# Do I have to use the same functional for dielectric function calculations, as the one used for relaxing the structure?

This is a general question regarding the practices of doing optical calculations and the role of the ionic contribution to the dielectric function (with heavy reference to VASP).

Based on VASP's tutorial on dielectric properties

the ionic contribution to the dielectric function requires the force constants matrix and phonon eigenvalues obtained via density functional perturbation theory (DFPT) or finite differences. I infer from this that the structure has to be well-relaxed (zero forces).

Does this mean that we can't use a different functional for the frequency-dependent dielectric function calculation (both electronic and ionic) than the one used to relax the structure?

For context, I would typically use PBE to do structure relaxations and compute band structures with a hybrid. I was expecting to be able to do something similar - PBE structure relaxations followed by using a hybrid for the dielectric function (electronic + ionic contributions), but this seems wrong if the ionic contribution is computed with the hybrid functional, which would likely yield non-zero forces for the structure.

• The functional used for calculating the force constants indeed must be the same as the functional used for relaxing the structure, due to the zero forces condition. However, I'm not sure if (1) one can use two structures relaxed using different functionals for the electronic and ionic dielectric functions; and if (2) one can use different functionals for the electronic and ionic dielectric functions themselves. Commented Jan 20, 2023 at 8:13
• @wzkchem5 Thanks for your response. I guess one possibility is to be pragmatic by performing these sort of calculations (e.g. relax geometry with PBE and compute the ionic dielectric function with PBE, but get the electronic part with HSE06 or even GW+BSE) and compare the results with experiment to assess how justified such a practice is. Commented Jan 25, 2023 at 15:21
• Yes, but sometimes theoretical consistency may be more important than numerical accuracy. For example, if you do the phonon calculations with a different functional than the one you used for relaxing the structure, then even if your results are better than if you used the same functional for both calculations, your results will still not be accepted by others, because there is no reason to expect such an improvement (which means the improvement is fortuitous). Commented Jan 25, 2023 at 16:03
• Here, although I don't see a reason to use the same functional for the electronic and ionic dielectric functions, I also cannot rule out the possibility that there is some deep reason that the same functional must be used, that I may have overlooked. Let's see if other people can comment on this. Commented Jan 25, 2023 at 16:06
• Just about 2 hours left on the bounty grace period, in case you didn't get enough pings from SE about it! Commented Jan 28, 2023 at 4:45

After 7 days of the bounty period not attracting any answers, I'll answer this question to the best of my abilities.

# General considerations

#### Geometry optimization with one method, and properties with another

This is fairly ubiquitous in matter modeling. High-accuracy methods such as FCI, CCSDTQ, and even double hybrid functionals are almost never used for geometry optimization because the computational cost would not be worth it, yet we still have those methods implemented and frequently used, meaning that they are frequently used on geometries that either come from experiments or from other computational methods.

#### Geometry optimization with one method, and dielectric functions with another

The link you provided about ionic and electronic contributions to the dielectric function, doesn't say anything about needing to use the same functional as the one that was used for the geometry optimization. It provides some VASP output saying that meta-GGA functionals can't be used with DFPT (implying that they can be used when doing finite differences):

#The ionic dielectric function can be calculated in two ways:################
#1# DFPT (faster), but does not allow for METAGGA use. ######################
IBRION = 8; LEPSILON=.TRUE.
#2# Finite differences (slower). ############################################


but if it was so important for the functional used for the dielectric function to be the same as the one used for geometry optimization, then it's peculiar that they never mentioned anything about that in the tutorial. The words "forces" and "force" never show up in that article either.

The article also cites two papers. This one never mentions "force" or "forces" and this one barely does, but a deeper look at those papers would be needed to see if they use (or recommend) to use the same functional for the dielectric function calculation as for geometry optimization.

# Pragmatic considerations

If it was pragmatic to do the geometry optimization with the hybrid functional, then you would (pragmatically) do it. So assuming you are limited to the cost of PBE for the geometry optimization, your choice is either to do the dielectric function calculations with PBE (same functional) or a different functional. When using the PBE geometry, does the dielectric result depend a lot on the functional? If no, then you can report results with all functionals that you used and say how small the spread of results was.

You can also do the geometry optimization with other functionals that have similar cost to using PBE. When using the hybrid functional for the dielectric function, for various geometries that were optimized with cheaper functionals, does it depend a lot on the geometry? If no, then you can report results with all geometries that you used and say how small the spread of results was.

What if there was strong dependence on the functional used for the dielectric function and/or the functional used for geometry optimization? Then it matters which functional you use, and from a theoretical standpoint the "best functional" for that system would usually be the one that you feature more prominently in the paper. Let's assume that PBE is the best functional you can use for the geometry optimization step, then our question becomes a matter of which result is better:

• PBE (geometry) + "best" hybrid for system (dielectric function)
• PBE (geometry) + PBE (dielectric function)

We can then return to your idea of comparing to experiments. Does PBE+"best" consistently match experiments better than PBE+PBE? Another thing you can do is pick a smaller system for which much more accurate calculations can be done, and see which functional/functional-combination recovers the accurate theory results the best. This might mitigate some of wzkchem5's concern about agreement with experiment being fortuitous.

#### Acceptance by others

In the same comment by wzkchem5 for which I provided a hyperlink directly above, there's a concern about acceptance by others (e.g. referees). As a researcher that finished your MPhil a few months ago (based on the website in your Stack Exchange profile), there would almost always be more senior co-authors that know more about what others in the same research field will accept (or at least they'd know people that could give advice about it), but not always. People sometimes work on projects outside of their comfort zone (which can be a good thing).

If no member of the research collaboration knows whether to use the same functional for both, or to use a better functional for the dielectric function, and there's no one clearly saying that you shouldn't use different functionals on an MMSE question with a bounty that lasted for its maximum duration, and no co-authors could find any advice in published papers or by personal contacts, then you can submit the paper with (PBE + "best"), knowing that one or more referee(s) might tell you that it should have been done with (PBE+PBE) or ("best"+"best"). By this time you'll probably be done the "best"+"best" calculation since it would usually take weeks or months to get referee feedback (plus whatever time it takes to prepare the paper for submission). Often, the better the journal, the better (and more scrutinizing) the referees (you can also try to give the journal good referee suggestions), but not everything gets caught by referees.

If using (PBE+"best") is really such a big deal (and was somehow ignored in that VASP webpage that you gave us), it's unlikely that no referee will comment on it, so you can be fairly confident about acceptance at that point, and the final test will be whether or not the wider community of article readers accepts the paper. Apart from the due diligence you already did here at MMSE, and all the other things I mentioned that I'd expect from the more senior (if any) co-authors (e.g. asking experts directly), you could present the work at a conference before publishing it, but other than those things there's not much else you can do to guarantee that the paper will be accepted in this wider sense, and this is a risk that's taken whenever embarking on a project like this.

• Thanks for the answer, I think you've covered the more "big picture" aspects well. Though, I think one key aspect is the ionic vs electronic contributions. I am fairly confident that it is acceptable to compute electronic contribution with a different functional, or even a different level of theory (e.g. optimize structure with PBE and use G0W0@PBE + BSE for the dielectric function). This is not as clear for the ionic contribution. Commented Jan 28, 2023 at 6:54
• From what I gather from the VASP tutorial, the ionic part requires a phonon calculation to be performed (they include the phonon frequencies in the output file, and the figure of the frequency-dependent ionic part seems to show a peak at one of the bolded phonon frequencies). If this is the case, it only makes sense to get phonon results using the same functional that optimizes its geometry. It would be great to understand how exactly the frequency-dependent ionic part is computed, but I can't really find anything on the VASP wiki or by simple googling (perhaps I'll ask in another question). Commented Jan 28, 2023 at 7:01
• It looks like we have a lot to talk about! You can ping me in this chat room. Commented Jan 28, 2023 at 16:55