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Is "alpha+bet" related to eq 53 in the following paper, evaluated for the reference atomic charge density?
https://perso.uclouvain.be/xavier.gonze ... al2014.pdf
That is the only thing that makes sense, but I can't quite make the connection based on what's in the RHOAT0 subroutine

P.S. I'm interested in this term for calculating the electrochemical potential of charged slabs in an electrolyte for a new implicit solvation model I've written for VASP. Specifically, I've found that a very large unit cell is required for the counterion concentration to decay to zero in the "vacuum" region - however, the error from using a much smaller unit cell is almost negligible when nonlinear ionic screening is used as long as one doesn't use the potential in the middle of the "vacuum" as the "zero" potential . On one hand, this "referencing" is not necessary b/c the ionic screening term pins the potential to an absolute scale. On the other hand, a correction is still needed corresponding to eq 53 in the above paper. Thus, the reason I am interested in this correction.

Dear craig_plaisance1,

The quantity "alpha+bet" is not actively used by VASP members and was from our perspective in applications we considered not particularly useful. That is why the best I can do at this moment is to point you to the original reference by J Ihm et al., J. Phys. C: Solid State Phys. 12 4409 (1979), which was used when this was implemented. However, we cannot comment on any connection with the reference you cited.

Best regards,
Marie-Therese