[Pw_forum] why are there two Fermi energies?

[Paolo Giannozzi]

On Apr 25, 2011, at 15:10 , Eduardo Ariel Menendez Proupin wrote:
>
> >The "two Fermi energies" of the constrained
> >case need not to be exactly the same as the (single)
> >Fermi energy of the unconstrained case, as long as the
> >occupancies for spin-up and spin-down are the same in the
> >two cases.
>
> Why not? Aren't the the energies and occupations related by
> the Fermi-Dirac function?

they are (Fermi-Dirac or whatever function applies), but if you have a
gap and a small broadening, the occupancies will do not (visibly)
depend upon Ef for some interval of values

> 2) tot_magnetization=1
>      the spin up/dw Fermi energies are     6.3853    6.1614 ev

> up: 4.8593   4.8594   5.2221   5.2221   5.2221   6.1335   6.1337    
> 6.1338
>       1.0000   1.0000   1.0000   1.0000   1.0000   1.0000    
> 1.0000   1.0000

Ef=6.3853eV is perfectly consistent with these occupations, as long  
as there
are no states between 6.14eV and 6.40eV or so

>
> dw: 4.8796   4.8796   5.2528   5.2530   5.2531   6.1595   6.1596    
> 6.1596
>       1.0000   1.0000   1.0000   1.0000   1.0000   0.6715    
> 0.6660   0.6625

this is quite the same as case with spin magnetization not set

P.
---
Paolo Giannozzi, Dept of Chemistry&Physics&Environment,
Univ. Udine, via delle Scienze 208, 33100 Udine, Italy
Phone +39-0432-558216, fax +39-0432-558222