kpoint weight for BSE oscillator strength

[xiaoming_wang]

Hello,

From the line 1738 of bse.F:
"CTRANS=CTRANS+CDER_BETWEEN_STATE*AMAT(NCV13,LAMBDA)*WEIGHT"
it seems that the kpoint weight is not taken into account when calculating the oscillator strength.

Can the developer please help me confirm that?

Best,
Xiaoming

[henrique_miranda]

Dear Xiaoming,

The BSE kernel is built in the full Brillouin zone so the weight is the same for all the oscillator strengths.

Cheers,
Henrique Miranda

[xiaoming_wang]

Hi Henrique,

Thanks for your reply. Right after the oscillator strength, when calculating the dielectric function EPS in line 1756 of bse.F, the kpoint weight was multiplied back:

"EPS(:,:,NOMEGA)=EPS(:,:,NOMEGA)+RSPIN*WHF%WDES%WTKPT(1)*CTRANS_SQUARE* &"

I'm wondering why it is not the kpoint weight square (WHF%WDES%WTKPT(1)**2) that should be multiplied. If there should be a WTKPT in the line 1738 for CTRANS, then wouldn't the CTRANS_SQUARE include WTKPT**2?

Best,
Xiaoming

[henrique_miranda]

If there should be a WTKPT in the line 1738 for CTRANS.

Why do you think so?

[xiaoming_wang]

If there should be a WTKPT in the line 1738 for CTRANS.

Why do you think so?

If there is no WTKPT, the oscillator strength would increase significantly as you increase your k mesh, because you are adding more and more k points and not dividing the summation by the number of k points. (It behaves so according to my calculations). Am I miss something?

For example, by using Gamma point I got intensity of 0.63, 2*2*2 k mesh gives 6.4, and 3*3*3 k mesh of 22.9.

Best,
Xiaoming

[henrique_miranda]

So if I understand correctly so far:
- you are observing a scaling of some quantity with the number of k-points. Are you referring to the dielectric function? Real or imaginary part? At which frequency are you looking?
- you suspect that the scaling is because there is factor 1/NK missing (NK being the total number of k-points in the FBZ) in the oscillator matrix elements.

Which system are you looking at? Is 3x3x3 anywhere near convergence?
Did you compare with the dielectric function at the independent particle level?
Could you post a plot of the dielectric function for the different meshes you tested along with the input files?

[xiaoming_wang]

- you are observing a scaling of some quantity with the number of k-points. Are you referring to the dielectric function? Real or imaginary part? At which frequency are you looking?

I'm looking at the oscillator strength (R_AND_INTENSITY in bse.F), because I would like to calculate the lifetime based on this value.

- you suspect that the scaling is because there is factor 1/NK missing (NK being the total number of k-points in the FBZ) in the oscillator matrix elements.

YES.


According to a lecture of Dr. Menno Bokdam wiki/images/2/29/VASP_lecture_BSE.pdf, the BSE oscillator strength is:
|\Sum_{c,v,k} (f_ck - f_vk)*F_cvk*w_k*A_cvk|^2
where F_cvk is the transition dipole matrix, w_k is kpoint weight, and A_cvk is the BSE eigenvector. So there is a w_k^2 in the equation (this is missing in line 1738 of bse.F), but in my calculations it seems that there is only a w_k missing in the printed oscillator strength. So I am confused.

Best,
Xiaoming

[henrique_miranda]

I understand your question.

What is stored in R_AND_INTENSITY and reported in 'opticaltransitions' in the xml file are the independent particle optical transition matrix elements weighted by the electron-hole eigenvector.
The eigenvector has norm 1 and mixes matrix elements from different k, valence and conduction bands.
When computing the optical absorption a factor of 1/Nk enters (not 1/Nk^2).

There was a mistake in the slides and I uploaded a new version.
Thanks for pointing it out.

[xiaoming_wang]

Thanks for clarifying this.

Best,
Xiaoming

[bo_peng]

Hi Xiaoming,

Did you figure out how to obtain the lifetime from BSE oscillator strength? Recently I am trying to do this but I cannot get correct unit. Thanks in advance!

Cheers,
Bo