Gap convergence with vacuum space between layers

[Fabiof]

Dear all,

I'm doing some small PPA calculations without truncation to study how the 2D h-Boron Nitride gap changes with the vacuum space between layers. And i got the following results:

Vaccum distance (Bohr) Gap (eV)
20 4.72
45 5.52
70 5.82
100 5.99
150 8.57
200 10.32
250 12.12


As you can see the gap increases a lot between 100 and 250 Bohr. This is not supposed to happen right?
I was hopping to see some convergence, which is happening between 20 and 100 Bohr. But after that the gap variation is very large. Do you know what this is happening?



Fabio

[amolina]

Dear Fabio,

indeed the gap for 150, 200 and 250 is too different from the values for smaller separation.

Assuming that the non-selfconsistent calculation are OK, maybe some parameters as BndsRnXp or the ecut change when increasing the vacuum. Try to converge the parameters for each distance. I hope it helps.

Alejandro.

[Daniele Varsano]

Dear Fabio,
No I think it should not happen.
What I think it is happening here is that the calculations having a lot of vacuum have not the same "degree" of convergence of the first values.
Here some possibility for the strange behaviour:

In your input file NGsBlkXp is assigned in Ry and it is ok, as the cell increase you will need more G vectors to have a sphere of 4Ry. EXXRLvcs instead is given
in absolute RL number, which correspond at different energy cutoff in the different cells: |G^2|/2 < E_cut.
Anyway this is a huge number, most probably the problem is in the number of bands included in BndsRnXp and GbndRnge, in a suopercell having 20au vacuum or 250 vacuum they do span
avery different if electron-hole energy and in the big supercell you will need a much bigger number of bands to cover the same energies (check in the report file the last KS energy for the different cases).
Last think, when changing the size of the supercell you are changing your Brillouin zone, becoming more and more irregular or better stretched. May be the RIM method could help in better evaluate the BZ integrals.
I think that if you separately the convergence with respect the vacuum of the exchange self energy (HF or nlXC in the report) and the correlation part you can understand where the problem come from.

Best,
Daniele

[Fabiof]

Dear Alejandro and Daniele,

Thanks for the answers.

You are saying that for sypercells with big vacuum space i have to increase the number of bands included in BndsRnXp and GbndRnge to cover the same energies of supercells with less vacuum space.

I tried to see what happens if i increase the number of bands of BndsRnXp and GbndRnge for supercell with vacuum distance of 100 and 150 Bohr letting the NGsBlkXp and EXXRLvcs fixed .

But there is no big changes in the values of gap. It seems that for the fixed value of NGsBlkXp and EXXRLvcs, the gap is converged already converged for the initial number os bands (100) that i used.


Fabio

[Daniele Varsano]

Dear Fabio,
if you plot separately the behaviour of Sigma_x (HF) or nlXC, and Sigmac (So) it can help to spot the problem.
Best,

Daniele

[Fabiof]

Dear Daniele,

For what i see, the problem is in the nlXC. Valence bands have diferente nlXC energies for different vacuum distances (but the differences in nlXC energies between the valence bands are almost equal for the difference vacuum distances).

But for conduction bands the nlXC energies are almost the same for different vacuum distances. So the transition energy from the last valence band and first conduction band is greater for a greater vacuum distance.


So the only way to solve this problem is to use RIM method with truncation in z?



Fabio

[Daniele Varsano]

Dear Fabio,
I'm not sure I understood your post. Can you post a couple of report files to show the problem?
Best,
Daniele

[Fabiof]

Dear Daniele,

I studied the convergence of the nlXC and So energies with the increase of vacuum distance as you suggested to understand where the problem como from.

What i saw is that the nlXC energies are almost equal for the conduction bands for different vacuum distances, but they are different for the valence bands. This means that the nlXC gap will be different for different vacuum distances, so that is why i think the problem is coming from the nlXC energies.

Data from c=20 and c=70 Bohr n=4 last valence band n=5 first conduction band:

c=20 Bohr
n nlXC
1 -20.08
2 -15.18
3 -14.55
4 -14.85
5 -2.910
6 -2.434
7 -4.567

c=70 Bohr
n nlXC
1 -21.13
2 -16.23
3 -15.60
4 -15.90
5 -2.917
6 -2.429
7 -4.603


The conduction band energies (5,6,7) have the same energy for c=20 and c=70, but the valences dont.

I don't know if this is really the source why the gap is increasing with the vacuum distance, but i don't see other explanation.


Fabio

[Daniele Varsano]

Dear Fabio,
can you please post the report file of these two calculations in order I can have a look to some details?
You can zip them and upload as attachment.

Best,
Daniele

[Fabiof]

Dear Daniele,

I had to repeat the calculations because i deleted the report files.

And perhaps what i said above is not valid because i was just referring to the seventh k_point.

Fabio