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The first and most well-studied step is the calculation of the \emph{electronic structure}, namely, how to go from structure to property (see Table~\ref{tbl:workflow}). Given a crystal structure, we seek to compute electronic properties such as the electron density, gap size, magnetic order and superconducting transition temperature. The computational method used for electronic structure highly depends on the strength of correlations. For weakly correlated systems, DFT is quite successful for understanding structure-property relationships. As the strength of correlations increase, we are forced to adopt more sophisticated methods. For example, in order to accurately predict gap sizes in semiconductors, GW corrections are needed to correct the underestimation of exchange at low frequencies in the DFT self-energy. In strongly correlated materials, the solid often contains atoms with partially-filled $d$ and $f$ shells. The electrons occupying these orbitals behave in an atomic-like fashion, while the remaining electrons form bands. Their interplay poses special challenges for theory, which led to the development of dynamical mean field theory (DMFT). The combination of DFT and DMFT enables accurate calculations of the spectra of correlated materials, for example, in classic Mott compounds like V$_2$O$_3$. We note that LDA+U can be viewed as the static limit of DMFT, which works well for magnetically or orbitally ordered materials. To summarize, the community has developed a hierarchy of tools for electronic structure capable of treating differing correlation strengths. As correlations increase, so does the complexity of the physics, which reflects in the required expertise and computational power for successful modeling in GW and DMFT.  The second step is \emph{structure prediction}: predict the crystal structure given a fixed chemical composition. A successful prediction would take a formula, like Ca$_3$GeO Fe$_2$O$_3$  for example, and return the correct crystal structure (this compound turns out to be an inverse perovskite). Generically, atoms are placed in a unit cell and a chosen algorithm is used to efficiently traverse structure--in this case,  the space of atomic configurations and cell geometries to arrive at composition forms in  the lowest energy structure. This step requires having an accurate method for producing corundum structure, called  the energy of $\alpha$ phase. For  a given configuration of atoms. Notice that we are interested here, not only in the lowest energy structure but also metastable structures, i.e. given C more complete characterization,  we would like seek  to find out that predict  not only carbon the ground state structure,  but nearby local minima as well, termed polymorphs. Again taking Fe$_2$O$_3$ as an example, this composition  also diamond and graphene exist. DFT has been quite successful at providing total energies which enable accurate comparisons of the generated structures. This is certainly true for weakly correlated electron systems, which has enabled for example predictions 50 ne 18-valent ternary semiconductors ( Gautier 2015) [ WE SHOULD ALSO MENTION ZUNGER ]. Surprisingly, DFT works well sometimes even for strongly correlated electron systems. Successes include the prediction of a new compounds forms  in the Ce-Ir-In system~\cite{Fredeman_2011}. Notable failures, include elemental Pu, where non magnetic DFT calculations underestimates spinel structure, found naturally as  the volume of mineral maghemite and termed  the $\delta$ phase by more than 25$\%$ while magnetic calculations predict a large magnetic moment ($ 5 {\mu}_B$ which is not observed experimentally). Notice however, that $\gamma$ phase, as well as cubic $\beta$ and orthorhombic $\epsilon$ phases. Polymorphs generally are formed  in spite of this failure, DFT + orbital polarization can predict the order different temperature and pressure regimes, and modeling these effects add an additional layer  of the structures. complexity.  However, for correlated materials, we argue that extensions taking into account simply enumerating  the effect low-energy local minima at zero temperature can already provide a broader picture  ofcorrelations on the total energy is important for obtaining  the correct ground-state structure for structural diversity of  agiven  composition. The third general procedure for structure prediction involves placing atoms in a unit cell and using a chosen algorithm to efficiently traverse the space of atomic configurations  and final cell geometries to arrive at low energy structures. This step requires having an accurate method for producing the energy of a given configuration of atoms. For weakly-correlated materials, DFT provides accurate energies, enabling successful structural prediction for novel compositions via searches within databases of known structures. This strategy was used to discover 54 new 18-valent ternary semiconductors~\cite{Gautier_2015} as well as two new structures in the Ce-Ir-In system~\cite{Fredeman_2011}. DFT has reached a high degree of stability and scalability, enabling software packages such as USPEX to implement genetic algorithms on top of DFT to successfully predict never before observed structures.  However, there are cases where DFT energies are insufficient for structure prediction: a notable failure is elemental plutonium, were paramagnetic DFT calculations underestimate the volume of the $\delta$ phase by roughly 25\% and magnetic calculations predict a large magnetic moment of 5$\mu_\text{B}$ which is not observed experimentally. Extending DFT by including orbital polarization--a correlation effect--brings the predictions in line with experiment. In general, for correlated materials, we argue that extensions to DFT capturing the effect of correlations on the total energy are important for structure prediction.  The third  step is global stability: \emph{global stability}:  given the lowest energy structure of a fixed composition, check whether it is stable against decomposition to all other compositions in the chemical system. This requires knowledge of all other known stable compositions, their crystal structures and total energies, made possible by the construction of materials databases containing data in standardized computable formats, such as the Materials Project, AFlowLib AFLOWlib  and NIMS. With this information, the energetic convex hull for a chemical system can be constructed and the target composition checked for stability. \begin{table}   \label{tbl:workflow} 
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global stability & chemical system $\to$ composition & convex hull from materials databases \\  \hline  \end{tabular}   \caption{Three-step workflow of materials design. While in nature, experiment  we start tend to begin  with a chemical system and progress upwards to properties, theoretical design has generally proceeded in the opposite direction.} \end{table}  The three stages are outlined in Table.~\ref{tbl:workflow}. In a sense, the steps are opposite of the order taken Table~\ref{tbl:workflow}. The theoretical workflow progresses  in reverse order from experimental  solid state synthesis. Here, There,  elements and simple compounds in a chemical system are combined and subjected to heating/cooling programs cycles  to provide the kinetic energy necessary for atomic rearrangement to form new stoichiometries (of which there may be more than one). Simultaneously, the The  stoichiometries crystallize to form structures which are then isolated for further study. Roughly, steps 2 and 3 are simultaneous in experiment. Only after a new crystal structure has been isolated is the electronic properties of the material studied.  For understanding the electronic properties of a material given a crystal structure, DMFT and GW perform remarkably well. Thus we adopt a hybrid workflow correlated materials, one where structural prediction is performed using LDA or LDA+U and once the final structure has been obtain, detailed analysis of the electronic structure is performed using DMFT or GW. It would be highly desirable to have GW or LDA+DMFT calcualtions in large systems, and there has been some significant progress in this direction recently [ CITE SAVRAOSV VOLLHARDT AND HAULE ]. However, only LDA+U can currently scale to produce total energies for simulations involving thousands study  of compounds  On the theoretical side, the treatment of correlations in solids state has followed a tiered model given computational constraints. Understanding their  electronic structure requires accurate determinations of the spectral function, which has historically received the most detailed modeling of correlations. Correct determination of local geometries for accurate crystal fields, realistic modeling of the Coulomb interaction and $ab initio$ treatment of the full charge density have been instrumental in bringing theoretical models in alignment with experiment. For the total energies needed for global stability and structure prediction, the vast majority of compounds can be successfully modeled by treating correlations at the LDA+U level. [citation with quantitative results?] { WE SAID THIS ALREADY ? ] properties.  %% Ideas For weakly-correlated materials, the entire workflow can be built around DFT. However, for strongly correlated materials, we adopt a hybrid approach guided by tradeoffs between accuracy and computational constraints. For global stability and structure prediction, we use DFT, or LDA+U if some treatment of correlations is necessary. Once the final structures are obtained, we proceed  to flush out [Gabi, I'm leaving this DMFT or GW for detailed analysis of the electronic structure. It would be desirable  to you].  %% \begin{itemize}  %% \item Correlated materials: still looking have GW or DMFT implementations  for qualitative ideas large systems,  and heuristics. Quote Mike Norman.  %% \item Current state: there has been recent progress  in this direction [CITE SAVRAOSV VOLLHARDT AND HAULE]. However, only LDA+U can currently scale to produce total energies for searches involving thousands of compounds. Finally, given the developing state of theory for  correlated materials one does bits and pieces.  %% \item Importance materials, experimental tests  of doing materials design in conjunction with experiments (given predictions provide valuable feedback for  the primitive stage refinement  of theory).  %% \end{itemize} theory.