[Wien] Correlation energy in DFT+U

[Tran, Fabien]

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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