# BSE and IQP oscillator strength from VASP

Recently I am trying to calculate the BSE and IQP transition dipole based on VASP lecture on BSE and BSE fatband. However, I have a few questions regarding the BSE and IQP oscillator strength. From the slides, it says that the BSE oscillator strength is:

$$\tag{1} | ( f_{ck} - f_{vk} ) F_{cvk} A_{cvk} |^2$$

where the IQP oscillator strength is:

$$\tag{2} F_{cvk} = \dfrac{\langle \psi_c | p_i | \psi_v \rangle}{E_{ck} - E_{vk}}$$

My question is about the parameters in the two formula and how they connect to each other:

1. In the BSE formula, is $$( f_{ck} - f_{vk} )$$ set to be 1? Or it depends on smearing?

2. Does $$i$$ in the formula for $$F_{cvk}$$ mean Cartesian coordinate? If so, do I need to add $$x$$, $$y$$, and $$z$$ contributions to get a total $$F_{cvk}$$?

3. Are $$\langle \psi_c | p_i | \psi_v \rangle$$ and CDER_BETWEEN_STATES(NB1,NB2,NK,ISP,1:3) the same parameter? If so, what is the unit of $$\langle \psi_c | p_i | \psi_v \rangle$$?

4. Since the WAVEDER contains spin up and spin down, do we need to add them up to get a total $$F_{cvk}$$?

5. For $$A_{cvk}$$, I notice that in BSEFATBAND, column 6 is the absolute value of coupling coefficient (radius of circles), and column 9/10 is the real/imaginary part of the coupling coefficient. I notice that we need to multiple $$Nk^3$$ to column 9/10 to make the absolute value equal to column 6. I do not know which $$A_{cvk}$$ should I use to get the BSE oscillator strength.

6. As we can get $$F_{cvk}$$ from WAVEDER, $$A_{cvk}$$ from BSEFATBAND, can we use these parameters to get the BSE oscillator strength output in vasprun.xml? I have tried to do this but I could not establish a correspondence between the BSE oscillator strength formula and the vasprun.xml output.

Any insights for any questions would be super helpful to my research. Thank you for your kind help!

Best regards,

Bo

• There a few things to address here. 1. The question is likely two broad as is. You should narrow it down to address one specific issue and if you are still confused after receiving an answer, you can ask additional questions as separate posts. 2. Mathematical expressions can be formatted using Mathjax as described here
– Tyberius
Nov 23, 2020 at 18:18
• I gave you a +1, but I do agree with Tyberius: (1) Every question has to be a separate post, and (2) please see the edits I made and make the appropriate changes yourself for the rest of the question. This will help you smoothly transition into using MathJax :) Nov 23, 2020 at 19:00

Your question is not so focus. I assume that you want to read the BSE oscillator strength from the VASP output.

I strongly advise you that take a look at this link:

After the (model)BSE calculation we first look into the [vasprun.xml] file to have a look at the BSE eigenvalues and the oscillator strengths (exact numbers can of course differ depending on the method you use and the density of your k-point grid).

in which the first column is the BSE eigenvalue, the second line the BSE oscillator.

You can obtain similar results with IQP calculation at DFT or RPA levels with [LOPITCS=TRUE] in the INCAR file.

• Thanks for this! What I am trying to do is to build a connection between the BSE oscillator strength in vasprun.xml, BSE amplitude of exciton wavefunction, and IQP oscillator strength. Do you have some idea how to do this? Nov 24, 2020 at 10:28
• @B.Peng Have you read the implementation paper? journals.aps.org/prb/pdf/10.1103/PhysRevB.92.045209 You may find more information from that.
– Jack
Mar 11, 2021 at 23:09