[Wien] Correlation energy in DFT+U

Sat Jun 12 16:08:24 CEST 2021

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.)

_____
Professor Laurence Marks
"Research is to see what everybody else has seen, and to think what nobody
else has thought", Albert Szent-Györgyi
www.numis.northwestern.edu

On Sat, Jun 12, 2021, 08:19 Peter Blaha <pblaha at theochem.tuwien.ac.at>
wrote:

> 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
> https://urldefense.com/v3/__http://www.wien2k.at__;!!Dq0X2DkFhyF93HkjWTBQKhk!FRt-39x5RmaC2H1J0fnCPPnT4AOLUTtiCOIJqbUlBQQoiRe2dnAVk6R-qklSubZZr8TgCQ$
> 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://urldefense.com/v3/__https://journals.aps.org/prb/abstract/10.1103/PhysRevB.50.16861__;!!Dq0X2DkFhyF93HkjWTBQKhk!FRt-39x5RmaC2H1J0fnCPPnT4AOLUTtiCOIJqbUlBQQoiRe2dnAVk6R-qklSubZHoRFDqA$
> 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://urldefense.com/v3/__https://journals.aps.org/prb/abstract/10.1103/PhysRevB.60.10763__;!!Dq0X2DkFhyF93HkjWTBQKhk!FRt-39x5RmaC2H1J0fnCPPnT4AOLUTtiCOIJqbUlBQQoiRe2dnAVk6R-qklSubblx38nrA$
> > 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:
> https://urldefense.com/v3/__http://susi.theochem.tuwien.ac.at/reg_user/textbooks/WIEN2k_lecture-notes_2013/Exercises_13.pdf__;!!Dq0X2DkFhyF93HkjWTBQKhk!FRt-39x5RmaC2H1J0fnCPPnT4AOLUTtiCOIJqbUlBQQoiRe2dnAVk6R-qklSubYYM3cLZA$
> , 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
> > _______________________________________________
> > Wien mailing list
> > Wien at zeus.theochem.tuwien.ac.at
> >
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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
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