deletions | additions       diff --git a/introduction.tex b/introduction.tex  index 0b8e52a..9b71e54 100644  --- a/introduction.tex  +++ b/introduction.tex 
...
\section{Introduction}  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 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, iron-based superonductors cuprates  and most recently, hydrogen sulfide in late 2014--have the iron-based superconductors--have  been discovered by chance. chance~\cite{Greene_2012}.  The dream of materials design is to leverage our theories of electronic structure, rather than ignoring them, combined and combine it  with our increasing computational and storage abilities ability  to discover new materials. Beyond its technological implications, the challenge of materials design is also one of great intellectual depth. In principle, we knowall  the fundamental equations equation  needed to model the behavior of a material: it is the Schr\"odinger equation, describing  electrons and nuclei. moving in the potential of a periodic lattice, mutually interacting via the Coulomb repulsion.  Solving these equations this equation  is another matter, matter.  Frontier: intersection of correlated theory and materials design.  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. and most recently, hydrogen sulfide in late 2014--have been discovered by chance.  For 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.  
...
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 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_{KS} $ is large at low frequencies. Strongly correlated materials, are those for which this is not the case, a famous example are materials such as LaCuO4 La2CuO4  which are predicted to be metals in LDA but which are experimentally antiferromagnetic Mott insulators. In quantum chemistry   \cite{Mori_S_nchez_2008} 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 {\it static } \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 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 discovered so far.