CCL: Radial atomic DFT solver inconsistencies

 Sent to CCL by: Susi Lehtola [susi.lehtola ~ alumni.helsinki.fi]
 On 3/18/24 11:51, Szabolcs Góger szgoger{:}gmail.com wrote:
 > Dear Community,
 >
 > I must also say that this was an amazing response, and I have a lot of
 > catching-up to do before being able to adequately address the issue.
 >
 > I want to add one thing, however: it was mentioned that "the radial 1s
 > orbital turns out to be quite similar between the two [spin-restricted and
 > spin-unrestricted PBE hydrogenic] calculations." My view is actually
 quite
 > the opposite: depending on /what/ expectation values we are interested, we
 > might get significantly different results. For example, even though the
 > density maxima (defined from \rho * r^2) occur at quite similar regions,
 > integrals of the densities can be quite different. Apart from the -very
 > different - expectation values of the energy, the matrix elements
 <0|r^3|0>
 > also happen to not match, being 8.7 a.u. vs. 10.5 a.u. - this is exactly
 the
 >  difference that is mentioned in the Q-Chem manuals. This, to me, hints
 that
 >  the overall shape of the density is quite different.
 Note that's bohr cubed, the difference is quite a bit smaller if you look at
 cbrt(<r^3>). HelFEM actually calculates all the radial moments: for
 restricted
 vs unrestricted I get the following values
 <r>(-2)      <r>(-1)       <r>(1)       <r>(2)
 <r>(3)       r(max)
 7.369885e-01 1.058618e+00 1.635790e+00 1.914003e+00 2.188965e+00 1.026772e+00
 7.045756e-01 1.005871e+00 1.541603e+00 1.799470e+00 2.054614e+00 9.827961e-01
 > Apart from the fundamental questions of the proper definition of atomic
 > solvers, I am also worried whether it is a problem that different
 definitions
 > exist in different software. Some dispersion corrections relying on free
 > atomic data already use empirical factors to correct for the mismatch of
 the
 > different definitions, which is not an elegant solution at all, but at
 least
 > the problem is addressed. I can't help to wonder whether there are other
 > points of divergence that most people do not know about...
 Yes, this is more than likely and is not limited to atomic calculations;
 differences occur also for density functionals like I discussed in a previous
 message, atomic basis sets (e.g. the Dunning cc basis sets can be different in
 different programs), etc. The central issue here is the lack of reproducibility
 in scientific software, especially proprietary ones that are not open source,
 which includes academic and commercial packages; the "war on supercooled
 water"
 (doi:10.1063/PT.6.1.20180822a) is an excellent example thereof. See our
 discussion in
 S. Lehtola and A. Karttunen, Free and open source software for computational
 chemistry education, Wiley Interdiscip. Rev. Comput. Mol. Sci. 12, e1610 (2022).
 doi:10.1002/wcms.1610 chemRxiv:2021-hr1r0-v3
 I believe that reusable open source libraries can afford a solution to this. At
 present, there is too much duplicated effort going on across packages, which is
 really benefiting nobody. Programming languages and models have developed a lot
 in the last decades, and software distribution is now also much easier than
 before.
 S. Lehtola, A call to arms: making the case for more reusable libraries, J.
 Chem. Phys. 159, 180901 (2023). doi:10.1063/5.0175165 arXiv:2309.02433
 I believe that computational chemistry software will slowly migrate towards
 relying more on common solutions, and my current efforts are focused on making
 such solutions available. Reusable software takes more effort to write, but it
 more than pays itself back by the significantly reduced maintenance costs. For
 instance, our Libxc has eliminated the need to maintain density functional
 implementations in over 40 program packages. More things are coming, reusable
 atomic solvers among them...
 Susi
 --
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 Mr. Susi Lehtola, PhD             Academy of Finland research fellow
 susi.lehtola|helsinki.fi          Associate professor, computational chemistry
 http://susilehtola.github.io/     University of Helsinki,
 Finland
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 Susi Lehtola, FT                  akatemiatutkija
 susi.lehtola|helsinki.fi          dosentti, laskennallinen kemia
 http://susilehtola.github.io/     Helsingin yliopisto
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