[QE-users] The sum of occupation number

[林俊宏]

Thank you for your reply and for resolving my issue.
I really appreciate your help and support.

thank you

Chun Linn

Nicola Marzari via users 於 2026-05-27 15:18 寫到:

> 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 <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 
>> [1]
>> 
>> Best Regards,
>> Chun Linn
>> 
>> _______________________________________________________________________________
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> 
> _______________________________________________________________________________
> 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 [2])
> users mailing list users at lists.quantum-espresso.org
> https://lists.quantum-espresso.org/mailman/listinfo/users


Links:
------
[1] 
https://docs.google.com/document/d/1f_hVjxORLTCa8xgCy3AkEkZuR7bnoIftWH1WdsEs5OA/edit?usp=sharing
[2] http://www.max-centre.eu
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