[QE-developers] Madelung constant values in Makov-Payne correction

[Jacob Williams]

Dear Pietro,

Thank you very much for your help. I was able to supply the last remaining detail missing from my understanding, which I write here in case it is useful for anybody in future.

In a simple cubic unit cell, the cube root of the cell volume, (omega) is equal to the length of the primitive lattice vectors (alat) and the side of the corresponding cell (alat again), so the Madelung constants are equivalent under all these length parameters. The other two cubic unit cells do not share this equivalence. The Lento et al. reference (hence QE’s Makov-Payne routine) uses L = omega^(1/3), while the Dabo et al. reference uses L = alat.

In an fcc unit cell, the volume of the primitive cell is (alat^3)/4, and as expected the Madelung constant where L = omega^(1/3) is smaller in magnitude than the constant where L = alat by a factor of 4^(1/3).
Likewise, in a bcc unit cell, the volume of the primitive cell is (alat^3)/2, and the L = omega^(1/3) constant is smaller than the L = alat constant by a factor of 2^(1/3).


Thanks again and have a nice day!

Sincerely yours,

Jacob Williams
PhD Student, Yang group
Duke University Dept. of Chemistry
On Jul 17, 2020, 11:16 AM -0400, General discussion list for Quantum ESPRESSO developers <developers at lists.quantum-espresso.org>, wrote:

It is because one can adopt  different definitions of the length parameter L, the cubic root of the cell volume, the length of the lattice vectors, the side of the corresponding cubic cell.
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.quantum-espresso.org/pipermail/developers/attachments/20200720/61c2de86/attachment.html>