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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.  For weakly correlated materials, DFT has become the underlying workhorse of the scientific community. Extensive benchmarks of software implementations~\cite{Lejaeghere_2016} have shown that DFT reliably produces the total energy of a given configuration of atoms, enablingstability  comparisons of stability  between different chemical polymorphs. The maturity of DFT, combined with growing databases searchable repositories  of experimental data  (ICDD, ICSD, NIMS) and data, has fostered the growth of databases of  computed data materials properties  (Materials Project, AFLOWlib, NIMS), has allowed the NIMS). The  field of weakly correlated systems 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 high  pressure near 190~K~\cite{Duan_2014}. Indeed, Subsequently,  hydrogen sulfide wasrecently  observed to superconduct near 200~K, the highest temperature superconductor discovered so far~\cite{Drozdov_2015}. In order to understand contrast, materials design for strongly correlated systems is less mature, stemming from  the challenges particular to correlations fundamental challenge of understanding the physics of electron correlations. Correlated systems exhibit novel phenomena not observed  in weakly-correlated materials: metal-insulator transitions, magnetic order and unconventional superconductivity are salient examples. While designing and optimizing  materials design, we need to better define what with these properties would advance both technology and our understanding of the underlying physics, in practice  we mean by lack  a correlated material, which we do in Section~\ref{sec:correlations}. tool akin to DFT capable of reliably modeling properties and scaling up to the thousands of calculations necessary.  % TODO: Define In this article, we seek to summarize outstanding challenges in  the problem: What IS design of area, especially as it pertains to  correlated materials? Describe the intersection materials, and propose strategies to solve them. We begin by providing a practical definition  of materials design with correlated materials. Also describe the need for large computable databases. correlations, followed  % Materials design also necessarily involves handling and organizing large bodies of data since In order to understand  the process of check => machine learning. challenges particular to correlations in materials design, we need to better define what we mean by a correlated material, which we do in Sec.~\ref{sec:correlations}.  Strongly-correlated compounds exhibit unique properties. In particular, they are sensitive to external perturbations, which naturally leads to technological applications. Small changes in pressure, temperature or % To be precise, we can phrase the question of materials design concretely as follows: given a  chemical doping often drives large changes in electronic or structural behavior, making them ideal for sensing applications. For example, changing system, determine  the temperature crystal structures and electronic properties of all stable compounds formed  by only several degrees Kelvin can drive the constituent elements. To give  a transition between concrete example, if the chemical system of interest is Li-Fe-P-O, determine all binaries, ternaries and quaternaries and compute their properties (turns out LiFePO$_4$ is  a metallic promising battery material). This problem involves coordinating many moving pieces, including structural prediction, determination of thermodynamic stability against competing phases  and insulating state, behavior not observed in weakly-correlated compounds. computation of electronic properties.  In addition this article, we seek  to metal-insulator transitions, these compounds display unusual magnetic properties, high-temperature superconductivity summarize outstanding challenges in the area, especially as it pertains to correlated materials,  and strange-metal behavior. propose strategies to solve them.  To be precise, we can phrase % TODO: Define  the question of materials problem: What IS  designconcretely as follows: given a chemical system, determine the crystal structures and electronic properties  of all stable compounds formed by the constituent elements. To give a concrete example, if correlated materials? Describe  the chemical system of interest is Li-Fe-P-O, determine all binaries, ternaries and quaternaries and compute their properties (turns out LiFePO$_4$ is a promising battery material). This problem involves coordinating many moving pieces, including structural prediction, determination intersection  of thermodynamic stability against competing phases and computation of electronic properties. In this article, we seek to summarize outstanding challenges in the area, especially as it pertains to materials design with  correlated materials, and propose strategies to solve them. materials. Also describe the need for large computable databases.