Negative band occupation with tetrahedron method with blöchl corrections

[IBRAHIM]

Dear All,
For some metallic systems I noticed that ISMEAR -5 gives some negative band occupations, occupations higher than one.
But with ISMEAR 0 the occupation is between 0 up to one including partial values.
What about these occupations in case of ISMEAR-5? Also, what about the total energy and DOS calculated by ISMEAR -5 in that case?

I have also tested the Si_example on vasp wiki
https://www.vasp.at/wiki/index.php/Fcc_Si_DOS

with negative occupation and occupation higher than two in this case (spin unpolarized).

Best regards,
Ibrahim

[ferenc_karsai]

In the tetrahedron method the weights can become negative or larger than 2 . This is even reported in the original paper by Blöchl:

Improved tetrahedron method for Brillouin-zone integrations, Peter E. Blöchl, O. Jepsen, and O. K. Andersen, Phys. Rev. B 49, 16223 – Published 15 June 1994

So you should use the tetrahedron method for DOS.

[IBRAHIM]

Thank you very much.

But how can we trust the calculated total energy and DOS with those unphysical occupations.

Yes, tetrahedron method with blöchl corrections is recommended for very accurate total energy (no relaxation for metal) and DOS. But in the above case, it gives those negative and larger than one band occupations.

Could it be acceptable because the systems are metallic?

[ferenc_karsai]

Negative weights and weights larger 1 can only happen for metals.
The weights in the tetrahedron method loose a little bit the physical meaning and are calculated as optimal weights for the integration tetrahedra.

Please see chapter 2 and 4 of
Improved tetrahedron method for Brillouin-zone integrations, Peter E. Blöchl, O. Jepsen, and O. K. Andersen, Phys. Rev. B 49, 16223 – Published 15 June 1994