Degeneracy breaking at Gamma point in cubic ZrO2 scGW calculations with PAW

Dear moderators,

I am trying to perform GW calculations in cubic ZrO2 system (space group n°225). I am using both, NCPP and PAW data sets from Pseudo-Dojo (particularly NC SR ONCVPSP v0.4.1 and PAW JTH v1.1 with XC=PBE and Accuracy=Standard, for Zr and O atoms. When using NCPP, I have been able to carry out perturbative G0W0, partially self-consistent GW0, model QSGW and in all cases, applying self-consistency on energies only or energy plus wave-functions. The symsigma flag is set to 0 in all cases where self-consistency on wave-functions is required, and in G0W0 calculations I have checked results with symsigma equal 0 and 1. For every case aforementioned, the QP energies of the lower conduction levels at the Gamma point match the degeneracy of having two equal lowest d(e_g) levels and three higher d(t_2g) levels corresponding to Zr d empty orbitals, same situation occurs with valence QP levels, which are triply degenerate oxygen p states (this feature is obtained in calculations at plain PBE level too). Convergence is attained after 5-6 iterations. Wannierization procedure after different schemes yields a fairly reasonable band structure using prtwant=3, with wave-functions showing a very small Im/Re part ratio.

On the other hand, I have tried to perform the same calculations with PAW and when symsigma=0 this degeneracy at the Gamma point is broken. I was able to check that the only case where degeneracy holds is when symsigma=1 in a perturbative G0W0 calculation is done. A G0W0 with symsigma=0 fails, the same as any calculation involving self-consistency on wave-functions. Particularly in a model QSGW, the fundamental gap of the system oscillates between two values and convergence is far from being reached after 6 iterations. Wannierization in these cases was not successful. The average of the QP energies of the degenerate states at Gamma when symsigma=0, equals each of the QP energies of the degenerate states when symsigma=1.

I am attaching input, output and log files of a reference G0W0 calculation with NCPP, and two calculations with PAW with symsigma=0 and 1 values. I thank you in advance any orientation you could provide me about this matter.

Kind regards,

zro2_PAW_symsigma1.txt (1.0 MB)

zro2_PAW_symsigma0.txt (1.2 MB)

zro2_NCPP_symsigma0.txt (1.6 MB)

Dear Juan,

The PAW implementation of GW in ABINIT is not super safe.
The breaking of degeneracy is something I observed in the past and there is no solution to this as of today.

We plan to work on this in the forthcoming year.

In the meantime, I strongly advise you to just rely on the norm-conserving pseudopotentials.
Best,

Fabien

Dear Fabien,

Thank you very much for the reply and advice. I will stick to NCPP calculations for the time being and I will be alert to any update of the subject.

Best regards,