[Pw_forum] why are there two Fermi energies?
Eduardo Ariel Menendez Proupin
eariel99 at gmail.com
Mon Apr 25 15:10:35 CEST 2011
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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