BSE, QP interpolation from a coarser grid

[ff10]

Dear all,

I would like to confirm if the following procedure is the correct approach to converging BSE calculations with respect to k-points.

I have a fully converged G0W0-PPA calculation with 12x12x1 k-points for a 2D material. I perform BSE calculations on top of this G0W0-PPA calculation (without QP) to converge the necessary parameters. After having all parameters converged, I calculate the absorption spectrum with QP and extract the excitonic energies for the main peaks.

The final step involves converging the BSE calculation with varying numbers of k-points. Here's what I did:
I initiated new Quantum Espresso (QE) calculations using the same parameters as the 12x12x1 calculation but with finer k-point grids, such as 15x5x1, 18x18x1, 21x21x1, and so on. For each of these new calculations, I computed the static screening using the previously converged parameters from the G0W0-PPA calculation with 12x12 k-points and used BSEBands, BSENGblk, BSENGexx that were previously determined during the BSE calculations with 12x12x1 k-points. Finally I include the QP (ndb.QP) obtained from the G0W0-PPA calculation with 12x12x1 k-points to calculate the absorption spectrum with QP and extract the excitonic energies for the main peaks.

I check whether the main peaks (excitonic energies) are close to each other and check the convergence from there.

Is this the correct procedure to converge the BSE calculations with respect to k-points, ?

[claudio]

Dear Fabio

this procedure should work without problems.
My advice is to first test the interpolation on the independent particle optics (yambo -o c -V QP) and then on the BSE.
Notice that there are two ways to interpolate QP:

XfnQP_DbGd_INTERP_mode= "NN"
(nearest neighbor)
that take the value of the nearest k-point

XfnQP_DbGd_INTERP_mode= "BOLTZ"
that use smooth Fourier interpolation, I advice you this approach
Warren E. Pickett, Henry Krakauer, and Philip B. Allen, Phys. Rev. B 38, 2721(1988)

best
Claudio

[sdwang]

Dear Claudio,
I have a similar question about the interpolation of QP when performing the BSE calculation: if we set the
XfnQP_DbGd_INTERP_mode= "BOLTZ"
in the BSE process, does that mean we can use the previous converged QP energies without considering the different number of K-point settings between GW and BSE?

Thanks!

Shudong

[claudio]

Dear Shudong

yes, you can use a QP database with different number of k-points and interpolate it

best
Claudio

[ff10]

Dear Claudio,

Thank you for your answer.

I have another question regarding the BSE calculation.
My GW-PPA band gap energy was converged within a threshold of 0.05 eV.
After that I converged my BSE calculations by looking at the first peaks of the absorption energy. I am getting the following excitonic energies:

Code: Select all

#    Maximum Residual Value =  0.23106E+00
#   
#    E [ev]             Strength           Index
#
     1.87987232        0.356577747E-1      1.00000000
     1.8830993         0.26507793E-09      2.0000000
     1.88651371        0.355634466E-1      3.00000000
     1.9339713         0.11919403E-09      4.0000000
     2.02341580        0.112938505E-5      5.00000000
     2.02754021        0.247319072         6.00000000
     2.02855229        0.246239379         7.00000000
     2.03071284        0.894167673E-8      8.00000000
     2.14275789        0.358490361E-3      9.00000000
     2.14660287        0.244623561E-5      10.0000000
     2.14787173        0.230103524E-5      11.0000000
     2.14989352        0.359145342E-3      12.0000000
     2.20504546        0.870284811E-2      13.0000000
     2.2088418         0.65820632E-09      14.000000
     .....
     

It seams that, for instance, the first three excitonic states are degenerate when considering the first decimal place, possibly comprising two bright states and one dark state.
Similarly, excitons with indices 5-8 also appear to be degenerate, with two bright states and two dark states.
Excitons with index from 9 to 12 also seem degenerate, but their strengths are weak, so I assume that they are dark.

Is it normal that, considering this set of excitons (1, 2, 3), (5, 6, 7, 8), and (9, 10, 11, 12) as degenerate, the exciton energies differ in the second decimal place?
For example: 1 -> 1.88 eV, 2-> 1.88 eV, 3->1.89 eV


Thanks.

[claudio]

Dear Fabio

>Is it normal that, considering this set of excitons (1, 2, 3), (5, 6, 7, 8), and (9, 10, 11, 12) as degenerate, the exciton energies differ in the second decimal place?
>For example: 1 -> 1.88 eV, 2-> 1.88 eV, 3->1.89 eV

you analysis is reasonable. In order to understand how many degenerate exciton you should expect, you should use group theory,
you can have an idea of this kind of analysis in Appendix B of https://arxiv.org/abs/2211.12241
and books cited there

best
Claudio