[Pw_forum] why are there two Fermi energies?

[Eduardo Ariel Menendez Proupin]

Hi Paolo,



>>* the restriction is in this code
*>>*          if ( ((MOD(NINT(tot_magnetization_),2) == 0) .and. (MOD
*>>* (NINT(nelec_),2)==1)) .or.   &
*>>*               ((MOD(NINT(tot_magnetization_),2) == 1) .and. (MOD
*>>* (NINT(nelec_),2)==0))      ) &
*>>*               CALL errore(' set_nelup_neldw
*>>* ',                          &
*>>*              'tot_magnetization is inconsistent with total number
*>>* of electrons ', 2 )
*
>in the new version, this restriction (now a warning, no longer an
>error) applies only if the
>number of electrons is integer and if the magnetization is integer.
>For noninteger charge
>or magnetization, it doesn't make sense.


In fact, increasing the k-point sampling, the unrestricted calculation
converges towards
0 total magnetization, with a lower energy than magnetization =1, but
setting tot_magnetization=0, or 0.1, 0.2, etc, stops due to the above
instruction in versiom 4.2.1.
This is one more reason to change to the newest version.


*You stated something in a previous post*
<pw_forum%40pwscf.org?Subject=%5BPw_forum%5D%20why%20are%20there%20two%20Fermi%20energies%3F&In-Reply-To=0CD095EE-2EC8-4E33-9F7F-334812E8089C%40sissa.it>
>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? I verified that the occupations are the
same, then I do not understand
why it is possible with different Fermi energies.
These are my KS energies and the occupations, using degauss=0.00019. I
think the differences are just numerical noise.

1)  tot_magnetization unset
     the Fermi energy is     6.1614 ev
!    total energy              =    -502.92571441 Ry     total
magnetization       =     1.00 Bohr mag/cell
up: 4.8593   4.8594   5.2221   5.2221   5.2222   6.1335   6.1336   6.1338


      1.0000   1.0000   1.0000   1.0000   1.0000   1.0000   1.0000   1.0000

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   0.6709   0.6661   0.6631

2) tot_magnetization=1
     the spin up/dw Fermi energies are     6.3853    6.1614 ev
!    total energy              =    -502.92571439 Ry     total
magnetization       =     1.00 Bohr mag/cell
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

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

Finally, I plotted Energy vs magnetization. Indeed, I have a minimum
at total magnetization equal 1. However, the
behavior is strange. The plot of E vs M is linear at each side of the
minimum, with a kink at M=1. Should'n it be rather like a parable ?
Please, see the plots here

http://www.gnm.cl/emenendez/pmwiki.php/Temp/Plots?action=upload&upname=impurity-energy.eps

http://www.gnm.cl/emenendez/pmwiki.php/Temp/Plots?action=upload&upname=impurity-fermi.eps


This was using gamma point fo sample the Brillouin zone. That is not
converged, using a 3x3x3 grid the lowest energy seems to be
for null magnetization (I am doing more calculations). Maybe the kinks
are due to insufficient Brillouin zone sampling.



Best regards


-- 


Eduardo Menendez
Departamento de Fisica
Facultad de Ciencias
Universidad de Chile
Phone: (56)(2)9787439
URL: http://fisica.ciencias.uchile.cl/~emenendez
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