HF Parameters for defects in GaN

[blair_tuttle]

I recently started a project to investigate point defects in GaN. I have been unable to reproduce the hyperfine parameters from previous calculations [PRL 109, 206402 (2012)]. Specifically, my spin density values are much more delocalized especially when taking core polarization effects into account. Attached are the calculations and a summary doc. please advise.

[blair_tuttle]

For more context, the author of the previous HF calculations [PRL 109, 206402 (2012)] mentioned that a relativistic expression for the HF parameters needs to be used for scalar relativistic pseudopotentials. I am not sure how this effects PAW results.

[alexey.tal]

Dear blair_tuttle,

Thank you for your question.

Indeed, I see that the values reported in [PRL 109, 206402 (2012)] differ from the ones you find with VASP. However, I found some traces of HSE calculation in you INCAR, i.e., HFSCREEN = 0.2. But on the other hand you use LHFCALC=.FALSE.. After looking at the paper I can't tell if the results you use as a reference are produced with PBE or HSE. As far as I know, the choice of xc functional can largely affect the hyperfine tensor calculation (see Szász et al., Phys. Rev. B, 075202 (2013)). That would also explain why the spin density is much more delocalized in your case as the PBE tends to delocalized the charge density compared to hybrid functionals. Are you sure that it is the PBE values you are using as a reference and not HSE?

Kind regards,
Alexey

[blair_tuttle]

the tests I presented are for PBE calculations because the 2012 PRL used PBE. However, I have performed both HSE and PBE calculations, which is why the INCAR file has some HSE flags. i assume that using LHFCALC=.FALSE. nullifies the HFSCREEN = 0.2 flag. BTW, the PBE and HSE VASP results are very similar and differ from the 1012 PRL and experiment. The main difference i see between my VASP and the 2012 PRL is that the latter used norm-conserving pseudopotentials and a larger PWQ cutoff. They mentioned the need for a relativistic formula for HF parameters but i did not see any mention of such a formula in the VASP manual. thanks for any help to explain this VASP error.

[alexey.tal]

Could you please share the OUTCARs from the HSE calculations? I don't know yet what causes this discrepancy but I will looking into it.

[blair_tuttle]

Attached is tar file showing PBE and HSE OUTCAR files for the same POSCAR with 299 atoms and with NSW = 0.

[blair_tuttle]

see attached. HSE is more localized than PBE but the 2012 PRL used PBE so why does VASP PBE perform so differently.

[alexey.tal]

Thank you.

PBE and HSE VASP results are very similar and differ from the 1012 PRL and experiment.

I'm a bit confused because I see that the HF parameters from the HSE calculation differ quite substantially from the PBE results.
What results did you find very similar between PBE and HSE?

Here is Total hyperfine coupling parameters from PBE (left) and HSE (right):

Code: Select all

  52     -27.118   -22.872   -27.461      -0.155          |    52     -98.393   -89.829  -101.906      -0.084
  53      -2.641    -2.312    -2.767      -0.119          |    53      -0.646    -0.418    -0.719      -0.317
  54      -1.184    -0.612    -1.251      -0.457          |    54      -2.564    -1.239    -2.659      -0.498
  55     -27.118   -22.872   -27.461      -0.155          |    55     -98.337   -89.730  -101.850      -0.085
  56      -2.641    -2.312    -2.767      -0.119          |    56      -0.648    -0.420    -0.721      -0.316
  57      -0.331    -0.221    -0.337      -0.325          |    57      -0.009     0.002     0.160       0.067
  58      -1.833    -1.646    -1.916      -0.097          |    58      -2.529    -2.270    -2.753      -0.094
  59      -1.077    -1.003    -1.099      -0.067          |    59      -0.234    -0.151    -0.257      -0.321
  60      -0.326    -0.303    -0.344      -0.066          |    60       0.034     0.025     0.075      -0.119
  61      -0.463    -0.324    -0.515      -0.271          |    61      -0.383    -0.259    -0.451      -0.275
  62      -0.443    -0.429    -0.466      -0.028          |    62       0.059     0.043     0.078      -0.201
  63      -0.326    -0.303    -0.344      -0.066          |    63       0.034     0.025     0.075      -0.119

[alexey.tal]

Also, did you compare your band gaps to the ones reported in the paper with PBE and HSE? If there is a discrepancy in the band gaps, it could indicate that something else in these calculations is different, for example, lattice parameter or potentials.

[alexey.tal]

To be sure that we are comparing the same HF values I repeated the PBE calculation with QE using the structure you provided and I got very similar results to the ones in the paper. So that eliminates much of the ambiguity and makes the comparison between the codes much more straightforward.

Now regarding your question about relativistic effects in the hyperfine tensor calculations. In QE I get this output:

Code: Select all

ISOTROPIC (FERMI-CONTACT) COUPLINGS WITHOUT ZORA:

However, in VASP we include ZORA by default. When I disable ZORA in VASP, the HF parameters increase substantially (~ 10MHz), but the VASP values are still much lower compared to the QE results.
So right now it looks like the Fermi-contact term strongly depends on the way one extrapolates the all-electron one-center spin-density onto the nuclei. We are going to test different PAW potentials to see how sensitive the results are to the choice of the potential.
I will let you know when we understand better what else contributes to this discrepancy.

[blair_tuttle]

Thanks for the news. When you write that you get the "same results as the paper." Do you mean my paper summarizing my PBE results or do you mean the 2012 PRL paper? If you meant the latter, can you tell me the difference in INCAR/POTCAR that leads to differences between my PBE and your PBE results?

[alexey.tal]

With QE I got similar HF to the ones reported in the 2012 PRL paper. The values I got with QE are around 65 MHz and the values in the paper are around 67-70 MHz for the Ga vacancy.