Overlapping pseudo-cores

[aaron_kaplan2]

Asking here in case any internal benchmarks from VASP have been performed against all-electron data:

When does the overlap of pseudo-cores start to lead to a breakdown in the pseudopotential approximation?

Especially for the d-block, the minimum nearest-neighbor separation for two species to avoid pseudo-core overlap is 2 - 2.5 Å (e.g., using the sum of RCORE for Fe or Cr). Those separations are comparable to lattice constants, so some compact but realistic crystal phases will have pseudo-core overlap.

[henrique_miranda]

Recently, there have been a couple of publications comparing VASP and other codes to other all-electron codes:
https://www.science.org/doi/10.1126/science.aad3000
https://www.nature.com/articles/s42254-023-00655-3

These do not directly address your question but are good indicators that you can get results comparable with all electron codes using VASP.
There are different versions of the Fe potential with different values of RCORE and more importantly different semi-core states treated in the valence.
For particular crystal phases or systems under pressure one should use 'harder' potentials.
This section in the documentation tries to help choosing the right potential for your application:
wiki/index.php/Available_pseudopotentia ... the_suffix

Now as to your question about wether internal tests have been performed it is hard for me to answer: I did not do but someone probably has done, I need to ask around.
But before that I need to ask you explicitely what test do you have in mind?
What physical property? What crystaline structure?

[aaron_kaplan2]

Thanks Henrique! I'm aware of both papers and yes agreed they generally indicate good agreement with AE calculations.

From the procedures/recommendations in the Bosoni et al. paper and internal benchmarks, I've primarily been using the hard pseudos for f-block elements. Still, there are only a few hard pseudos for the main group in the 64 release

I'm asking in the context of developing datasets for ML interatomic potentials where a fixed set of pseudopotentials is require to avoid ambiguities in the vacuum levels of different pseudopotentials (e.g., using a harder pseudo only for higher-pressure phases can change the vacuum level even with the same XC functional). The properties I'm looking at would be total energies, Hellmann-Feynman forces, and stress, and especially for distorted / higher-pressure phases

I have two major concerns then, based mostly on older literature:
* The Kresse and Joubert PAW paper makes it clear that terms in the total energy involving overlap of pseudo-cores are neglected. So in cases with "strong" overlap, there could be significant errors in the PAW formalism
* Another paper from Kresse and coworkers suggests errors in energy differences on the order of 10 meV/atom due to overlap of pseudocores

The question would be: How significant are these errors given modern PAWs and have there been any recent tests of errors due to pseudocore overlap?

[henrique_miranda]

Hi Aaron,

There will always be some error due to the overlapping pseudo-cores.
Bessel functions still approximate AE results reasonably well even inside the augmentation spheres but as the overlap increases the errors will too.
Note that the pseudo-potentials are often generated based uppon user requests. Usually that means that the need to generate more expensive pseudopotentials that work under higher pressure still did not arrise. (That does not mean that there is never a need for them of course).

I asked around and it seems that there is currently no such systematic study comparing AE and PAW total energies, Hellmann-Feynman forces, and stress for all pseudopotentials across different structures and pressures.
The papers I mentioned above focus on equilibrium volumes and do not explicitly probe high-pressure or very distorted phases.
A systematic study would imply choosing a "gold standard" and comparing these computed properties.

For that FLAPW (e.g., WIEN2k or FLEUR) is usually the reference.
The question then is how much error is acceptable for your application e.g., <10 meV/atom for forces?
Can the machine learned potentials reach that level of precision?
By using more expensive pseudopotentials you might need to reduce the amount of training data for the same compute power which in the end might lead to an overall worse force-field.

This being said, I agree that it would be very interesting to quantify more precisely how much error is made due to the overlapping pseudo-cores.