Thank you Dr. Gavin Abo I agree that the occupation for spin-up (the addition of an electron) is 4 and 5 ε3d_up = (4*0.109629972+5*0.126221709)/9 = 0.11884760366667
but when we remove an electron for spin-Dn we have to put 4 and 3 or 4 and5? ε3d_dn = -(4*-0.292400769+(5or3)*-0.274004694)/ ... 2018-05-13 0:19 GMT+02:00 Gavin Abo <gs...@crimson.ua.edu>: > Yes, I believe that is correct that Constraint_U.pdf is performing the > same calculation as Anisimov's paper. > > As illustrated nicely on slide 11 in > > http://www.fhi-berlin.mpg.de/~xinguo/talks/jiang_cdft-coffeetalk.pdf , > just as you say, an electron is added for spin-up and an electron is > removed for spin-dn. That is what the case.inc* files are used for in > section III part A. and B. in Constraint_U.pdf. > > As you can see in F^0_eff EPL vol. 69, 777 (2005), it look like equation 4 > comes from equation 9 Anisimov's Phys. Rev. B vol. 43, 7570 (1991) paper [ > https://doi.org/10.1103/PhysRevB.43.7570 ]. Relating that to Anisimov's > equation 10 and 11 in Phys. Rev. B vol. 44, 943 (1991), it looks like we > could write the equation for Ueff as: > > Ueff ≈ F^0_eff = J + U > > In the NiO example, the U from the difference of the Fermi energies [ > https://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg14460.html > ]: > > U = -εF_up + εF_dn = -(0.4780996800)+0.5181842639 = 0.0400845839 > > while the J from the difference of the "3d eigenvalues": > > ε3d_up = (4*0.109629972+5*0.126221709)/9 = 0.11884760366667 > > ε3d_dn = -(4*-0.292400769+5*-0.274004694)/9 = -0.28218072733333 > > J = ε3d_up - ε3d_dn = 0.11884760366667 - (-0.28218072733333) = 0.401028331 > > Ueff ≈ F^0_eff = J + U = 0.0400845839 + 0.401028331 = .4411129148 Ry > > > I agree with you regarding the calculation of Ueff using the method > described in the following file > http://susi.theochem.tuwien.ac.at/reg_user/textbooks/Constraint_U.pdf > > But according to Anisimov's paper , J=E3d'up'(n+0.5,n-0.5)- E3d'dn > '(n+0.5,n-0.5) > So we add an electron for the spin-up and we removed a electron for spin-dn > and we calculate the difference Eup_3d-Edn3d for a one calculation > > that's what I did > > Is this correct? > > > > _______________________________________________ > 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 > >
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