Chuck-Hou Yee Remove duplicate content on correlations from workflow  over 7 years ago

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\section{Materials Design Workflow}  \label{sec:workflow}  The search for new materials starts with some intuitive idea of what classes of materials should be explored,and explored, and  how certain chemistry enhances desireable solid state observables. In areas where there is good theoretical understanding and working computational tools, this intution intuition  can then be supplemented by more quantitative calculations. When this understanding is lacking, one can appeal to analogies, descriptors and machine learning .[ CITE NORMAN'S REVIEW ? arXiv:1601.00709 ]. Designing a proper strategy, thus requires an understanding of the nature of correlations in a given class of materials. Irrespectively of the degree of correlation, it is natural to divide the workflow of materials design into three different steps, of course, how to carry them out in practice will depend on the level of correlation. The first, and most well-studied, is the calculation of the electronic structure, structure.  namely how to go from structure to property, i.e. given a crystal structure, compute its electronic properties, such as gap size, magnetic ordering, and superconducting transition temperature. Here, density functional theory, has been quite successful for weakly correlated systems. Sometimes, like in the case of semiconducting materials, where the standard implementations of DFT considerably underestimates the effects of exchange at low enerties, the first correction in the screened Coulomb interactions, namely the GW self energy, $\Sigma_{GW} - {V^{LDA}}_{XC}$ is required to get good results. %% The basic feature of correlated materials is their electrons cannot be described as non-interacting particles. Often, this occurs because the material contains atoms with partially-filled $d$ or $f$ orbitals. The electrons occupying these orbitals retain a strong atomic-like character to their behavior, while the remaining electrons form bands; their interplay poses special challenges for theory. Consequently current implementations of DFT cannot describe their electronic structure accurately. This led to the development of combinations of DFT and dynamical mean field theory (DMFT) which can treat and the GW approximation. LDA+U can be viewed as a static limit of LDA+DMFT ( when the impurity solver used is the Hartree Fock approximation) and works in the presence of magnetic and orbital order.  Irrespectively of the method used, we call this step ``electronic structure''.  Thebasic feature of correlated materials is their electrons cannot be described as non-interacting particles. Often, this occurs because the material contains atoms with partially-filled $d$ or $f$ orbitals. The electrons occupying these orbitals retain a strong atomic-like character to their behavior, while the remaining electrons form bands; their interplay poses special challenges for theory. Consequently current implementations of DFT cannot describe their electronic structure accurately. This led to the development of combinations of DFT and dynamical mean field theory (DMFT) which can treat and the GW approximation.  LDA+U can be viewed as a static limit of LDA+DMFT ( when the impurity solver used is the Hartree Fock approximation) and works in the  presence of magnetic and orbital order.   % In principle,  %lattice properties can be computed as well, such as phonon vibrational modes,  %stress tensors and thermal expansion coefficients,  Irrespectively of the method used, we call this step  ``electronic structure''.  The  second step is structure prediction: given a fixed chemical composition--take Ce$_2$Pd$_2$Sn for example--predict its ground state crystal structure. Generically, atoms are placed in a unit cell and a chosen algorithm is used to efficiently traverse the space of atomic configurations and cell geometries to arrive at the lowest energy structure. This step requires having an accurate method for producing the energy of 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 we would like to find out that not only carbon but 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 in the Ce-Ir-In system~\cite{Fredeman_2011}. Notable failures, include elemental Pu, where non magnetic DFT calculations underestimates the volume of 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 in spite of this failure, DFT + orbital polarization can predict the order of the structures. However, for correlated materials, we argue that extensions taking into account the effect of correlations on the total energy is important for obtaining the correct ground-state structure for a given composition. 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 of compounds  The third and final step is 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 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} 

\item Current state: in correlated materials one does bits and pieces.  \item Importance of doing materials design in conjunction with experiments (given the primitive stage of theory).  \end{itemize}