<div dir="auto"><div>Let me add one thing about EECE: it is effectively an environment-dependent U. Hence if you are doing a surface or supercell calculation, it will adjust the "U" in hopefully the right direction. (In my tests it is in the right direction.)</div><div dir="auto"><br><div data-smartmail="gmail_signature" dir="auto">_____<br>Professor Laurence Marks<br>"Research is to see what everybody else has seen, and to think what nobody else has thought", Albert Szent-Györgyi<br><a href="http://www.numis.northwestern.edu">www.numis.northwestern.edu</a></div><br><div class="gmail_quote" dir="auto"><div dir="ltr" class="gmail_attr">On Sat, Jun 12, 2021, 08:19 Peter Blaha <<a href="mailto:pblaha@theochem.tuwien.ac.at">pblaha@theochem.tuwien.ac.at</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Let me add just 2 comments:<br>
<br>
a) As far as I can remember, the authors of the nldau=2 model explained <br>
that in their paper. Probably in the double counting term they assume a <br>
non-spinpolarized LDA. You may also have a look at the textbook section <br>
on <a href="https://urldefense.com/v3/__http://www.wien2k.at__;!!Dq0X2DkFhyF93HkjWTBQKhk!FRt-39x5RmaC2H1J0fnCPPnT4AOLUTtiCOIJqbUlBQQoiRe2dnAVk6R-qklSubZZr8TgCQ$" rel="noreferrer noreferrer" target="_blank">https://urldefense.com/v3/__http://www.wien2k.at__;!!Dq0X2DkFhyF93HkjWTBQKhk!FRt-39x5RmaC2H1J0fnCPPnT4AOLUTtiCOIJqbUlBQQoiRe2dnAVk6R-qklSubZZr8TgCQ$</a> and read the articles by P. Novak. Maybe he has more on <br>
this.<br>
<br>
b) Let me remind you, that there is also EECE (hybrid-DFT) for <br>
"correlated electrons". This version of hybrid-DFT uses an atomic onsite <br>
approximation for the exact-exchange (HF) term only for the correlated <br>
electrons (Ni-3d). It would not work for Si, but the big advantage is <br>
that it is as fast as LDA+U.<br>
<br>
And while in LDA+U you have U, J and the double counting as <br>
"parameters", in EECE it is only alpha, i.e. the amount of HF exchange, <br>
which probably savely can be left at 0.25.<br>
<br>
Of course, with LDA+U you have much more "flexibility" to reach the <br>
result you like ...<br>
<br>
Regards<br>
<br>
Peter Blaha<br>
<br>
Am 12.06.2021 um 11:56 schrieb Lorenzo Mariano:<br>
> Thanks a lot, now it is clear.<br>
><br>
> 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.<br>
> 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?<br>
><br>
> Thanks again,<br>
><br>
> Lorenzo<br>
> ----- Mail original -----<br>
> De: "Tran, Fabien" <<a href="mailto:fabien.tran@tuwien.ac.at" target="_blank" rel="noreferrer">fabien.tran@tuwien.ac.at</a>><br>
> À: "A Mailing list for WIEN2k users" <<a href="mailto:wien@zeus.theochem.tuwien.ac.at" target="_blank" rel="noreferrer">wien@zeus.theochem.tuwien.ac.at</a>><br>
> Envoyé: Vendredi 11 Juin 2021 22:44:10<br>
> Objet: Re: [Wien] Correlation energy in DFT+U<br>
><br>
> Hi,<br>
><br>
> Your value (U/2)Tr[n_(m,sigma)(1-n_(m,sigma)] = 0.0546 Ry for sigma=up is correct.<br>
> I could see that it is only for the sum of the two spins that there is equality:<br>
> (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)<br>
> 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.<br>
><br>
><br>
> ________________________________________<br>
> From: Wien <<a href="mailto:wien-bounces@zeus.theochem.tuwien.ac.at" target="_blank" rel="noreferrer">wien-bounces@zeus.theochem.tuwien.ac.at</a>> on behalf of Tran, Fabien <<a href="mailto:fabien.tran@tuwien.ac.at" target="_blank" rel="noreferrer">fabien.tran@tuwien.ac.at</a>><br>
> Sent: Friday, June 11, 2021 7:49 PM<br>
> To: A Mailing list for WIEN2k users<br>
> Subject: Re: [Wien] Correlation energy in DFT+U<br>
><br>
> For sure Ecorr = 2.71166 Ry is not what you want. As I wrote previously, you have<br>
> to remove trdmv: Ecorr-trdmv=1.59348 Ry, because I think that Eldau and Edc/2 correspond to<br>
> E^ee(n) and E^dc(n), respectively.<br>
><br>
> I don't fully understand your formula (U/2) sum_(m,sigma) Tr[n_(m,sigma)(1-n_(m,sigma)] .<br>
> It is not possible to have at the same time a sum over m and a trace.<br>
><br>
> ________________________________________<br>
> From: Wien <<a href="mailto:wien-bounces@zeus.theochem.tuwien.ac.at" target="_blank" rel="noreferrer">wien-bounces@zeus.theochem.tuwien.ac.at</a>> on behalf of Lorenzo Mariano <<a href="mailto:antonio-lorenzo.mariano@grenoble-inp.fr" target="_blank" rel="noreferrer">antonio-lorenzo.mariano@grenoble-inp.fr</a>><br>
> Sent: Friday, June 11, 2021 4:09 PM<br>
> To: A Mailing list for WIEN2k users<br>
> Subject: Re: [Wien] Correlation energy in DFT+U<br>
><br>
> Hi,<br>
><br>
> 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 <a href="https://urldefense.com/v3/__https://journals.aps.org/prb/abstract/10.1103/PhysRevB.50.16861__;!!Dq0X2DkFhyF93HkjWTBQKhk!FRt-39x5RmaC2H1J0fnCPPnT4AOLUTtiCOIJqbUlBQQoiRe2dnAVk6R-qklSubZHoRFDqA$" rel="noreferrer noreferrer" target="_blank">https://urldefense.com/v3/__https://journals.aps.org/prb/abstract/10.1103/PhysRevB.50.16861__;!!Dq0X2DkFhyF93HkjWTBQKhk!FRt-39x5RmaC2H1J0fnCPPnT4AOLUTtiCOIJqbUlBQQoiRe2dnAVk6R-qklSubZHoRFDqA$</a> 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?<br>
><br>
> Best regards,<br>
><br>
> Lorenzo<br>
><br>
> ----- Mail original -----<br>
> De: "Tran, Fabien" <<a href="mailto:fabien.tran@tuwien.ac.at" target="_blank" rel="noreferrer">fabien.tran@tuwien.ac.at</a>><br>
> À: "A Mailing list for WIEN2k users" <<a href="mailto:wien@zeus.theochem.tuwien.ac.at" target="_blank" rel="noreferrer">wien@zeus.theochem.tuwien.ac.at</a>><br>
> Envoyé: Vendredi 11 Juin 2021 13:45:06<br>
> Objet: Re: [Wien] Correlation energy in DFT+U<br>
><br>
> Hi,<br>
><br>
> In this paper<br>
> <a href="https://urldefense.com/v3/__https://journals.aps.org/prb/abstract/10.1103/PhysRevB.60.10763__;!!Dq0X2DkFhyF93HkjWTBQKhk!FRt-39x5RmaC2H1J0fnCPPnT4AOLUTtiCOIJqbUlBQQoiRe2dnAVk6R-qklSubblx38nrA$" rel="noreferrer noreferrer" target="_blank">https://urldefense.com/v3/__https://journals.aps.org/prb/abstract/10.1103/PhysRevB.60.10763__;!!Dq0X2DkFhyF93HkjWTBQKhk!FRt-39x5RmaC2H1J0fnCPPnT4AOLUTtiCOIJqbUlBQQoiRe2dnAVk6R-qklSubblx38nrA$</a> <br>
> there is Eq. (24), which should correspond to<br>
> Ecorr = Eldau - Edc/2.d0 - trdmv<br>
> in the file vldau.f in the directory SRC_orb. If this is right, then the quantity that you want is<br>
> Eldau - Edc/2.d0 = 8.38769-13.58842/2 = 1.59348 Ry<br>
> where Eldau and Edc are also printed in case.outputorbup<br>
><br>
><br>
> From: Wien <<a href="mailto:wien-bounces@zeus.theochem.tuwien.ac.at" target="_blank" rel="noreferrer">wien-bounces@zeus.theochem.tuwien.ac.at</a>> on behalf of Lorenzo Mariano <<a href="mailto:antonio-lorenzo.mariano@grenoble-inp.fr" target="_blank" rel="noreferrer">antonio-lorenzo.mariano@grenoble-inp.fr</a>><br>
> Sent: Friday, June 11, 2021 12:43 PM<br>
> To: A Mailing list for WIEN2k users<br>
> Subject: [Wien] Correlation energy in DFT+U<br>
><br>
> Dear wien2k users,<br>
><br>
> I am running some DFT+U calculation on NiO compound following instruction reported in this series of exercises: <a href="https://urldefense.com/v3/__http://susi.theochem.tuwien.ac.at/reg_user/textbooks/WIEN2k_lecture-notes_2013/Exercises_13.pdf__;!!Dq0X2DkFhyF93HkjWTBQKhk!FRt-39x5RmaC2H1J0fnCPPnT4AOLUTtiCOIJqbUlBQQoiRe2dnAVk6R-qklSubYYM3cLZA$" rel="noreferrer noreferrer" target="_blank">https://urldefense.com/v3/__http://susi.theochem.tuwien.ac.at/reg_user/textbooks/WIEN2k_lecture-notes_2013/Exercises_13.pdf__;!!Dq0X2DkFhyF93HkjWTBQKhk!FRt-39x5RmaC2H1J0fnCPPnT4AOLUTtiCOIJqbUlBQQoiRe2dnAVk6R-qklSubYYM3cLZA$</a> , 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.<br>
> 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).<br>
> 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?<br>
><br>
> How the terms Eldau and Edc in case.outputorbup/dn are computed?<br>
><br>
> Thank you in advance for your help,<br>
><br>
> Lorenzo<br>
> _______________________________________________<br>
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-- <br>
-----------------------------------------------------------------------<br>
Peter Blaha, Inst. f. Materials Chemistry, TU Vienna, A-1060 Vienna<br>
Phone: +43-158801165300<br>
Email: <a href="mailto:peter.blaha@tuwien.ac.at" target="_blank" rel="noreferrer">peter.blaha@tuwien.ac.at</a><br>
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