BSE and IQP oscillator strength

[bo_peng]

Dear VASP team,

Recently I am trying to calculate the BSE and IQP transition dipole based on VASP lecture on BSE [wiki/images/2/29/VASP_lecture_BSE.pdf] and BSE fatband in [wiki/index.php/Plotting_the_BSE_fatband_structure_of_Si]. However, I have a few questions regarding the BSE and IQP oscillator strength. From the slides, it says that the BSE oscillator strength is:
| ( f_{ck} - f_{vk} ) F_{cvk} A_{cvk} |^2
where the IQP oscillator strength is
F_{cvk} = < psi_c | pi | psi_v > / ( E_{ck} - E_{vk} )
My question is about the parameters in 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 is 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 < psi_c | pi | psi_v > and CDER_BETWEEN_STATES(NB1,NB2,NK,ISP,1:3) the same parameter? If so, what is the unit of < psi_c | pi | psi_v >?
(4) Since the WAVEDERF contains spin up and spin down, do we need to add them up to get a total total F_{cvk}?
(5) For A_{cvk}, I notice that in BSEFATBAND, column 6 is absolute value of coupling coefficient (radius of circles), and column 9/10 is real/imaginary part of 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 WAVEDERF, 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.

Sorry for a string of questions, but it would be super helpful to my research. Thank you for your kind help!


Best regards,
Bo

[ferenc_karsai]

Please find the answers in the following papers. The implemented code follows the formulas in these papers:
T. Sander et al., Phys Rev B 92, 045209 (2015)
https://journals.aps.org/prb/abstract/1 ... .92.045209

and

M.Bokdam et al., Scientific Reports 6, 28618 (2016)
https://www.nature.com/articles/srep28618