Re: [Wien] Correlation energy in DFT+U
Thanks a lot to all of you (Fabien Tran, Peter Blaha and Laurence Marks) for your advice. Best regards, Lorenzo - Mail original - De: "Laurence Marks" À: "A Mailing list for WIEN2k users" Envoyé: Samedi 12 Juin 2021 16:08:24 Objet: Re: [Wien] Correlation energy in DFT+U 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 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" > > À: "A Mailing list for WIEN2k users" > > 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 on behalf of Tran, > Fabien > > 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 on behalf of > Lorenzo Mariano > > 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$ >
Re: [Wien] Correlation energy in DFT+U
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 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" > > À: "A Mailing list for WIEN2k users" > > 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 on behalf of Tran, > Fabien > > 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 on behalf of > Lorenzo Mariano > > 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
Re: [Wien] Correlation energy in DFT+U
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 www.wien2k.at 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" À: "A Mailing list for WIEN2k users" 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 on behalf of Tran, Fabien 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 on behalf of Lorenzo Mariano 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" À: "A Mailing list for WIEN2k users" 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 on behalf of Lorenzo Mariano 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)].
Re: [Wien] Correlation energy in DFT+U
Technically, a DFT+U calculation can only be run with runsp_lapw (or runsp_c_lapw to constrain the magnetic moment to be zero). Whatever is the version of DFT+U that you use, the results should be technically ok. The question is more which DFT+U version is the most appropriate for the physics for your system. This paper provides a very good summary: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.79.035103 From: Wien on behalf of Lorenzo Mariano Sent: Saturday, June 12, 2021 11:56 AM To: A Mailing list for WIEN2k users Subject: Re: [Wien] Correlation energy in DFT+U 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" À: "A Mailing list for WIEN2k users" 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 on behalf of Tran, Fabien 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 on behalf of Lorenzo Mariano 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" À: "A Mailing list for WIEN2k users" 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 on behalf of Lorenzo Mariano 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
Re: [Wien] Correlation energy in DFT+U
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" À: "A Mailing list for WIEN2k users" 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 on behalf of Tran, Fabien 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 on behalf of Lorenzo Mariano 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" À: "A Mailing list for WIEN2k users" 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 on behalf of Lorenzo Mariano 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 ___ Wien mailing list Wien@zeus.theochem.tuwien.ac.at http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien SEARCH the MAILING-LIST at: http://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/index.html
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 on behalf of Tran, Fabien 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 on behalf of Lorenzo Mariano 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" À: "A Mailing list for WIEN2k users" 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 on behalf of Lorenzo Mariano 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 ___ Wien mailing list Wien@zeus.theochem.tuwien.ac.at http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien SEARCH the MAILING-LIST at: http://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/index.html ___ Wien mailing list Wien@zeus.theochem.tuwien.ac.at http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien SEARCH the MAILING-LIST at: http://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/index.html ___ Wien mailing list Wien@zeus.theochem.tuwien.ac.at http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien SEARCH the MAILING-LIST at: http://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/index.html ___ Wien mailing list Wien@zeus.theochem.tuwien.ac.at http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien SEARCH the MAILING-LIST at: http://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/index.html
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 on behalf of Lorenzo Mariano 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" À: "A Mailing list for WIEN2k users" 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 on behalf of Lorenzo Mariano 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 ___ Wien mailing list Wien@zeus.theochem.tuwien.ac.at http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien SEARCH the MAILING-LIST at: http://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/index.html ___ Wien mailing list Wien@zeus.theochem.tuwien.ac.at http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien SEARCH the MAILING-LIST at: http://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/index.html ___ Wien mailing list Wien@zeus.theochem.tuwien.ac.at http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien SEARCH the MAILING-LIST at: http://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/index.html
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" À: "A Mailing list for WIEN2k users" 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 on behalf of Lorenzo Mariano 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 ___ Wien mailing list Wien@zeus.theochem.tuwien.ac.at http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien SEARCH the MAILING-LIST at: http://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/index.html ___ Wien mailing list Wien@zeus.theochem.tuwien.ac.at http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien SEARCH the MAILING-LIST at: http://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/index.html
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 on behalf of Lorenzo Mariano 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 ___ Wien mailing list Wien@zeus.theochem.tuwien.ac.at http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien SEARCH the MAILING-LIST at: http://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/index.html
