[Wien] Correlation energy in DFT+U

Sat Jun 12 15:19:40 CEST 2021

Let me add just 2 comments:

a) As far as I can remember, the authors of the nldau=2 model explained 
that in their paper. Probably in the double counting term they assume a 
non-spinpolarized LDA. You may also have a look at the textbook section 
on www.wien2k.at and read the articles by P. Novak. Maybe he has more on 
this.

b) Let me remind you, that there is also EECE (hybrid-DFT) for 
"correlated electrons". This version of hybrid-DFT uses an atomic onsite 
approximation for the exact-exchange (HF) term only for the correlated 
electrons (Ni-3d). It would not work for Si, but the big advantage is 
that it is as fast as LDA+U.

And while in LDA+U you have U, J and the double counting as 
"parameters", in EECE it is only alpha, i.e. the amount of HF exchange, 
which probably savely can be left at 0.25.

Of course, with LDA+U you have much more "flexibility" to reach the 
result you like ...

Regards

Peter Blaha

Am 12.06.2021 um 11:56 schrieb Lorenzo Mariano:
> Thanks a lot, now it is clear.
>
> A last question concerning the use of the "Mean field Hubbard model" (nldau=2). In the file vldau.f it is specified that this implementation of DFT+U has to be used with LDA and not LSDA. Despite that, I can run spin-polarized calculation with this DFT+U flavor and the code does not complain. In addition, in the vldau.f file, the MFH method seems to be implemented for spin-polarized calculations.
> Could you please tell me if it makes sense to run a spin-polarized calculation with nldau=2 and if yes how can I do that properly?
>
> Thanks again,
>
> Lorenzo
> ----- Mail original -----
> De: "Tran, Fabien" <fabien.tran at tuwien.ac.at>
> À: "A Mailing list for WIEN2k users" <wien at zeus.theochem.tuwien.ac.at>
> Envoyé: Vendredi 11 Juin 2021 22:44:10
> Objet: Re: [Wien] Correlation energy in DFT+U
>
> Hi,
>
> Your value (U/2)Tr[n_(m,sigma)(1-n_(m,sigma)] = 0.0546 Ry for sigma=up is correct.
> I could see that it is only for the sum of the two spins that there is equality:
> (U/2)Tr[n_(m,up)(1-n_(m,up)] + (U/2)Tr[n_(m,down)(1-n_(m,down)] = Eldau(up) - 0.5Edc(up) + Eldau(down) - 0.5Edc(down)
> where Eldau and Edc are printed in case.outputorbup/dn. Edc is the same for both spins because it is the sum of both spins.
>
>
> ________________________________________
> From: Wien <wien-bounces at zeus.theochem.tuwien.ac.at> on behalf of Tran, Fabien <fabien.tran at tuwien.ac.at>
> Sent: Friday, June 11, 2021 7:49 PM
> To: A Mailing list for WIEN2k users
> Subject: Re: [Wien] Correlation energy in DFT+U
>
> For sure Ecorr = 2.71166 Ry is not what you want. As I wrote previously, you have
> to remove trdmv: Ecorr-trdmv=1.59348 Ry, because I think that Eldau and Edc/2 correspond to
> E^ee(n) and E^dc(n), respectively.
>
> I don't fully understand your formula (U/2) sum_(m,sigma) Tr[n_(m,sigma)(1-n_(m,sigma)] .
> It is not possible to have at the same time a sum over m and a trace.
>
> ________________________________________
> From: Wien <wien-bounces at zeus.theochem.tuwien.ac.at> on behalf of Lorenzo Mariano <antonio-lorenzo.mariano at grenoble-inp.fr>
> Sent: Friday, June 11, 2021 4:09 PM
> To: A Mailing list for WIEN2k users
> Subject: Re: [Wien] Correlation energy in DFT+U
>
> Hi,
>
> thanks a lot for the reference where the DFT+U implementation in the FLAPW framework is very well explained. However, I still have some doubts. The quantity that I want to obtain is the term E^ee(n)-E^dc(n) that appears in eq.1. Following  https://journals.aps.org/prb/abstract/10.1103/PhysRevB.50.16861 this term should correspond to eq.8 that in the rotationally invariant formulation is given by (U/2) sum_(m,sigma) Tr[n_(m,sigma)(1-n_(m,sigma)] (always considering J=0). This term in the specific NiO calculation that I reported is, for sigma=up, ~ 0.0546 Ry.  This value does not correspond to the reported E_corr = 2.71166 Ry. Is what I am saying correct or I missed something?
>
> Best regards,
>
> Lorenzo
>
> ----- Mail original -----
> De: "Tran, Fabien" <fabien.tran at tuwien.ac.at>
> À: "A Mailing list for WIEN2k users" <wien at zeus.theochem.tuwien.ac.at>
> Envoyé: Vendredi 11 Juin 2021 13:45:06
> Objet: Re: [Wien] Correlation energy in DFT+U
>
> Hi,
>
> In this paper
> https://journals.aps.org/prb/abstract/10.1103/PhysRevB.60.10763
> there is Eq. (24), which should correspond to
> Ecorr = Eldau - Edc/2.d0 - trdmv
> in the file vldau.f in the directory SRC_orb. If this is right, then the quantity that you want is
> Eldau - Edc/2.d0 = 8.38769-13.58842/2 = 1.59348 Ry
> where Eldau and Edc are also printed in case.outputorbup
>
>
> From: Wien <wien-bounces at zeus.theochem.tuwien.ac.at> on behalf of Lorenzo Mariano <antonio-lorenzo.mariano at grenoble-inp.fr>
> Sent: Friday, June 11, 2021 12:43 PM
> To: A Mailing list for WIEN2k users
> Subject: [Wien] Correlation energy in DFT+U
>
> Dear wien2k users,
>
> I am running some DFT+U calculation on NiO compound following instruction reported in this series of exercises: http://susi.theochem.tuwien.ac.at/reg_user/textbooks/WIEN2k_lecture-notes_2013/Exercises_13.pdf, execise 7. I would like to obtain the correlation  energy contribution (E_corr) to the total DFT+U energy: E_DFT+U(rho) = E_DFT(rho) + E_corr.
> Because I am using the 'SIC method' for the expression of the double counting term with J=0, I expect that E_corr= (U/2) sum_(m,sigma) Tr[n_(m,sigma)(1-n_(m,sigma)]. I calculated this term for the spin up channel (sigma=up) of the first Ni atom starting from  the density matrix reported in case.scfdmup (attached the NiO.scfdmup file). With U=0.514 Ry the calculated correlation energy is ~ 0.0546 Ry. This value does not correspond to the one reported in the case.outputorbup file (attached the NiO.outputorbup file).
> I know that in wien2k E_corr is computed starting from the contribution of the Hubbard potential to the eigenvalues. Should I expect that the E_corr value reported in the case.outputorbup/dn corresponds to the one computed starting from the density matrix elements?
>
> How the terms Eldau and Edc in case.outputorbup/dn are computed?
>
> Thank you in advance for your help,
>
> Lorenzo
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-- 
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Peter Blaha,  Inst. f. Materials Chemistry, TU Vienna, A-1060 Vienna
Phone: +43-158801165300
Email: peter.blaha at tuwien.ac.at
WWW:   http://www.imc.tuwien.ac.at      WIEN2k: http://www.wien2k.at
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