It’s the integral all over kpoints that needs to be correct; at any given kpoint, in a metal, sometimes it will be higher, sometimes lower.
Nicola Sent from a tiny keyboard... Contact info: http://theos-wiki.epfl.ch/Main/Contact On 27 May 2026, at 04:27, 林俊宏 <[email protected]> wrote: Dear All, I performed the spin-polarized SCF calculation of NiO using Fermi-Dirac smearing and focused on its occupation numbers. In the scf output file, the total number of electrons is 32. But the sum of occupation numbers for an arbitrary k-point is not equal to 32 (spin up + spin down); in fact, it exceeds it. Why the sum is not equal to the total number of electrons? Following shows the truncated output: bravais-lattice index = 0 lattice parameter (alat) = 9.6512 a.u. unit-cell volume = 244.6666 (a.u.)^3 number of atoms/cell = 4 number of atomic types = 4 number of electrons = 32.00 number of Kohn-Sham states= 20 kinetic-energy cutoff = 40.0000 Ry charge density cutoff = 160.0000 Ry ... ------ SPIN UP ------------ ... k = 0.0000 0.0000 0.5539 ( 1050 PWs) bands (ev): -8.0602 -7.1852 4.2164 5.1908 5.3054 6.0558 6.8531 7.1036 9.2355 9.8018 9.9846 10.2167 10.2600 10.6732 10.8402 10.8480 11.7452 12.2874 16.2553 19.9253 occupation numbers 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9998 0.9981 0.9964 0.9915 0.9901 0.9563 0.9222 0.9201 0.2986 0.0549 0.0000 0.0000 ------ SPIN DOWN ---------- ... k = 0.0000 0.0000 0.5539 ( 1050 PWs) bands (ev): -8.0602 -7.1852 4.2164 5.1908 5.3055 6.0559 6.8531 7.1036 9.2355 9.8019 9.9846 10.2167 10.2601 10.6733 10.8402 10.8480 11.7452 12.2874 16.2553 19.9253 occupation numbers 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9998 0.9981 0.9964 0.9915 0.9901 0.9563 0.9222 0.9201 0.2986 0.0549 0.0000 0.0000 ... The input file used for calculation is at https://docs.google.com/document/d/1f_hVjxORLTCa8xgCy3AkEkZuR7bnoIftWH1WdsEs5OA/edit?usp=sharing Best Regards, Chun Linn _______________________________________________________________________________ The Quantum ESPRESSO Foundation stands in solidarity with all civilians worldwide who are victims of terrorism, military aggression, and indiscriminate warfare. -------------------------------------------------------------------------------- Quantum ESPRESSO is supported by MaX (www.max-centre.eu) users mailing list [email protected] https://lists.quantum-espresso.org/mailman/listinfo/users
_______________________________________________________________________________ The Quantum ESPRESSO Foundation stands in solidarity with all civilians worldwide who are victims of terrorism, military aggression, and indiscriminate warfare. -------------------------------------------------------------------------------- Quantum ESPRESSO is supported by MaX (www.max-centre.eu) users mailing list [email protected] https://lists.quantum-espresso.org/mailman/listinfo/users
