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"oddity" with odd number of states Date: 2010/10/06 03:16 Name: N.Kolchenko   <nkolchenko@mail.ru> Dear prof. T.Ozaki and OpenMX users, This message continue "locked" thread "different energy with different initial spin". I don't understand some calculations results. System under investigation is rather complex (~300 states), so to avoid questions with PP and PAO generation, system and algorithm parameters setting etc., I list several results with example file Mol_MnO.dat (19 electrons), which demonstrate similar behaviour. I changed in Mol_MnO.dat only (scf.MaxIter = 200; scf.criterion = 1.0e-10) and sometimes enlarge scf.Mixing.History to obtain convergence. Let's perform calculations with different initial spin charges on Mn (below - numbers in brackets - (nSpinUp nSpinDown)). So, results: ---------------------------------------- 1. (8 5) - Initial file. Convergence (C) good (~ 30 - 40 iteration); Dipole moment (D) = 4.86; U_tot = -90.74; Number of states (NS) = 18.999999999; HOMO-up level (Hu) = 12; Homo-down (Hd) = 7; total spin (TS) = 2.4999999.. Everything - OK. (NS (TS) - are not integer (half-integer) - but I believe this is output file (FORMATTING) effect, below - roundoff values). ---------------------------------------- 2. (6.5 6.5) - symmetrical initial spin distribution. C - good; D = 4.01; U_tot = -90.63; NS = 19; Hu = 10; Hd = 10; TS = 0.0 (! - for odd number of electrons). (NS.NotEqual.(Hu+Hd) !) These results correspond "scf.SpinPolarization = off" for this system. ---------------------------------------- 3. (6.4 6.6) - small asymmetry. C - poor (real convergence begin only after NIter ~ 80); D = 4.265; U_tot = -90.67; NS = 19; Hu = 10; Hd = 9; TS = 0.5 ---------------------------------------- 4. (7 6) - medium asymmetry. The results completely correspond to case 1. (8 5), only convergence not so fast. ----------------------------------------- 5. Now restore initial file - (8 5) and set scf.system.charge = -1 (20 electrons in system) C - good; D = 0.52; U_tot = -90.84; NS = 20 (19.99999); Hu = 12; Hd = 8; TS = 2.0 . ------------------------------------------ 6. The same as (5.) but with symmetrical initial spin distribution (6.5 6.5) C - medium; D = 0.01; U_tot = -90.73; NS = 20; Hu = 10; Hd = 10; TS = 0.0 . ------------------------------------------- So, the final data depends strongly on initial spin distribution. I know little (less than little) about MnO, and may be the results with different multiplicity (except case 2.) are meaningful... It is not question now. It seems that it will be sufficient to keep assymetry in initial spin distribution to avoid unphysical (case 2.) results for system with odd number of electrons. But for larger system (sometimes with added electrons) this recipe may be inefficient, and I can get something about: NS = 316.9999999; Hu = 160; Hd = 160 (159 - is sufficient - isn't it ?); TS = 0.00009. Or, at last, NS = 320.9999999; Hu = 160; Hd = 160; TS = 0. For (NS = evenNumber) results looks better. Information about the OCCUPATION NUMBERS is nesessary. I could't find it in output's (different modes for output files were used). ---------------------------------------- Questions : How can I get occupation numbers for Kohn-Sham eigenstates ? How OpenMX calculate HOMO_Up(Down) ? Or, by another words, what algorithm OpenMX use for electrons distribution after eigenSolver ? (any Ref.[ ] or FileNameS.c in /source may be useful...) How OpenMX set initial spin for added (scf.system.charge <> 0) electrons (holes) ? And, can anybody explain me WHERE is (n+1)-th electron WHEN (sometimes...) (HOMO_Up+HOMO_Down) = n ? I hope my version of English permit to decode this message in the main. Thank you. Best regards, N.Kolchenko

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Re: "oddity" with odd number of states ( No.1 ) Date: 2011/10/12 20:51 Name: T.Ozaki Hi, > How can I get occupation numbers for Kohn-Sham eigenstates ? > How OpenMX calculate HOMO_Up(Down) ? > Or, by another words, what algorithm OpenMX use for electrons distribution > after eigenSolver ? > (any Ref.[ ] or FileNameS.c in /source may be useful...) OpenMX uses the Fermi-Dirac function to determine an occupation number for each state. In this calculation, we introduce higher and lower chemical potentials, and then calculate the total number of electrons for each chemical potential. Of course, the trial chemical potentials may not be a correct one, which means that the calculated total number of electrons deviates from the correct total number of electrons in the system. Then, a better chemical potential is estimated by using a bisection method. After repeating several iterations of the process, one can find the proper chemical potential so that the total number of electrons is conserved. This is the algorithm to determine the chemical potential and occupation numbers of the KS eigenstates. The determination of HOMO is made by looking the occupation number, and the highest state is regarded as HOMO among states with an occupation number of more than 0.5. > How OpenMX set initial spin for added (scf.system.charge <> 0) electrons (holes) ? The initial charge distributions of up and down states are calculated by the superposition of spin polarized atomic charges which are specified by the input file. > And, can anybody explain me WHERE is (n+1)-th electron WHEN (sometimes...) > (HOMO_Up+HOMO_Down) = n ? Sorry, I cannot catch your point, but I hope above the explanation may help your understanding. Regards, TO Re: "oddity" with odd number of states ( No.2 ) Date: 2011/10/12 20:27 Name: N.Kolchenko  <nkolchenko@mail.ru> Dear prof. T.Ozaki, Thank you very much. Your explanation completely solve the problem with "stealth electron". Regards, NK

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