nanowire system and coulomb cutoff

[asanchez]

Hi all,

I'm trying to obtain the GW corrected band gap for a nanowire (1D) system. I'm having trouble converging the coulomb cutoff box. I've read around all posts I could find on the subject but still can't seem to figure out what I'm doing wrong.

I've converged k-points, EXXRLvcs, BndsRnXp, NGsBlkXp, GbndsRnge & RandGvec in that order. I didn't vary the number of points in the RIM and just used the default 1000000. I also haven't tried increasing the number of bands on my scf calculation (quantum espresso). My system has 56 occupied bands and I'm calculating the first 100 (probably need more? Haven't done convergence tests on that).

In order to finish convergence tests faster, I'm only using parameters that get me convergence of around <30-50 meV (except for RandGvec for which I'm using 1 RL, and k-points, for which I'm using the fully converged value)

I'm currently struggling with the coulomb box as I can't seem to get a converged value. My wire is oriented along the X direction, and its size along Y/Z is around 17/14 angs. I've set 20 angs of vacuum in the SCF to avoid interaction with periodic images (initially had 10, then moved to 20 to see if it'd be easier to converge the coulomb cutoff box). This makes my cell 37/34 angs in the Y/Z directions.

According to what I've read around in other posts I initially set my input file as follows:

CUTGeo = "box yz"
% CUTBox
0.0 | 35.0 | 32.0 |
%
which means my box is inf x 35 x 32 a.u. ( inf x 18.5 x 16.93 angs), so about half my cell size. I've then varied the box size in 2 a.u. steps in both directions (making it bigger / smaller) and bandgap values vary 25-90 meV between consecutive steps.

I'd appreciate any help with this matter as I can't seem to figure out what I'm missing.

Thanks in advance.

*EDIT: I'm getting increasing values for the bandgap from 1.83 eV for a box size of 21 a.u. along the Y direction to 2.34 eV for a size of 39 a.u.

[Daniele Varsano]

Dear Alfonso,

We noticed that the cutoff coulomb potential can have problems in some cases, I'm actually now working on that and hopefully in the next release of the code it will be largely simplified.

Anyway, looking at your post, there is some problems in your input setup.

First the cutoff box dimension. It is not documented, but it is written in several posts: there is a factor 2 missing in the definition of the cutoff side. If you want to cut beyond 30 au, you need to put 60 au in input. Sorry for that, this is something we need to fix or document, but as I told you I'm thinking about a huge reorganization in this part of the code for the next release.
A reasonable value of the cutoff side is to set it nearly as the size of your supercell, ie around 68 au.
A box size 21, it means that your density interact up to 10.5 au, ie you are cutting interaction between electrons inside your system. So it is not surprising that you have big variation going from 21 to 39. What you should verify is that considering values around that values (let's say 65-69 for the y direction) your gap is stable.

Next, not related with the coulomb cutoff:

My system has 56 occupied bands and I'm calculating the first 100 (probably need more? Haven't done convergence tests on that).

Yes, it is highly probable you need more bands, considering 56 bands occupied.

# Sx RL components : 12611

May be you have tested it, anyway it could be raised, does not cost too much, considering you have a total number of G in the wfs of 164209

% BndsRnXp
# | 41 | 72 | # [Xp] Polarization function bands
# | %

Discarding the occupied bands in the screening it is very dangerous, it is reasonable when calculating absorption spectra, but more delicate when calculating the screening, as you need also the real part of the epsilon matrix.

% GbndRnge
# | 41 | 72 | # [GW] G[W] bands range
# | %

This is even more dangerous, as this account for a closure relation sum_i |i><i|=1 so you need to consider all the occupied bands. Note next that the QP levels will converge very slowly with respect this parameter, but if you are interested in the gap (so differences between qp energies) it converge faster even if it is always quite slow.

Hope it helps.

Daniele

[asanchez]

Dear Daniele,

First the cutoff box dimension. It is not documented, but it is written in several posts: there is a factor 2 missing in the definition of the cutoff side. If you want to cut beyond 30 au, you need to put 60 au in input. Sorry for that, this is something we need to fix or document, but as I told you I'm thinking about a huge reorganization in this part of the code for the next release.
A reasonable value of the cutoff side is to set it nearly as the size of your supercell, ie around 68 au.
A box size 21, it means that your density interact up to 10.5 au, ie you are cutting interaction between electrons inside your system. So it is not surprising that you have big variation going from 21 to 39. What you should verify is that considering values around that values (let's say 65-69 for the y direction) your gap is stable

Thanks for the clarification. I had read about the factor of two but was confused about it.

# Sx RL components : 12611

May be you have tested it, anyway it could be raised, does not cost too much, considering you have a total number of G in the wfs of 164209

Yes, this corresponds to 7Ry, the converged value I got is actually 15 Ry, but have been working with 7 Ry to speed things up a bit during convergence tests for other parameters (although I have noticed increasing is computationally cheap)

% BndsRnXp
# | 41 | 72 | # [Xp] Polarization function bands
# | %

Discarding the occupied bands in the screening it is very dangerous, it is reasonable when calculating absorption spectra, but more delicate when calculating the screening, as you need also the real part of the epsilon matrix.

% GbndRnge
# | 41 | 72 | # [GW] G[W] bands range
# | %

This is even more dangerous, as this account for a closure relation sum_i |i><i|=1 so you need to consider all the occupied bands. Note next that the QP levels will converge very slowly with respect this parameter, but if you are interested in the gap (so differences between qp energies) it converge faster even if it is always quite slow.

I thought you needed to “open a window" around the bands you're interested in. Thanks again for making this clear.

I tried running 65/67/69 a.u. boxes and the resulting gap seems quite stable

Thanks for your help!