BSE for CNTs - w/ and w/o cutoff

[wachr]

Dear yambo developers,

I have questions concerning the usage of the random-Integration-method (RIM) (w/ and w/o Coulomb-cutoff) for the optical spectrum of CNTs in the BSE-framework. My goal is to calculate absorption spectra of CNTs as well as excitonic binding energies.

It has been shown and intensively discussed that the Coulomb-cutoff is important for GW for low-D-systems to prevent unphysical supercell-supercell-interactions. In my understanding, that should be necessary for BSE-calculations, too. However, when I perform a supercell-convergence-test with different unit cells (ranging from 13 to 23 Angstrom size using 1x1x40 kpoints = 20 irred. kpts), the peaks w/o cutoff seem to be pretty stable whereas including the cutoff, they shift a lot (see figure below). For the GW-results of the same system, this behaved the other way round - as I/we expected and results with Coulomb truncation and with RIM are preferred.

As the k-mesh is maybe not fully converged, yet, I want to perform calculations of refined k-meshes, 1x1x100 (50 irred. kpts) and 1x1x200 (to get spectra with more features and to know, if the peaks shift wrt. kpts). These calculations converge easily w/ RIM and w/ Coulomb cutoff - but w/o RIM, they do not (which is understandable, after a thorough reading of your RIM-documentation - it is even surprising that the 20 kpts calculations look reasonable).

To investigate the influence of the Coulomb cutoff, only, I set up calculations w/ RIM and w/o Coulomb-cutoff. Surprisingly, the peaks are even more blue-shifted w/o Coulomb cutoff than w/ Coulomb cutoff.

So my questions:
1) Is the combination BSE + RIM tested? Is this recommended?
2) What could be the origin of the strong difference between the more robust results w/o RIM compared to the less robust ones w/ RIM?
3) And why is w/ RIM + w/o Coulomb cutoff even farther from the no-cut/no-rim spectra than w/ RIM + w/ Coulomb cutoff?

I think that these questions are interesting for everybody who deals with low-D-systems and BSE. Btw, I have not seen literature results on CNTs including BSE applying the Coulomb cutoff method. That's why this is interesting for us.

Thank you very much!
Christian

I appended the inputfiles and the outputfiles - including the results. Two more figures are following in the next post. In this figure, straight lines are w/ RIM & Coulomb cutoff whereas dashed lines are w/o RIM and w/o Coulomb cutoff.

P.S. minor edit for better understanding. Another edit to upload input files.

80_CNT_BSE_unit_cell.png

[wachr]

The other figures:

80_CNT_BSE_comparison.png

80_CNT_BSE_20vs50_kpts.png

[Daniele Varsano]

Dear Christian,

Reduced dimensionality calculations are always tough, slow convergence with respect vacuum, problem in the Bz integrations, not well defined quantities as epsilon etc ...

Anyway let me clarify some points:

1) When using 1D (or 2D) calculation you have divergencies of the coulomb potentials near gamma (as 1/q^2) does not converge in less than 3D, and performing integrals as \int V(qi) ~ V(qi)*Vol(qi),( as yambo does for 3D system and also here if you do not specify RIM of CUT) brings to divergences. This is not evident for coarse grids (indeed you meaningful results of 20k sampling), but when increasing k-points, so sampling q points near gamma (gamma itself is regolarized), this became evident: you can look at your spectrum without RIM and cutoff with 50kpt which is meaningless. So for non 3D system the RIM is mandatory and you should may be repeat your test vs volume by including the RIM. The fact you have good results with the 20 kpt without rim and without cutoff is somehow fortuitous, or at least it is impossible to understand if it is converged as for more k points divergences are evident.

2) Cutoff: what is disturbing is such big variation of the spectra wrt volume when the cutoff is used. It should not depend that much. Anyway the RIM and the CUTOFF are exclusive, does not make sense to use both (beside the case BOX where the RIM is used to calculate the cutoff coulomb potential component), and the code should use the cutoff if present.

From the last figure you posted I can see that comparing the two calculation done with cutoff they are more or less converged wrt k points. The case without cutoff with rim is a little bit at higher energies (here you could check what happen increasing volume, if thinks are working properly the RIM results should somehow converge to the cutoff results, very strange anyway the huge variation with respect the volume of the cutoff potential).
The case without rim and cutoff is not trustable (as you saw increasing kpoints).


Usually the effect of the coulomb potential do compensate in GW and BSE, so if you apply the scissor consistently you arrive to more or less the same excitation energy, but of course different binding energy.

Alternatively you can try to use the box cutoff, just to test if the cylinder is failing for some reason: CUTGeo="box xy", in this case the RIM has to be activated and note that the size of the box you cut should be multiplied by 2 (internal reason), ie put it just a little bit smaller than your cell size.

In order to compare with the results of Katalin Spataru, check also the GW gap, in their work they do use a cylindrical cutoff very similar to the one used by yambo.

If you are able to converge the results wrt cell volume, they should be the more trustable but to my experience it is very hard, as increasing the volume, convergence parameters (G components, unoccupied bands) should be scaled consistently making the calculations unfeasible for very large cells.


Nowadays we are working on a different cutoff implementation, that should be more stable, hopefully it will be released soon.

Best,
Daniele

[wachr]

Dear Daniele,

first of all: Thanks a lot for your fast, clear and detailed answer!

Reduced dimensionality calculations are always tough, slow convergence with respect vacuum, problem in the Bz integrations, not well defined quantities as epsilon etc ...

Right, but it's also very exciting physics - at least, when things work .

1) When using 1D (or 2D) calculation you have divergencies of the coulomb potentials near gamma (as 1/q^2) does not converge in less than 3D, and performing integrals as \int V(qi) ~ V(qi)*Vol(qi),( as yambo does for 3D system and also here if you do not specify RIM of CUT) brings to divergences. This is not evident for coarse grids (indeed you meaningful results of 20k sampling), but when increasing k-points, so sampling q points near gamma (gamma itself is regolarized), this became evident: you can look at your spectrum without RIM and cutoff with 50kpt which is meaningless. So for non 3D system the RIM is mandatory and you should may be repeat your test vs volume by including the RIM. The fact you have good results with the 20 kpt without rim and without cutoff is somehow fortuitous, or at least it is impossible to understand if it is converged as for more k points divergences are evident.

Thanks for that detailed and concise explanation. That is very helpful!

2) Cutoff: what is disturbing is such big variation of the spectra wrt volume when the cutoff is used. It should not depend that much. Anyway the RIM and the CUTOFF are exclusive, does not make sense to use both (beside the case BOX where the RIM is used to calculate the cutoff coulomb potential component), and the code should use the cutoff if present.

OK, that was not clear to me - thanks for pointing that out. I got that CUTOFF-procedure from the forum - and as box-cutoff was discussed most of the times, I tried to combine RIM & CUTOFF. Thus, I will try using RIM, only. And box-cutoff, too. And hopefully, this behaves a bit more friendly.

The case without rim and cutoff is not trustable (as you saw increasing kpoints).

That's what I expected, too .

Usually the effect of the coulomb potential do compensate in GW and BSE, so if you apply the scissor consistently you arrive to more or less the same excitation energy, but of course different binding energy. [...]
In order to compare with the results of Katalin Spataru, check also the GW gap, in their work they do use a cylindrical cutoff very similar to the one used by yambo.

That's good news to hear. The GW gap agrees approximately - I extrapolated (1.85 +/- 0.1) eV from different convergence tests wrt. #bands, NgsBlkXd, etc. pp. - and Katalin Spataru had 1.75 eV.

Alternatively you can try to use the box cutoff, just to test if the cylinder is failing for some reason: CUTGeo="box xy", in this case the RIM has to be activated and note that the size of the box you cut should be multiplied by 2 (internal reason), ie put it just a little bit smaller than your cell size.

I will definitely try this - one of my last hopes to get converged spectra . Thanks for the instruction - reading through your Coulomb-cutoff-publication (Phys. Rev. B 73, 205119 (2006)), it somehow becomes clear why defining half the box for the cutoff makes sense. It's counter-intuitive for users .

Nowadays we are working on a different cutoff implementation, that should be more stable, hopefully it will be released soon.

This sounds promising! I wish you good luck!

Kind regards!
Christian