Resonant, antiresonant and coupling terms in TDDFT

[lorenzo.sponza]

Dear developers and users,
I would like to calculate some EELS spectra of 2D materials using Yambo. As far as I can tell, for EELS to be accurate both the resonant (R) and the anitresonant (A) parts of the response have to be included, the coupling between the two being less important. Moreover, I would like to make comparisons between the R and the R+A results.

I would like to know how to enable and disable A components, what is the default in TDDFT and if all this is compatible with the SLAB Z Coulomb cutoff method.

Many thanks !

Cheers

[Daniele Varsano]

Dear Lorenzo,

I should have to look more in details on that as it has been changed recently, but I think that setting the variable:

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BSEmod= "retarted"  

it should do the job, i.e. R+A
while setting it to "resonant"

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BSEmod= "resonant"  

only R is considered.

And yes, all should be compatible with a slab cutoff.

Best,
Daniele

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[Davide Sangalli]

Ciao Lorenzo,
few more comments.

First, and most important to me. When you go to a 2D material there is not distinction anymore between chi and chi-bar. So you cannot use this distinction to distinguish between absorption and eels. Indeed the EELS of a 2D material is not coded in yambo and you would need to define it.

Being aware of this, Daniele already explained how to select R only vs A+R.
In 3D materials there will be some extra comments and subtleties about how the G=0 term of the eh-exchange is handled, but this is not apply to 2D materials. See point above. So I skip them

Then, TDDFT can be solved both in G-space and in transition space. However, for a 2D material, I'd suggest transition space, because I suspect the convergence in G-space would be problematic.
For TDDFT in transition space in general I strongly suggest to use this branch: https://github.com/sangallidavide/yambo ... -dichroism
It is a personal branch I developed, please consider acknowledging this somehow if you use it.

Best,
D.

[lorenzo.sponza]

Thank you very much for the answers.
1) I thought BSEmod was used only in BSE algorithms, not also in TDDFT. Are BSE variables always taken into account in TDDFT, or only if I run TDDFT in transition space?
2) I will have a look at Davide's branch and of course I will cite it if we produce data with that. For the moment is more for debugging other stuff.
3) Thanks Davide for the precision about about EELS and absorption on 2D materials. However, to me, this subject is still not settled. I have been working for a while on this (https://arxiv.org/pdf/2011.07811.pdf) but our investigation stopped because of covid, lack of time and other issues. In any case, that's not really for this that I want to look at the R and R+A signals. It's more for benchmarking other codes.

Many thanks! Cheers

[Davide Sangalli]

1) I thought BSEmod was used only in BSE algorithms, not also in TDDFT. Are BSE variables always taken into account in TDDFT, or only if I run TDDFT in transition space?

Only if you run TDDFT in transition space. In G-space you can use

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GrFnTpXd="R"            # 'Green`s function (T)ordered,(R)etarded,(r)senant,(a)ntiresonant [T, R, r, Ta, Ra]' 

If you set "r" you get the equivalent of BSEmod="resonant", if you set "R" you get the equivalent of BSEmod="coupling"
There is not way in which you can get the BSEmod="retarded" result, e.g. if you include the anti-resonant part, the couplign cannot be set to zero.

3) Thanks Davide for the precision about about EELS and absorption on 2D materials. However, to me, this subject is still not settled. I have been working for a while on this (https://arxiv.org/pdf/2011.07811.pdf) but our investigation stopped because of covid, lack of time and other issues. In any case, that's not really for this that I want to look at the R and R+A signals. It's more for benchmarking other codes.

Thanks for the reference. I'll have a look into it. I agree that there is confusion in the literature, with some open points. Indeed I also have some notes on the topic which I did not finalize ...

However I think there is agreement on this point: L=Lbar in d < 3.
Here Lbar, as defined in yambo, is the solution of the Dyson equation for L without the v_{G=0} term. Indeed, in the converged or physical limit (e.g in the limit in which the dimension along the non-periodic dimension(s) is(are) sent to infinity) v_{G=0}=0 .

Best,
D.