Query Regarding K-Point Dependence of GW0 Band Gap

[alok_shukla1]

Dear Experts,

I am calculating the band gap of a 6-atom heterostructure using the GW0 method in VASP. I am currently checking the convergence of the calculated band gap with respect to the k-point sampling.

However, I find that the GW0 band gap changes significantly when I change the k-point mesh. The band gaps I obtained are:

k-point mesh GW_0 band gap (eV)
6*6*1 2.2066
7*7*1 2.4651
9*9*1 2.1481
11*11*1 2.0854
15*15*1 2.0610
17*17*1 1.79
21*21*1 2.0006

As can be seen, the band gap does not show a clear convergence trend with increasing k-point density. The system contains only 6 atoms, but the GW0 calculations are computationally expensive. With my available computational resources, a 21*21*1 mesh is approximately the maximum k-point density that I can practically use.

I would therefore like to ask whether there may be something in my calculation setup that I should check or modify.

I have attached my POSCAR and INCAR files. I need suggestions to obtain a reliable GW0 band gap.
https://drive.google.com/drive/folders/ ... drive_link

[christopher_sheldon1]

Dear alok_shukla1,

Thank you for your question. I cannot access your Google Drive. Could you attach the files here so that I can read them? Or permit me to access the Google Drive.

At a glance, it looks like the 17x17x1 step is out of step with the series, so I'd check to see if anything has gone wrong there.

Best wishes,

Chris

[christopher_sheldon1]

Could you also upload the OUTCAR files? This will help to diagnose the problem.

Best,

Chris

[alok_shukla1]

Dear Chris,
Yes, files are uploaded. Please check.

[christopher_sheldon1]

Dear Alok,

Thank you. I try to repeat the calculations and see if I can find out what has been going on.

Best wishes,

Chris

[alok_shukla1]

Dear Chris,
Did you find anything? It would be helpful if you could please share.

[christopher_sheldon1]

Dear Alok,

17x17 being out of place is due to it not including the high-symmetry K point in you k-point mesh. This is the point where the valence band minimum is (VBM). Without K, you find the gap at a nearby point, and increase it, hence 7x7 being so large. These are the Gamma, M, K, and K' high-symmetry points in the following k-meshes:

Mesh Γ M K, K′
3×3 yes no yes
6×6 yes yes yes
7×7 yes no no
8×8 yes yes no
9×9 yes no yes
10×10 yes yes no
11×11 yes no no
12×12 yes yes yes
14×14 yes yes no
15×15 yes no yes
17×17 yes no no
18×18 yes yes yes
21×21 yes no yes

Since the VBM is at K, being a hexagonal cell, you need to converge this with a k-mesh that is a multiple of 3, i.e., 3x3, 6x6, 9x9. This gives me the following trend:

gap_vs_kmesh_3n.png

So it converges more smoothly. Mine are G0W0 tests but the same is true for GW0, as you can see in your results (green line).

I can't find any specific issue with the 17x17, but it does not include the K point, so does not look at the VBM directly. I'd need the files of the other calculations to try to understand better. Let me know if this answers your question. Sorry about the delay, the calulations took a while.

Best wishes,

Chris

[alok_shukla1]

Dear Chris,

Thank you for your response and for sharing your results. They are very helpful.

Following your suggestion, I performed single-shot G0W0 calculations using 18*18*1 and 21*21*1 k-point meshes, both of which are multiples of 3. I obtained band gaps of 1.776 eV and 1.751 eV, respectively. However, for the 18*18*1 mesh, your reported value is approximately 1.81 eV.

As per the literature survey, your result appears to be somewhat closer to the reported fundamental gap than mine.

For my calculations, I used optB86b-vdW for structural relaxation. Since optB86b-vdW is not directly supported in the standard G0W0 workflow. Therefore, after taking the CONTCAR from the relaxation step, I removed optB86b-vdW from the SCF and from the rest of the steps.

Also, should I need to use GW-specific PAW datasets (the '_GW' POTCAR files) for the G0W0 calculations? Could the choice of PAW potentials or any other computational settings be responsible for the difference in the calculated band gaps?

If possible, could you please share your input files, particularly the INCAR settings and POTCAR dataset information, so that I can compare the computational setups and better understand the discrepancy?

Thank you again for your time and help.

Best regards