[Pw_forum] Highest occupied level is higher than the lowest unoccupied level and the band-gap problem

[Uri Argaman]

Dear QE users and developers,
I calculate the energy using pw.x of GeTe in non-equilibrium positions and
unit-cell. I get the following results:

"highest occupied, lowest unoccupied level (ev):     8.7256    7.626."

I know that the material is a metal or semi-metal. The same thing happens
with bismuth (in A7 structure) which is a semi-metal. I understand that
this kind of calculations should be done with smearing and I read in
previous messages by Paolo that it is known to happen in semi-metals and
relates to the band-gap problem. I know the band-gap problem in DFT but I
do not understand why a level which is lower in energy than the highest
occupied level will not be occupied, and instead a higher level is
occupied. I would expect that the calculation will not converge but I do
not understand why it converges to the wrong state.
Is it similar to the Janak theorem and fractional occupation in the Fe
atom?


The relevant levels for GeTe are:
          k = 0.0000 0.0000-0.8124 (  1520 PWs)   bands (ev):

   -17.0056 -17.0056 -16.9992 -16.9979 -16.9979  -3.7630  -1.5570   7.1574
     7.1574   8.7256   8.7360   8.7360   9.2246  16.8372  16.8922  17.9505
    17.9505  18.5818  18.5818  23.8031

     occupation numbers
     1.0000   1.0000   1.0000   1.0000   1.0000   1.0000   1.0000   1.0000
     1.0000   1.0000   0.0000   0.0000   0.0000   0.0000   0.0000   0.0000
     0.0000   0.0000   0.0000   0.0000


         k = 0.1861-0.8594-0.2708 (  1512 PWs)   bands (ev):

   -17.0067 -17.0055 -16.9990 -16.9971 -16.9963  -3.3095  -1.0166   5.5826
     5.8078   6.6930   7.6261   9.8147   9.9726  16.4111  16.5968  17.8171
    17.8592  21.5515  21.7205  23.8798

     occupation numbers
     1.0000   1.0000   1.0000   1.0000   1.0000   1.0000   1.0000   1.0000
     1.0000   1.0000   0.0000   0.0000   0.0000   0.0000   0.0000   0.0000
     0.0000   0.0000   0.0000   0.0000

Uri Argaman
Ben-Gurion University
Israel
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