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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 intuition-guided serendipity being the most fruitful path. For example, all major classes of superconductors--from elemental mercury in 1911, to the heavy fermions, cuprates, iron-based superonductors and most recently, hydrogen sulfide in late 2014--have been discovered by chance.  The dream of materials design is to leverage our theories of electronic structure, rather than ignoring them, combined 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. matter, and we distinguish to classes of materials in this respect. For weakly correlated electron materials, we have a well develop theory of the excitation spectra, the Fermi liquid theory, and practical tools for their computation.  Fora 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 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. 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}. [ PROBLEM REFERENCES AND CONTEXT ISINCOMPLETE HERE ]  It starts with  the Kohn-Sham formulation~\cite{kohn_sham} of density functional theory.