[Wien] Correlation energy in DFT+U

[Lorenzo Mariano]

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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