[QE-users] The sum of occupation number

[林俊宏]

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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