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With the advent of more computational power than ever in the recent years, interest in in silico design of interesting compounds has grown as well. I am wondering about the state of the art for the case of designing novel materials:

  • What methods are commonly used (DFT, semi-empirical, more / less expensive)?
  • What size of lattices is one able to treat in high-througput screening approaches?
  • What is the effort in terms of runtime one needs to put in?
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    $\begingroup$ Isn't this question a bit too broad? $\endgroup$ – stafusa May 19 at 23:48
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    $\begingroup$ I removed the last subpart of the question if you worry about that. It has actually been answered in materials.stackexchange.com/questions/157. The others really belong together for me, because if you talk about runtime you have to refer to the method which was used and the size of systems which can be treated. $\endgroup$ – Michael F. Herbst May 20 at 5:32
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    $\begingroup$ +1 I think it's much more focused now. $\endgroup$ – stafusa May 20 at 9:23
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    $\begingroup$ Related: materials.stackexchange.com/a/555/5 $\endgroup$ – Nike Dattani May 21 at 4:50
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After a little research I found a great article [1], which provides a good overview to what I asked above in Figure 2. Summarising in a table:

| Method                 | effort | reliability  | system size |
+------------------------+--------+--------------+-------------+
| Interatomic potentials | high   | high* / low* |        10^8 |
| Linear-scaling DFT     | high   | medium-high  |        10^6 |
| Tight binding          | high   | medium-high  |        10^6 |
| LDA DFT                | low    | medium-low   |        10^3 |
| GGA DFT                | low    | medium       |        10^3 |
| GGA+U DFT              | low    | medium-high  |        10^3 |
| Hybrid DFT             | low    | high         |        10^2 |
| GW                     | high   | high         |        10^1 |
+------------------------+--------+--------------+-------------+

* high for geometries and energetics, but low for excited states
  or the dielectric function

where effort refers to the manual effort from the researcher, reliability gives the reliability of the method and system size is the typical system size in the number of atoms. In the table I am providing a condensed (and maybe biased) overview, focusing on properties such as geometry, energetics, dielectric function, excited states or bandgap. See [1] for the full details.

References

[1] K. T. Butler, J. M. Frost, J. M. Skelton, K. L. Svane and A. Walsh. Chem. Soc. Rev., 2016, 45, 6138. DOI 10.1039/c5cs00841g

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    $\begingroup$ Great answer and a very good resource $\endgroup$ – Thomas May 20 at 14:43
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I am sure there are A LOT of authors publishing papers to answer this very question. Mainly because the theories employed have face a paradigm since "one-size-doesn't-fit-all".

Here are the variables that affect this use of a certain method:

(i) Molecular models or periodic solids

(ii) Chemical Accuracy (energies with accuracy of < 1kcal/mol) - e.g. in polymorph stability such as crystal structure prediction or molecular solids

(iii) Electronic structure (band gap/density of states/ band structure/excitonic effects) can be calculated using PBE+U (or PBE+D3+U) that is Fast vs Hybrid (PBE0/HSE06/etc.) or quasiparticle GW calculations that can be quite slow

A good read on theoretical comparisons:

(i) Philosophical+technical: https://science.sciencemag.org/content/355/6320/49/tab-figures-data

(ii) Technical benchmarking of a recent density functional across various model solids: https://journals.aps.org/prx/abstract/10.1103/PhysRevX.6.041005

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    $\begingroup$ +1. Another good one from gogo! $\endgroup$ – Nike Dattani May 21 at 3:55

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