\ref{Kohn-Sham} and~\ref{KS2} are not to be interpreted as excitation energies. Instead the excitation spectra should be extracted from the poles of the one particle Green's function: \begin{equation}  G\left( \omega \right) = \frac{1}{ \left[ \omega+\nabla^2+\mu-V_{Hartree}-V_{cryst} \right] - \Sigma \left( \omega \right) }. \label{eq:gwk} \end{equation}  Here $\mu $ is the chemical potential and we have singled out in Eq.~\ref{eq:gwk} the Hartree potential expressed in terms of the exact density and the crystal potential, and lumped the rest of the effects of the correlation in the self energy operator which depends on frequency as well as on two space variables. In chemistry, a quantum mechanical system is strongly correlated when $\Sigma( i \omega) - \Sigma_{HF} $ is large at  small energies. Here $\Sigma_{HF} $ is the self energy computed in the Hartree Fock approximation. At infinite frequency,  $\Sigma $ is given by the Hartree Fock graph evaluated with the exact Greens function, hence the Hartree Fock approximation is not exact even at infinite frequency, but it is a good starting point for the treatment of atoms and molecules. Solid state physicists adopt a very different definition of strong correlations. Here, a good reference system is the Kohn-Sham Greens function evaluated in some implementation of the density functional theory such as the LDA. Hence, for condensed matter scientists, by definition, a strongly correlated material is one where $\Sigma - V_\text{xc} $ is large at low frequencies. Strongly correlated materials, are those for which this is not the case, a famous example are materials such as La2CuO4 which are predicted to be metals in LDA but which are experimentally antiferromagnetic Mott insulators.  In quantum chemistry~\cite{Mori_S_nchez_2008}, there is a classification of the errors introduced by the use of approximate density functionals, as being of two types, static correlation and dynamic correlation\cite{Yang_2012}. Similar ideas, also appear in the solid state context, but the nomenclature is exchanged. A \emph{static} self energy (i.e. a self energy which varies weakly with frequency at low energies) corresponds to the concept of dynamical correlations.  For weakly correlated electron systems, the tools for predicting the properties of solids have advanced to the point that one can contenplate contemplate  materials design using these tools and their extensions. [ Materials Project AFLOW, what else ] , and these methods are being currently used to predict new materials, as for example in Feenie 2008, Gautier 2015 and Fredeman 2011. A clear example that theoretical approaches in the field of weakly correlated electron materials is coming of age, is the recent prediction of superconductivity in HS3 under pressure, which was recently found to superconduct near 200 K, the highest temperature superconuctor superconductor  discovered so far. Strongly-correlated compounds have many unusual properties. For example, there are very sensitive to external perturbation, which makes them technologically useful. Small changes in pressure, temperature or chemical doping often drives large changes in electronic or structural behavior. For example, changing the temperature by only several degrees Kelvin can drive a transition between a metallic and insulating state, behavior not observed in weakly-correlated compounds. In addition to metal-insulator transitions, these compounds display unusual magnetic properties, high-temperature superconductivity and strange-metal behavior.  % TODO: Define the problem: What IS design of correlated materials? Describe the intersection of materials design with correlated materials. Also describe the need for large computable databases.  TODO: Define the problem: What IS design of correlated materials? Describe the intersection of materials design with correlated materials. Also describe the need for large computable databases. %  [Chuck: cite examples where LDA+U doesn't quite construct the correct convex hull -- maybe Gutzwiller could do better.] % Materials design also necessarily involves handling and organizing large bodies of data since the process of check => machine learning.