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\section{Introduction}  \label{sec:intro}  The ability to design new materials witha  desiredset 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 ability to design new materials with desired properties is a key challenge.  % Its solution would have far-reaching implications in both fundamental science 
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In practice, we can classify materials by how well we can solve their corresponding Schr\"odinger equation. For the class of compounds encompassing simple metals, insulators and semiconductors, termed weakly correlated materials, we have a well-developed theory of their excitation spectra called Fermi liquid theory. From a practical viewpoint, the theoretical framework of density functional theory (DFT) naturally lends itself to computational implementations for modeling properties. Materials which are not well-described by DFT are colloquially termed strongly correlated materials.  % The underlying workhorse for all materials design is a box which takes as input  % the coordinates of the atoms within a unit cell and produces the total energy  % of the configuration. For materials without partially-filled $d$ or $f$ shells,  % density functional theory performs quite well, providing total energies that  % are accurate to within 50meV. For weakly correlated materials, DFT has become the underlying workhorse of the scientific community. Crucially, Extensive benchmarks of software implementations~\cite{Lejaeghere_2016} have shown that  DFT provides reliably produces  the total energy of a given configuration of atoms, enabling the  Combined with the development of algorithms for stability comparisons between different chemical polymorphs.  The maturity of its various software implementations means researchers can routinely know only the approximate atomic coordinates of a new compound, and compute its optimized structure and myriad of electronic properties.  Combined DFT, combined  with growing databases of experimental [ICSD] (ICDD, ICSD, NIMS)  and computed data [MatProj, AFLOW, NIMS], (Materials Project, AFLOWlib, NIMS), has allowed  the field of weakly correlated systems has to  advanced to the point where one can successfully design materials~\cite{Fennie_2008, Gautier_2015, Fredeman_2011}. A clear example that theoretical approaches are coming of age is the recent prediction of superconductivity in H$_3$S under pressure at XXX~K. near 190~K~\cite{Duan_2014}.  Indeed, hydrogen sulfide was recently observed to superconduct near 200 K, 200~K,  the highest temperature superconductor discovered so far. far~\cite{Drozdov_2015}.  In order to understand the challenges particular to correlations in materials design, we need to better define what we mean by a correlated material, which we do in Section~\ref{sec:correlations}.