How to calculate the parameter F0 uesd in the LRC kernel

[chinaye]

Dear Developers,
We are not clear on how to calculate the parameter F0 uesd in the LRC kernel.
Compared with the eq(2) in PRB 69 155112 (2004), the parameter F0 is equal to -alfa/4*Pi, with alfa=4.615/epsilon0-0.213.
For LiF, epsilon0 is around 8.3. So alfa is 0.34, and F0 is -0.027. However, in tutorial F0 is -8.7. Thank you.

[Daniele Varsano]

Dear Chinaye,

first of all let me ask you to include in your profile your affiliation in the signature. This is a rule of this forum.

In eq(2) in PRB 69 155112 (2004), it is stated that alfa is a material dependent parameter, it is empirical and it is not obtained ab-initio. While it is known that the kernel have to assume that form in the long range regime, the value of alfa is not known, it is somehow empirical and it is set in order to reproduce the experimental result. The relation you cite is obtained by fitting some materials, and it is not so sure that it is general. It is obtained fitting the spectra of semiconductors presenting continuum excitons, and I think that such relation can break down in presence in bound excitons as in the case of LiF.

For a totally ab-initio kernel you can have a look to the following papers:
G. Adragna, R. Del Sole and A. Marini PRB 68, 165108 (2003)
A. Marini, R. Del Sole and A. Rubio PRL 91, 2564021 (2003)
F. Sottile, V. Olevano and L. Reining PRL 91, 56402 (2003)

If you look in the inset of Fig.1 (middle panel) of the second paper where ab-initio spectra are calculated for LiF you can see that you can extract a value of alfa of about 11. It makes me think that there is some misleading between alfa and Fo in the tutorial.
Beside that, here the problem is also that the example shown in the tutorial are pedagogical and they are thought to be run in few minutes and for this reason they are often out-of-convergence. If you look at the additional exercise they invite to reach the convergence.
Now, the alfa parameter it is set to match the excitation energy of the Bethe-Salpeter calculation obtained out-of-convergence. Pushing the convergence of the Bethe-Salpeter calculation also the value of alfa have to be changed.

I hope it helps,

Best regards,
Daniele