How to align the HSE and PBE average potentials

[eariel99]

I want to obtain the G0W0@HSE eigenvalues and align them with respect to PBE Kohn-Sham eigenvalues. The problem is that the eigenvalues are given with respect to the average electrostatic potential and this is different in HSE and PBE, but it is set to zero. So I looked at the average electrostatic potential at the core. My first test was
to obtain the core average potentials with PBE and HSE, in both cases with the SAME charge density. I used ALGO=None and read the same WAVECAR in both runs. Therefore, the charge density is the same and the electrostatic potential must be the same. However I get quite different values:


HSE:
emenendez@paniri:~/CdTe-GW/Serie4/Alineamiento$ grep -A3 core OUTCAR |tail -4
average (electrostatic) potential at core
the test charge radii are 1.1405 1.1897
(the norm of the test charge is 1.0000)
1 -62.9889 2 -86.8225


PBE:
emenendez@paniri:~/CdTe-GW/Serie4/Alineamiento$ grep -A3 core PBE/OUTCAR. |tail -4
OUTCAR.AlgoEigenval OUTCAR.cargaHSE OUTCAR.scfPBE
emenendez@paniri:~/CdTe-GW/Serie4/Alineamiento$ grep -A3 core PBE/OUTCAR.cargaHSE |tail -4
average (electrostatic) potential at core
the test charge radii are 1.1405 1.1897
(the norm of the test charge is 1.0000)
1 -68.8753 2 -90.7112

In both calculations I use ISTART=1, ISMEAR = -2, ALGO=None and read the same WAVECAR. The difference between INCAR's is
emenendez@paniri:~/CdTe-GW/Serie4/Alineamiento$ diff INCAR PBE/INCAR
38,39c38,39
< LHFCALC = .TRUE. ; HFSCREEN = 0.2
< AEXX = 0.250
---
> # LHFCALC = .TRUE. ; HFSCREEN = 0.2
> # AEXX = 0.250
42c42
< PRECFOCK = Fast ! used
---
> # PRECFOCK = Fast ! used

Hence, I can't underestand why obtain different core average potentials .