Vacuum spacing in 2D materials

Concerns issues with computing quasiparticle corrections to the DFT eigenvalues - i.e., the self-energy within the GW approximation (-g n), or considering the Hartree-Fock exchange only (-x)

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Laura Caputo
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Vacuum spacing in 2D materials

Post by Laura Caputo » Wed Sep 08, 2021 1:30 pm

Hello,

I'm going to calculate band gap corrections for 2D materials with GW. Since I need to converge the vacuum thickness, should it be enough to calculate the band gap taking into account small constant k point mesh for every vacuum thickness considered for the convergence to have feasible calculations?
Laura Caputo
Ph.D. Student
Université Catholique de Louvain
https://uclouvain.be/fr/repertoires/laura.caputo

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Daniele Varsano
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Re: Vacuum spacing in 2D materials

Post by Daniele Varsano » Wed Sep 08, 2021 1:57 pm

Dear Laura,

yes, you can perform tests out-of-convergence considering also that you do not have k points (and dispersion) in the direction orthogonal of the 2D plane.
Note that GW convergence with respect the vacuum is extremely slow, unless you use coulomb cutoff potentials (box, or ws in case you have an orthorhombic unit cell).
If you use the box, you should change the box_z value (slightly lower than your cell Lz size) for the different vacuum considered.

Best,

Daniele
Dr. Daniele Varsano
S3-CNR Institute of Nanoscience and MaX Center, Italy
MaX - Materials design at the Exascale
http://www.nano.cnr.it
http://www.max-centre.eu/

Laura Caputo
Posts: 88
Joined: Sun Apr 11, 2021 3:02 pm

Re: Vacuum spacing in 2D materials

Post by Laura Caputo » Wed Sep 08, 2021 1:59 pm

Hello,

Thank you for the very fast reply. I am just checking the vacuum using the truncated Coulomb potential and using slightly smaller box to respect to the 'true' cell parameter used, as explained in the yambo tutorials.

Thank you again!
Laura Caputo
Ph.D. Student
Université Catholique de Louvain
https://uclouvain.be/fr/repertoires/laura.caputo

Laura Caputo
Posts: 88
Joined: Sun Apr 11, 2021 3:02 pm

Re: Vacuum spacing in 2D materials

Post by Laura Caputo » Tue Nov 02, 2021 3:45 pm

Hello again,

I have done vacuum convergence test on my 2D systems (graphene doped with BN). Since the systems are quite large, I have used a simple 3x3x1 grid to convergence the vacuum thickness using the truncated Coulomb potential (on DFT I use a 9x9x1 and for GW calculations a grid of 18x18x1). As advised, I have used a slightly smaller box value compared to the cell parameter.
However, when I convergence the gap I have these values

7A 3,7696
8A 3,7686
9A 3,7671
11A 3,7607

Is it normal to have such small differences even when considering small vacuum values such as 7/8 Angstroms?
Laura Caputo
Ph.D. Student
Université Catholique de Louvain
https://uclouvain.be/fr/repertoires/laura.caputo

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Daniele Varsano
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Re: Vacuum spacing in 2D materials

Post by Daniele Varsano » Tue Nov 02, 2021 4:46 pm

Dear Laura,
I would say that the change are reasonable, ie not that big. However, please take into account that k point sampling in the plane affects the quality of the truncated potential.
In case your supercell is orthorhombic I suggest to use the cutoff "ws", but also there, there is a dependence on the used k point sampling in the plane.

Best,
Daniele
Dr. Daniele Varsano
S3-CNR Institute of Nanoscience and MaX Center, Italy
MaX - Materials design at the Exascale
http://www.nano.cnr.it
http://www.max-centre.eu/

Laura Caputo
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Joined: Sun Apr 11, 2021 3:02 pm

Re: Vacuum spacing in 2D materials

Post by Laura Caputo » Tue Nov 02, 2021 4:51 pm

Dear Daniele,

Thanks for your reply. Since the sampling on the plane affects the quality of the truncated potential, should I use larger sampling for the vacuum convergence or using such a small one is enough? What I did was firstly do the convergence of the vacuum with a small kpoint (3x3x1) and, after finding the converged thickness, I have done the convergence tests for the kpoints (along with of course all the other GW convergence).

Unfortunately, my supercell is not orthorhombic, I've read that the 'ws' cutoff could not be stable (or could not work) with non orthorhombic cell. Is it true?
Laura Caputo
Ph.D. Student
Université Catholique de Louvain
https://uclouvain.be/fr/repertoires/laura.caputo

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Daniele Varsano
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Re: Vacuum spacing in 2D materials

Post by Daniele Varsano » Tue Nov 02, 2021 4:59 pm

Dear Laura,

the k point grid affects the quality of the truncated coulomb potential:
1) In case of the box shape you have integrations over the BZ to calculate each single components of the potential
2) In case of ws you have wigner-seitz shape extending over a finite size supercell given by nk*alat

So, in both case the k points matters. We have developed a different technique to isolate 2D system allowing to greatly accelerate convergence of GW and BSE wrt k points, a paper will be submitted soon and then the algorithm will be released, but at the moment is not yet available.

My suggestion is to include enough vacuum (the double of your system dimension taking into account some spill out of the charge, e.g. 3-4 Angstrom) and then use a converged grid.
The you can verify that your vacuum is converged by performing another calculation with a smaller cell, bue keeping the same number of k points.

Best,
Daniele
Dr. Daniele Varsano
S3-CNR Institute of Nanoscience and MaX Center, Italy
MaX - Materials design at the Exascale
http://www.nano.cnr.it
http://www.max-centre.eu/

Laura Caputo
Posts: 88
Joined: Sun Apr 11, 2021 3:02 pm

Re: Vacuum spacing in 2D materials

Post by Laura Caputo » Tue Nov 02, 2021 5:08 pm

Dear Daniele,

Just to make sure, I guess the double of the dimension on the non periodic axis. So, I have a system that is formed by a planar sheet and used 10Angstrom for GW. I have done some calculations on the k point convergence and extrapolated the convergence band value since it required a very dense kpoint mesh.

To verify that the vacuum is enough, I should do the same calculation but with 9/8Angstrom?
Laura Caputo
Ph.D. Student
Université Catholique de Louvain
https://uclouvain.be/fr/repertoires/laura.caputo

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Daniele Varsano
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Re: Vacuum spacing in 2D materials

Post by Daniele Varsano » Tue Nov 02, 2021 5:15 pm

Dear Laura,
To verify that the vacuum is enough, I should do the same calculation but with 9/8Angstrom?
Yes, that's what I meant.

Best,
Daniele
Dr. Daniele Varsano
S3-CNR Institute of Nanoscience and MaX Center, Italy
MaX - Materials design at the Exascale
http://www.nano.cnr.it
http://www.max-centre.eu/

Laura Caputo
Posts: 88
Joined: Sun Apr 11, 2021 3:02 pm

Re: Vacuum spacing in 2D materials

Post by Laura Caputo » Tue Nov 02, 2021 5:23 pm

Just one last question: if I used an extrapolation for calculating the value of the band gap, should I use the densest kpoint mesh for confronting the gap values at 8A...10A? For each system with different z values, should I use the same number of bands, EXXRLvcs etc.?

I did this calculation for 9A and 10A obtaining as difference between the gaps 0.01eV, could this be considered converged?
Laura Caputo
Ph.D. Student
Université Catholique de Louvain
https://uclouvain.be/fr/repertoires/laura.caputo

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