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I am currently designing a toy model to calculate an interatomic potential (for an infinite repeating lattice) this toy model needs to scale and perform better than DFT simulations. But sadly I have little knowledge of DFT simulations.

I did find this paper ( https://www.nature.com/articles/nphys1370 ) but it only specifies that the calculation time scales with O(N^3) (where N is the total number of atoms taken into account, or only in the unit cell?) and sadly I can't find any real numbers or benchmarks for the calculation time.

The reason why I care about the real calculation time is that for example an algorithm which scales like O(N^2) but takes 20 seconds per 'sub calculation' is going to perform worse than a O(N^3) algorithm which takes 1 second per 'sub calculation' as long as N<20.

So my question: Does anybody know of any benchmarks of DFT simulations?

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    $\begingroup$ The simplest thing to do is to run a calculation on the same machine. Note that some researchers claim to have achieved lower scalings than cubic, albeit for molecular systems. $\endgroup$
    – TAR86
    Jun 30 '20 at 19:44
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    $\begingroup$ Welcome to our community! $\endgroup$
    – Camps
    Jun 30 '20 at 22:12
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    $\begingroup$ +1. Welcome to our site, and we hope to see much more of you !! B3LYP with QChem seems to have taken 9 minutes to converge (after 14 convergence iterations) for a 21-atom system of carbon, hydrogen and oxygen: github.com/PedroJSilva/qmspeedtest. But that was 7 years ago, and according to this: mattermodeling.stackexchange.com/q/1354/5, there's not been a lot of benchmarks around since then. Since you might not find any better or more recent benchmarks, you might want to pick a specific system, and simulate it with DFT, as TAR86 suggested. $\endgroup$ Jun 30 '20 at 23:09
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    $\begingroup$ Also note that the speed test is for 1 CPU process. If you use more you can expect a nice speedup. In fact, I saw a super linear speedup! $\endgroup$
    – Cody Aldaz
    Jul 2 '20 at 3:47
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    $\begingroup$ Also keep in mind that most existing codes are optimised to death using all sorts of tricks (screening, adaptive cutoffs etc), whereas your new algorithm probably won't for starters. So to have a fair initial comparison and see if it's worth the effort to optimise on your new idea, you probably should try to implement your toy model inside a package that also supports DFT to be able to select a similar level of tricks and parameters to compare on the same footing. $\endgroup$ Jul 3 '20 at 6:48
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As the comments to your question suggest, there isn't a simple answer as there are many issues involved like system size, numerical tricks, hardware configuration, etc.

There is an specific project that it is being developed at National Institute of Standards and Technology (NIST) under the name of DFT Benchmarking.

The major accomplishments of the project are:

  • Investigation the convergence of important physical quantities like lattice constant and bulk modulus as afunction of k-points and smearing;
  • Computation of lattice constant, elastic constants, and relative energies for single elements in various structures (fcc, bcc, hcp, sc, diam, ..) using various exchange-correlation functionals.

The project manager is Francesca Tavazza (francesca.tavazza @ nist.gov).

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