# 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 '20 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 :) – Nike Dattani Nov 23 '20 at 19:00