[Wien] Correlation energy in DFT+U

[Tran, Fabien]

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