You likely have to derive the Kohm–Sham equations and solve them for the wavefunction solutions (and look into the WIEN2k source code) for the detailed answers to your questions. I haven't done it myself, so I cannot help you there. I think the go to references for that were:

Planewaves, Pseudopotentials and the LAPW Method by David J. Singh and Lars Nordström [ ]

My attempt at general answers:

No parameters are monitored to make the 2 densities equal. As seen on slide 21 of , there are two equations, one for Psi_up and one for Psi_down, but for the non-spin polarized case both equations are the same such that Psi_up = Psi_down = Psi. So only one equation for the wavefunction Psi needs to be solved for. As seen on slide 66 in , the calculation is given an initial charge density (during init_lapw), then the charge (and spin) density should be computed from the self consistent field (scf) cycles (run_lapw).

On the other hand, the spin-polarized calculation (runsp_lapw) has to solve two separate equations instead of one as shown on slide 24 in rolask_rela.pdf. Which is why for example there is lapw1 -up and lapw1 -dn for the spin-polarized calculation and only just lapw1 for the non-spin polarized. The simplified equations it uses for the spin-polarized case was made possible by choosing the z-axis for the direction of the magnetic field [ Ab Initio Study of NiO-Fe Interfaces: Electron States and Magnetic Configurations by L. D. Giustino, (page 24) ].

The Bef term is crossed out on slide 21, so there should be no exchange magnetic potential Bxc, since Bef = Bext + Bxc (from slide 19). However, whether Bef term is not there or how the Bef term is set to 0, I don't know and someone else might; I didn't look into the source code to try to determine that.

On 10/19/2016 5:18 PM, Abderrahmane Reggad wrote:

Thank you Dr Gavin for your reply and also for your interesting for my questions.

I have checked the 2 presentations but I didn't find what I look for .

It's mentionned that in non spin-polarized calculation the spin-up density = the spin-down density . Which parameters are they monitored to make these 2 densities equal. I have read that in this case the exchange magnetic potential will be equal to zero. I want to know if it's so or not .

Best regards
Mr: A.Reggad
Laboratoire de Génie Physique
Université Ibn Khaldoun - Tiaret
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