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Quantum-chemical calculations are quite expensive with a cost that scales greatly with the number of atoms in the system. What is the largest material that has been modeled using density functional theory (DFT), by number of atoms?

Edit: For the purposes of intellectual curiosity, please feel free to answer with unusually "large" DFT calculations even if it's not the largest.

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    $\begingroup$ Nice. I've just removed the last part you just added about other quantum chemical methods, because someone has already asked this same question but about coupled-cluster, and it would be unfair to try to swallow that question after they have already written it :) $\endgroup$
    – Nike Dattani - No Free Time
    Commented May 2, 2020 at 2:41
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    $\begingroup$ I just saw that! I agree with your decision there. $\endgroup$
    – Andrew Rosen
    Commented May 2, 2020 at 2:42

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I know of several papers over the million-atom mark:

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    $\begingroup$ Thanks for the answer. It's kind of crazy to think that a 2 million atom simulation was carried out nearly 10 years ago! $\endgroup$
    – Andrew Rosen
    Commented May 1, 2020 at 20:46
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    $\begingroup$ @AndrewRosen Linear-scaling DFT is an amazing advance. It's somewhat surprising to me that more work on this size isn't done more often (nanoparticles, supercell defects, etc.) $\endgroup$
    – Geoff Hutchison
    Commented May 1, 2020 at 23:34
  • $\begingroup$ Nicely spotted @SusiLehtola. $\endgroup$
    – Nike Dattani - No Free Time
    Commented Jun 1, 2020 at 19:00
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    $\begingroup$ @GeoffHutchison For cp2k, I think the paper you're looking for is doi.org/10.1021/ct200897x (1 million H2 molecules, i.e. "qm weightlifting" mentioned below is probably the appropriate term here) $\endgroup$
    – leopold.talirz
    Commented May 28, 2021 at 14:07
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Here is a DFT simulation of a virus, in solution!

"Combining Linear-Scaling DFT with Subsystem DFT in Born-Oppenheimer and Ehrenfest Molecular Dynamics simulations: from Molecules to a Virus in Solution."

enter image description here

But I like the way Frank Neese (lead author of ORCA) described his coupled cluster calculation of a protein: "this is what I call quantum mechanical weightlifting .. it's when we are only doing the calculation because we want to see who can lift the most."

Bear in mind that if all we cared about was "quantum mechanical weightlifting" competitions, those records from 2010 could have been broken several times by people making more and more approximations and using more and more hardware.

My preferred criteria when evaluating things like this, is that the calculation was a necessary part of predicting something that was later shown to be true in an experiment, or was necessary to reach agreement with experiment, or was crucial in the correct analysis of an experiment, or something along those lines. But I still also do love seeing these "quantum mechanical weightlifting" records being broken either way, and therefore I do love questions like these!

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    $\begingroup$ It was a nice paper, but to be technical, it was 'only' slightly over a million. Neese is correct that the 2 million record could certainly be broken with more hardware - the question would be on what one would learn. $\endgroup$
    – Geoff Hutchison
    Commented May 2, 2020 at 0:06
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    $\begingroup$ Precisely. This is the reason why my preferred criteria would include that the calculation is also useful for some experiment (for example). I did see that the caption to one of the figures said that slightly over a million atoms were included in that simulation. I thought it was worth mentioning though since others under 2 million were also mentioned and this was the study of an entire virus :) $\endgroup$
    – Nike Dattani - No Free Time
    Commented May 2, 2020 at 0:11
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    $\begingroup$ That's amazing Nike. $\endgroup$
    – Peter Morgan
    Commented May 2, 2020 at 0:32
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    $\begingroup$ Thanks for this great example @NikeDattani! I agree that my question is really along the lines of "quantum mechanical weightlifting", but who doesn't like to see the bar being raised just for the sake of raising it every now and then? If anyone has other answers, even if 'only' a million atoms, I'd love to hear about them! Hopefully they're useful for something too... $\endgroup$
    – Andrew Rosen
    Commented May 2, 2020 at 0:41
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    $\begingroup$ As for me, simulating spectroscopy (agree accurately with experimental measurements) is one of the important applications. Spectroscopy is one of the few limited ways that people could probe the microscopic (quantum) world. $\endgroup$
    – Paulie Bao
    Commented May 2, 2020 at 4:17
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In 2011, the electronic states of a silicon nanowire with 107,292 atoms was modeled using 6,144 cores over a ~24 hour runtime, as discussed here. I'm not sure of any larger example than this one, although one may exist.

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  • $\begingroup$ I'd be interested to see how TeraChem handles petachem.com/performance.html $\endgroup$
    – Cody Aldaz
    Commented May 1, 2020 at 20:39
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    $\begingroup$ @CodyAldaz - TeraChem is great, but they'd need a really huge GPU cluster to run 100K or millions of atoms. $\endgroup$
    – Geoff Hutchison
    Commented May 1, 2020 at 23:35
  • $\begingroup$ I understand the need to run simulations for big systems, but what is the funny to run the simulations in HPC with thousand/million of CPU/GPU cores? Not every mortal have access to such computational resources. $\endgroup$
    – Camps ♦
    Commented May 2, 2020 at 13:02

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