plotting exciton wavefunctions with TDHF in VASP 6.5.0

[guyohad]

Dear VASP Developers and Users,

I am trying to understand whether the exciton wavefunction plotting feature described here: https://www.vasp.at/wiki/index.php/Plot ... vefunction is intended to support only GW-BSE calculations, or if it is also compatible for TDDFT calculations (using ALGO = TDHF).

I was able to successfully reproduce the hBN example for the GW-BSE case. However, when I perform TD-PBE or TD-HSE calculations with NBSEEIG = 2 and BSEHOLE = 0.0 0.0 0.0, I get CHG.xx files, but the resulting exciton wavefunction appears non-physical - the exciton wavefunction appears uniform and does not decay with distance.

I am using VASP 6.5.0, and I have attached the relevant files for reference.

Could you provide me with some details about this?

Thanks a lot,
Guy

[pedro_melo]

Dear Guy,

I see that you are trying to use a model dielectric function. I will be taking over this issue, but I would like to point out a couple of things:

• The model dielectric function is activated with LMODELHF

• This model is good only on isotropic systems, since the dependency of the dielectric function on a G-vector is assumed to be through |G|. Using this model is probably not a good idea on materials such as hBN.

• You need a couple more tags in your INCAR, namely AEXX, LMODELHF. Note that LHFCALC is set to .TRUE. if LMODELHF=.TRUE.

• For BN, a better value for HFSCREEN is 1.7. You can see some values for other materials here

Again, I am not entirely sure that this will work correctly for hBN, as the material is not isotropic. I will come back to you with more information once I am done running some more tests.

Kind regards,
Pedro

[pedro_melo]

Dear Guy,

I have looked at your files and checked the code paths. I can say that VASP is indeed plotting an excitonic wave function that results from the calculations you submitted. However, there is a caveat: while VASP can output a wave function from TDHF calculation, that does not mean that it is going to give you a physical result.

In summary: the DFT-based interactions that you are providing VASP for building the excitonic Hamiltonian will not result in good approximations for the excitonic states. The resulting wave functions and energies are therefore likely to be unphysical.

More detailed: In both cases you use DFT-based functionals (PBE and HSE) to compute both the screened and the unscreened interactions between the electrons and holes. This approach is not good for excitonic properties, since the electron-hole interaction is fundamentally wrong. VASP needs the electron-hole interaction to build the excitonic Hamiltonian, and if this is not good enough then the results won't be accurate. There are several papers pointing to the lack the proper long-range behaviour in q (~\(-1/q^{2}\)) in DFT functionals. As they do not have this long range tail they will fail at reproducing optical properties of excitons.

You could try to employ a model-dielectric function, has I mentioned in my previous post. But hBN is anysotropic, and this model was developed for isotropic systems, so it is not guaranteed that it will work. Even if you provide it with better parameters. You can look at this from the perspective that in hBN, being a monolayer, the dielectric function should be close to 1 almost everywhere in space, since most of it is empty (i.e. vacuum). So a model that does not take this into account will also fail at reproducing physical results for monolayers.

A better approach would be to perform a intermediate GW calculation and use the resulting WFULLxxxx.tmp files to evaluate the excitonic Hamiltonian. This approach is more costly, but it has been shown to give good results for materials such as hBN.

Hope this clears it up. Let me know if you need more details. Kind regards,
Pedro

N.B I should also point out that optical properties of 2D materials such has hBN require very dense k-point grids to reach convergence, close to 30x30 k-points.