BSE calculations based on DFT WAVECAR and WAVEDER

[hong_tang1]

Dear VASP team,

I am trying to do BSE calculations based on DFT (DFT+SOC+U) WAVECAR and WAVEDER. The system is semiconducting.

I tried to use ALGO=TDHF, LADDER=.True. and LRPA = .False.
However, I got the result is the same as IP (independent particle).
Please see attached files for details.

The code I used vasp.5.4.4.
I suppose that I can get BSE results based on the DFT input (no GW calculations at all). But why the excitonic effects are not included? (please check the end of OUTCAR, it says " simple RPA calculation, excitonic effects (ladders) are not included").


Please help!


Hong

[alexey.tal]

Dear Hong,

The excitonic effects are not included in your calculation because you set AEXX=0 in your INCAR. AEXX defines the fraction of the exact exchange. In the context of the TDHF algorithm it defines the screening of the electron-hole interaction, and in your calculation the e-h interaction is fully screened. We have written a comprehensive tutorial on the BSE and TDDFT methods, so you can find a lot of details and examples there.

Could you explain what type of TDDFT calculation you would like to perform?

[hong_tang1]

Dear Alexey,

Thank you so much for help!
1. can I do BSE based on DFT (such as PBE, SCAN, no hybrid) calculated WAVECAR and WAVEDER? I mean no GW calculation at all, no W0001.tmp or WFULL0001.tmp files.

2. For ALGO=TDHF, if I want to do BSE (I mean LADDER=.True.), do I have to do a hybrid functional calculation first? with LHFCALC = .TRUE. ? If I did not do LHFCALC = .TRUE. first, then with ALGO=TDHF, I can only do TDDFT with ALDA kernel or just a IP (independent particle) calculation.

3. for LMODELHF = .TRUE. and ALGO=TDHF, a hybrid LHFCALC = .TRUE. calculation is also needed first, right?


Best,
Hong

[alexey.tal]

1. can I do BSE based on DFT (such as PBE, SCAN, no hybrid) calculated WAVECAR and WAVEDER? I mean no GW calculation at all, no W0001.tmp or WFULL0001.tmp files.

If you don't have Wxxxx.tmp or WFULLxxxx.tmp files, you can only do calculations that don't require these files, i.e., TDHF calculations. In the standard BSE calculation you need the full dielectric tensor for describing the screening in the ladder diagrams.

2. For ALGO=TDHF, if I want to do BSE (I mean LADDER=.True.), do I have to do a hybrid functional calculation first? with LHFCALC = .TRUE. ? If I did not do LHFCALC = .TRUE. first, then with ALGO=TDHF, I can only do TDDFT with ALDA kernel or just a IP (independent particle) calculation.

You can include the ladder diagrams in TDHF or BSE calculations starting from any ground state GW, hybrid, or any xc funcitonal . If you don't perform a GW step, you need to provide parameters for the description of the screening, i.e., AEXX and optionally LMODELHF, HFSCREEN, depending on what type of screening you would like to include.

3. for LMODELHF = .TRUE. and ALGO=TDHF, a hybrid LHFCALC = .TRUE. calculation is also needed first, right?

TDHF calculation with the model dielectric function (LMODELHF) can be performed starting from any ground state WAVECAR and WAVEDER.

Let me know if something is still not clear.

[hong_tang1]

Dear Alexey,

I really thank you so much for help!

1. If I have PBE+SOC based WAVECAR and WAVEDER files for a semiconductor, I want to use ALGO=TDHF and LADDER=.True. to get the exciton effect. I also add LHARTREE = .TRUE. and AEXX = 0.25, but I don't set LMODELHF and HFSCREEN. It should work, right? Then How to choose the value for AEXX? You said here AEXX is the screening of the electron-hole interaction. How to choose this value under LMODELHF=.False. ?

2. Similar as in 1. If I turn on LMODELHF=.True. , then I need AEXX and HFSCREEN. Again, how to get the values of the AEXX and HFSCREEN? Can I use the same procedure as mentioned in your tutorial (get 1/epsilon_infinite, and fit the RPA dielectric function vs. G)? even here my ground state is from PBE+SOC, not from a hybrid functional?



Best,
Hong

[alexey.tal]

1. If I have PBE+SOC based WAVECAR and WAVEDER files for a semiconductor, I want to use ALGO=TDHF and LADDER=.True. to get the exciton effect. I also add LHARTREE = .TRUE. and AEXX = 0.25, but I don't set LMODELHF and HFSCREEN. It should work, right?

If these are the tags in your TDDFT INCAR, then yes. If you would use the same PBE0 hybrid functional for the ground state, this approximation would be equivalent to proper TD-PBE0. However, what you are proposing here would be a combination of PBE for the ground state and TD-PBE0 for optical properties, which is also possible in VASP.

Then How to choose the value for AEXX? You said here AEXX is the screening of the electron-hole interaction. How to choose this value under LMODELHF=.False. ?

This is not an easy question. In TDDFT, AEXX comes from the fraction of exact exchange in the exchange-correlation potential, but this choice is not a well-defined procedure. Essentially, your question is related to the general choice of the hybrid functional and it doesn't have an easy answer.
Usually, in TDDFT calculations, the same hybrid functional is used for the ground state calculation (ALGO=Normal) and the optical absorption calculation (ALGO=TDHF). But as I said earlier, in VASP, any ground state can be used with any approximation in TDHF.

2. Similar as in 1. If I turn on LMODELHF=.True. , then I need AEXX and HFSCREEN. Again, how to get the values of the AEXX and HFSCREEN? Can I use the same procedure as mentioned in your tutorial (get 1/epsilon_infinite, and fit the RPA dielectric function vs. G)? even here my ground state is from PBE+SOC, not from a hybrid functional?

Yes, you can start your TDHF calculation with the model dielectric function (LMODELHF) from any ground state calculation. In the scheme you described, that would be PBE.
The approach with the model dielectric function (LMODELHF) can be seen as an approximation for the RPA dielectric function, so one has to provide the parameters for the model, i.e., AEXX and HFSCREEN. One way to approach it is to fit the RPA dielectric function as done in
Ref. [1,2]. In other works, the parameters for this model were determined without the costly RPA calculations [3,4].
In the tutorial, we use DDH calculations with the model dielectric function for the ground state and TD-DDH for the optical absorption calculations, which allows us to use the same hybrid functional consistently for the ground state as well as the optical excitations and yields accurate results [5].

[1] M. Bokdam, T. S, er, Aless, r. Stroppa, S. Picozzi, D.D. Sarma, C. Franchini, G. Kresse, Sci Rep 6, 28618 (2016)
[2] W. Chen, G. Miceli, G. Rignanese, A. Pasquarello, Phys. Rev. Materials 2, 073803 (2018)
[3] C. Zhi-Hao, W. Yue-Chao, Z. Min-Ye, X. Xi, J. Hong, J. Phys. Chem. Lett. 9, 2338-2345 (2018)
[4] H. Wang, A. Tal, T. Bischoff, P. Gono, A. Pasquarello, npj Comput Mater 8, 237 (2022)
[5] A. Tal, P. Liu, G. Kresse, A. Pasquarello, Phys. Rev. Research 2, 032019 (2020)

[hong_tang1]

Thanks! Alexey,

It is clear!

Best,
Hong