[QE-users] The sum of occupation number

[Nicola Marzari]

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

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On 27 May 2026, at 04:27, 林俊宏 <d10222004 at ntu.edu.tw> 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

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