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搬运一下CCL上某人对此文章的看法，有一定道理。即便只是讨论密度的准确性，测试体系的局限性也太大
A recent issue of Science contained an interesting article "Density functional theory is
straying from the path toward the exact functional"[1].
I agree with the article's main idea that new DFT functional development should focus on both reproducing the energies and the electron densities. I also agree with the article's statement that one should be cautious to make sure new functionals obey appropriate limits and norms without using an excessive number of empirically fitted parameters.
However, there is a notable limitation in their methodology. Specifically, in the article they claim that "The results for molecules would be ambiguous because for typical approximate functionals, accurate molecular energies and densities arise only from an understood but uncontrollable error cancellation between a functional’s exchange and correlation components" I do not agree with this, because many energetic properties of molecules have been measured unambiguously using spectroscopic techniques. Also, it is possible to unambiguously compute the energy and geometry that is theoretically predicted by each functional for a chosen molecule. So, it is in fact possible to unambiguously compare theoretically computed and experimentally measured energies for molecules. Moreover, the authors used CCSD calculations as the reference data for the electron densities of single atoms, and the CCSD method can be applied to molecules not just single atoms.
The authors reported the electron density errors for isolated closed-shell atoms and atomic cations only, while citing the energy errors for entirely different types of systems (i.e., the large dataset of Peverati and Truhlar [2]). While the study raises many interesting questions, it did not in fact compare the accuracy of functionals for reproducing both the energies and the electron densities of the same materials. So, any conclusions about how one functional gets the energies better but the electron densities worse are limited by the fact that those measures were quantified for entirely different classes of materials.
Specifically, we do not know whether the functionals that got the energies better for molelcules performed better or worse for the electron densities of those materials, because that was never measured. Moreover, we do not know whether the functionals that performed better for the electron densities of the isolated closed-shell atoms and atomic cations performed better or worse for the energies of those materials, because that data was not reported.
The study has shown is that some functionals, which perform better for electron density of one type of system have also performed worse for the energies of other types of systems. However, I think the study has serious limitations because the energies and electron densities were not compared for the same systems. Nonetheless, it raises some interesting questions that should be explored in future studies. Specifically, do the recent functionals that perform well for molecules and solids get the electron density distributions for those materials more or less accurately than the earlier functionals?
[1] M. G. Medvedev, I. S. Bushmarinov, J. Sun, J. P. Perdew, and K. A. Lyssenko, Science 355 (2017) aah5975.
[2] R. Peverati, D. G. Truhlar, Philos. Trans. R. Soc. A 372 (2014) 20120476.
Tom
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Hi Susi,
Thanks for pointing that out. I agree with many of your critiques on the Science article.
It would be interesting if someone would do a more rigorous study comparing more functionals with proper comparisons of both energies and electron distributions for a diverse set of materials.
One of the things that I struggle with is that with so many newly developed DFT functionals in recent years, I have no idea which of them actually perform well across diverse materials.
A study that compares not only energetics, but also computed electron densities, across diverse materials (molecules, solids, transition states, etc.) could be extremely valuable for figuring out which recently developed functionals actually perform well.
One of the things the Science article claims is that the recent functionals are getting worse on the electron densities, but as you have pointed out, we don't necessarily know whether this is truly the case. Particularly, because the Science article tested such a limited set of materials (i.e., single closed shell atoms and atomic cations) for the densities but cited energies for entirely different material types, and as you pointed out the functionals tested omitted many recent approaches developed by diverse research groups.
It would be great if someone could do a more rigorous and inclusive study.
Tom
On Thu, Jan 26, 2017 at 2:56 PM, Susi Lehtola susi.lehtola * alumni.helsinki.fi <owner-chemistry##ccl.net> wrote:
Sent to CCL by: Susi Lehtola [susi.lehtola---alumni.helsinki.fi]
On 01/26/2017 10:16 AM, Thomas Manz thomasamanz_._gmail.com wrote:
A recent issue of Science contained an interesting article "Density
functional theory is
straying from the path toward the exact functional"[1].
This has already been discussed on the list in the thread
"DFT discovers it's recapitulating QSAR"
I'd like to repeat my arguments in
http://www.ccl.net/cgi-bin/ccl/message-new?2017+01+06+006
that you could rewrite the result of the study as a much less catching "Minnesota functionals fail to reproduce electron density in small atoms and cations"
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Mr. Susi Lehtola, PhD Chemist Postdoctoral Fellow
susi.lehtola|-|alumni.helsinki.fi Lawrence Berkeley National Laboratory
http://www.helsinki.fi/~jzlehtol USA
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