[CP2K-user] [CP2K:21089] Re: Self-consistent Hirshfeld: How were ref atoms made, and can I extract them?

[Alexander Davis]

Hi Prof Lu,

It is great news that it is possible to extract the reference ion densities 
used by MultiWFN for Hirshfield-I calculation. I am an appreciative 
MultiWFN user—in fact I use it in my own Hirshfeld-I implementation to 
create reference atom cube files on the appropriate grid—and with the 
reference atom densities in hand, it seems that I could use MultiWFN for 
the whole charge calculation, since I will be able to use those .rad files 
to reconstruct the weight function after the charge calculation.

However, it seems that the MultiWFN reference atoms have the issue that I 
am trying to avoid: unattached electrons in the anions. I plotted the 
radial densities of the nitrogen references found in "examples/atmrad":

[image: nitrogen_rad_white.png]

As expected and desired, the cation densities get wider as electrons are 
added. However, the anion densities stay exactly the same all the way up to 
past an angstrom from the nucleus. The additional electron density all ends 
up out past the covalent radius of nitrogen.

The reason for this is that N- and N2- are artificial. The electron 
affinity of nitrogen is near zero. N- is not really stable, or perhaps 
barely stable, and N2- is certainly not stable. As a result, the electrons 
are unattached in the reference densities.

This issue was discussed extensively by Vanpoucke, Bultinck, and Van 
Driessche in their paper "Extending Hirshfeld-I to Bulk and Periodic 
Materials <https://doi.org/10.1002/jcc.23088>", and generated considerable 
discussion: a comment by Thomas Manz <https://doi.org/10.1002/jcc.23191>, 
followed by a reply to that comment by the original authors 
<https://doi.org/10.1002/jcc.23193>. It is not a simple issue with a neat 
solution, and the main reason I am looking around at Hirshfeld-I 
implementations other than my own is that I'm hoping that someone else has 
worked out a satisfactory alternative.

In any case thanks for the information, and I love MultiWFN. Wishing you 
the best,
Alex
On Wednesday, January 29, 2025 at 6:42:56 AM UTC-5 Tian Lu wrote:

> Hello, 
>
> I would like to mention that in the recent updates, Multiwfn (
> http://sobereva.com/multiwfn) has supported calculating Hirshfeld-I 
> charge and MBIS charge (another method based on iterative atomic spaces) 
> based on the .molden file or electron density .cube file exported by CP2K. 
> Both isolated and periodic systems are supported. For the Hirshfeld-I 
> calculation, radial electron density files for almost every element at 
> every charged states have been provided in Multiwfn package 
> ("examples\atomrad\" subfolder) and can be directly used. I have a blog 
> article to describe and illustrate how to perform the calculations using 
> Multiwfn in combination with CP2K: http://sobereva.com/712 (currently 
> written in Chinese, please use Google translator. English version may be 
> available later). Please feel free to contact me if you have any problem.
>
> Best regards,
>
> Tian Lu
>
> On Wednesday, January 29, 2025 at 8:05:13 AM UTC+2 Alexander Davis wrote:
>
>> Hi,
>>
>> I have been calculating self-consistent Hirshfeld charges using my own 
>> post-processing script, but I am thinking of switching to the CP2K 
>> implementation. However, there are two questions I would need answered.
>>
>> One question is how it handles a well-known issue with this method, which 
>> is that it obtains the shape function from the electron densities of free 
>> ions, but sometimes these ions don't really exist. This is why my 
>> implementation is unsatisfactory: I have references for N- and N2-, but the 
>> electrons are not really attached, so the reference densities are too wide. 
>> Every self-consistent Hirshfeld implementation as to handle this somehow, I 
>> would like to know how CP2K handled it. The documentation says "This scales 
>> only the full shape function, not the added charge as in the original 
>> scheme", which is suggestive of a solution, but where can I read more about 
>> it? If the details are in one of the publications, I missed it.
>>
>> My second question is whether I save the reference atoms as cube files, 
>> or even better, the actual weight function used for integration (which is 
>> a(r)/(a(r)+b(r)), where a and b are the reference atom densities). It's a 
>> quirk of my application, I need precisely the weight function that was used 
>> to calculate the charges.
>>
>> Thanks,
>> Alex
>>
>

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