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\section{Materials Design Workflow}
\label{sec:workflow}
In materials design, our playground is the combinatorial phase space of all possible materials.
Attempts to search Searching for novel compositions and predict stable structures in this huge space by brute force computation would require unreasonble computational resources and timescales. In practice, we begin with an intuitive idea of what classes of materials to explore, and how chemistry would enhance desireable solid state properties. Restricting ourselves to a few materials classes renders the search space tractable. In areas with firm theoretical understanding, we perform quantitative calculations with established computational tools which can confirm or refute our intuition, and the process iterates. Occasionally, we find that no material matches our design criteria within our restricted materials classes and we need to expand the search space. In classes where the state of theory is less developed, namely strongly correlated materials, we can appeal to analogies, descriptors and pattern recognition to help guide the design process~\cite{Norman_2016}. In
the following, general, we
describe find it natural to divide the
three steps in our workflow for process of materials design
and note the role correlations play in
each step. three key steps, which we've assembled in a workflow presented below.
%% The
search for new materials starts with some intuitive idea of what classes of materials should be explored, and how certain chemistry enhances desireable solid state observables. In areas where there is good theoretical understanding and working computational tools, this 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, first and most
well-studied, well-studied step is the calculation of the
electronic structure. namely \emph{electronic structure}, namely, how to go from structure to
property, i.e. given property (see Table~\ref{tbl:workflow}). Given a crystal structure,
we seek to compute
its electronic
properties, properties such as
the electron density, gap size, magnetic
ordering, order and superconducting transition temperature.
Here, density functional theory, has been quite successful The computational method used for
weakly correlated systems. Sometimes, like in electronic structure highly depends on the
case strength of
semiconducting materials, where correlations. For weakly correlated systems, DFT is quite successful for understanding structure-property relationships. As the
standard implementations strength of
DFT considerably underestimates 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
effects underestimation of exchange at low
enerties, the first correction frequencies 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 DFT self-energy. In strongly correlated
materials is their electrons cannot be described as non-interacting particles. Often, this occurs because materials, the
material solid often contains atoms with partially-filled $d$
or and $f$
orbitals. shells. The electrons occupying these orbitals
retain a strong behave in an atomic-like
character to their behavior, fashion, while the remaining electrons form
bands; their bands. Their interplay poses special challenges for
theory. Consequently current implementations of DFT cannot describe their electronic structure accurately. This theory, which 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''. (DMFT). 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 combination of
atomic configurations DFT and
cell geometries to arrive at the lowest energy structure. This step requires having an DMFT enables accurate
method for producing the energy of a given configuration calculations 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 spectra 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 materials, for
strongly correlated electron systems. Successes include the prediction of a new compounds example, 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, classic Mott compounds like V$_2$O$_3$. We note that
in spite of this failure, DFT + orbital polarization LDA+U can
predict be viewed as the
order static limit of
the structures. However, DMFT, which works well for
correlated materials, we argue that extensions taking into account magnetically or orbitally ordered materials. To summarize, the
effect community has developed a hierarchy of
correlations on the total energy is important for obtaining the correct ground-state structure tools for
a given composition.
For understanding the electronic
properties structure capable 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 treating differing correlation strengths. As correlations increase, so does the
final structure has been obtain, detailed analysis complexity of the
electronic structure is performed using DMFT or GW. It would be highly desirable to have GW or LDA+DMFT calcualtions physics, which reflects in
large systems, the required expertise 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 computational power for
simulations involving thousands of compounds 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 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 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.
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.
...
\hline
Name & Step & Description \\
\hline
electronic structure & structure $\to$ property &
"bread-and butter" of electronic structure codes, DFT, DFT+DMFT \\
structure prediction & composition $\to$ structure & evolutionary
algorithm, algorithms, Monte Carlo, minima hopping \\
global stability & chemical system $\to$ composition & convex hull from materials databases \\
\hline
\end{tabular}
...
The three stages are outlined in Table.~\ref{tbl:workflow}. In a sense, the steps are opposite of the order taken in solid state synthesis. Here, elements and simple compounds in a chemical system are combined and subjected to heating/cooling programs to provide the kinetic energy necessary for atomic rearrangement to form new stoichiometries (of which there may be more than one). Simultaneously, 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.
On the theoretical side, For understanding the
treatment electronic properties of
correlations in solids state has followed a
tiered model material given
computational constraints. Understanding electronic structure requires accurate determinations of 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
spectral function, which final structure has
historically received the most been obtain, detailed
modeling of correlations. Correct determination of local geometries for accurate crystal fields, realistic modeling analysis of the
Coulomb interaction and $ab initio$ treatment of the full charge density electronic structure is performed using DMFT or GW. It would be highly desirable to have
been instrumental GW or LDA+DMFT calcualtions in
bringing theoretical models large systems, and there has been some significant progress in
alignment with experiment. For the this direction recently [ CITE SAVRAOSV VOLLHARDT AND HAULE ]. However, only LDA+U can currently scale to produce total energies
needed for
global stability and structure prediction, the vast majority simulations involving thousands of compounds
can be successfully modeled by treating correlations at the LDA+U level. [citation with quantitative results?] { WE SAID THIS ALREADY ? ]
Ideas to flush out [Gabi, I'm leaving this to you].
\begin{itemize}
\item Correlated materials: still looking On the theoretical side, the treatment of correlations in solids state has followed a tiered model given computational constraints. Understanding 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
qualitative ideas accurate crystal fields, realistic modeling of the Coulomb interaction and
heuristics. Quote Mike Norman. $ab initio$ 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 ? ]
%% Ideas to flush out [Gabi, I'm leaving this to you].
%% \begin{itemize}
%% \item Correlated materials: still looking for qualitative ideas and heuristics. Quote Mike Norman.
%% \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}
