[Pw_forum] why are there two Fermi energies?
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 6.38536.1614 ev > up: 4.8593 4.8594 5.2221 5.2221 5.2221 6.1335 6.1337 > 6.1338 > 1. 1. 1. 1. 1. 1. > 1. 1. 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. 1. 1. 1. 1. 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
[Pw_forum] why are there two Fermi energies?
I am sorry, Murphy's law has just acted. Find the figures here http://www.gnm.cl/emenendez/uploads/Temp/impurity-energy.eps http://www.gnm.cl/emenendez/uploads/Temp/impurity-fermi.eps 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 (above) Eduardo Menendez Departamento de Fisica Facultad de Ciencias Universidad de Chile Phone: (56)(2)9787439 URL: http://fisica.ciencias.uchile.cl/~emenendez -- next part -- An HTML attachment was scrubbed... URL: http://www.democritos.it/pipermail/pw_forum/attachments/20110425/9473060a/attachment.htm
[Pw_forum] why are there two Fermi energies?
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*
>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. 6.1335 6.1336 6.1338
1. 1. 1. 1. 1. 1. 1. 1.
dw: 4.8796 4.8796 5.2528 5.2530 5.2531 6.1595 6.1596 6.1596
1. 1. 1. 1. 1. 0.6709 0.6661 0.6631
2) tot_magnetization=1
the spin up/dw Fermi energies are 6.38536.1614 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. 1. 1. 1. 1. 1. 1. 1.
dw: 4.8796 4.8796 5.2528 5.2530 5.2531 6.1595 6.1596 6.1596
1. 1. 1. 1. 1. 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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[Pw_forum] why are there two Fermi energies?
On Apr 22, 2011, at 17:10 , Eduardo Ariel Menendez Proupin wrote:
> 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.
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
[Pw_forum] why are there two Fermi energies?
Alexander
>Shift in eigenvalues can be seen as produced by external magnetic fiels (a
>Zeeman term) then the state with two different Fermi energies may be
thought of a >true ground state with only one Fermi level but in the
presence of this stabilizing >magnetic field proportional to the difference
in Fermi energies.
Why not a true ground state with one Fermi level and an external plus an
internal magnetic field that is due to the spin polarization, causes a shift
ib the KS energies, and is self adjusted to have thermodynamical
equilibrium, i.e., one Fermi level.
Fixing total magnetization would be equivalent to setting and external
magnetic field, and shifting the eigenvalues would be equivalent to an
internal magnetic field.
By the way, what are the physical restrictions to the values of
tot_magnetization ?
In my system, having 255 electrons, I can fix tehe tot_magnetization to
0.5, 0.7, 1, 1.2, 1.3, 3.0
For 1.5 <= tot_magnetization<2.5 I get error
from set_nelup_neldw : error # 2
tot_magnetization is inconsistent with total number of electrons
well I see the restriction is in this piece of code
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 )
I understand that with integer occupations the magnetization could have only
even or odd integer values values depending on the number of electrons. But,
with smearing, allowing real occupations, what is the problem with having
even magnetization with odd number of electrons or close real values?
Best wishes
--
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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[Pw_forum] why are there two Fermi energies?
Hello 2011/4/21 Eduardo Ariel Menendez Proupin > Hi, > Let me clarify that I found no difference between version 4.2.1 and others. > I have used only 4.2.1. > > I suspected that the Fermi level was a way to control the occupations. > However, using different fermi levels will produce different charge > densities because the occupation numbers will be different. If both types of > calculations produce the same energy, then the ground state is degenerate, > but the one with two Fermi energies seems incompatible with thermodynamics. > I used Fermi smearing, by the way. > > I am committed to teaching duties today. Thanks for your answers, and I > will come back tomorrow, or maybe late today, and I will look at the > occupations using verbosity = .true. > > Mathematically it seems logical that to control the number of electron > (one degree of freedom) one needs one parameter, which is the Fermi level. > To control an additional degree of freedom, the magnetization, one needs an > additional parameter, then it is reasonable to use two Fermi levels or an > equivalent set of two parameters. > For example, one could define a single Fermi level and apply a shift to the > spin down eigenvalues. This needs a physical interpretation, as well as > having to Fermi levels. > Shift in eigenvalues can be seen as produced by external magnetic fiels (a Zeeman term) then the state with two different Fermi energies may be thought of a true ground state with only one Fermi level but in the presence of this stabilizing magnetic field proportional to the difference in Fermi energies. The true ground state with equal Efs do not need of course this magnetic field. regards, Alexander > > Moreover, reversing the reasoning, I wonder why or how one gets the same > number of electrons and magnetization using only one parameter (Fermi level) > in the case of not using tot_magnetization. Is it a hazard or is there a > trick that bias the calculation to the integer magnetization? > > Best regards > -- > > > Eduardo Menendez > Departamento de Fisica > Facultad de Ciencias > Universidad de Chile > Phone: (56)(2)9787439 > URL: http://fisica.ciencias.uchile.cl/~emenendez > > ___ > Pw_forum mailing list > Pw_forum at pwscf.org > http://www.democritos.it/mailman/listinfo/pw_forum > > -- next part -- An HTML attachment was scrubbed... URL: http://www.democritos.it/pipermail/pw_forum/attachments/20110421/389322cb/attachment.htm
[Pw_forum] why are there two Fermi energies?
On Thu, 2011-04-21 at 11:28 +0200, Gabriele Sclauzero wrote: > Yes, I know there have been some changes in the last versions. > I think Paolo can be more helpful here. I don't think so. There are no substantial differences in the last version wrt the previous one in this case. I do not see anything anomalous in Eduardo's results, by the way. The results with constrained and unconstrained magnetizations are the same => the constrained-magnetization result is the ground state. 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. P. -- Paolo Giannozzi, IOM-Democritos and University of Udine, Italy
[Pw_forum] why are there two Fermi energies?
Hello, I'm also interested in going deeper into this topic. I tell what (I think) I've understood, so maybe we can trigger a discussion with Paolo or Stefano ;) Il giorno 21/apr/2011, alle ore 01.35, Eduardo Ariel Menendez Proupin ha scritto: > Hi, > Why are there two Fermi energies in certain spin-polarized calculations ? It's just a practical way to deal with spin polarized calculations when you fix a net non-zero total magnetization in the unit cell. Since you know the total charge and the total magnetization, you can determine univocally the number of spin up and of spin down electrons. This in turns allows you to treat the up and down Fermi energies independently, using the same techniques for spin-unpolarized calculations to determine the two Fermi energies. > > input starting_magnetization(1) = 0.0, > starting_magnetization(2) = 0.5, > output the Fermi energy is 6.1598 ev >!total energy =-502.92538790 Ry > > input tot_magnetization = 1 > output the spin up/dw Fermi energies are 6.38216.1598 ev > !total energy =-502.92538790 Ry > > What is the meaning of the spin up Fermi level in the second case? Did you get this with smearing? Otherwise the Fermi energy should not be printed. Specifying starting_magnetization or tot_magnetization is not equivalent, the former is just used to break the symmetry. You might end with a different magnetization, if that set by tot_magnetization does not correspond to the ground state. In your case it looks like the GS has M_tot=1, since you got exactly the same energy. What do you get as total magnetization in the first case? At first glance I don't see why in the first case you get the lowest of the two Fermi energies, I would rather expect the other. What changes between the two calculations is how the occupations are computed (see PW/weights.f90). You can print them on output by specifying verbosity='high'. > > This numbers are for a 64 atoms Si unit cell with one Si replaced by Al, and > only one k-point, but the same happens with more k-points. I also used Fermi > smearing with a very low smearing. > There is a difference if I set the starting magnetization or the total > magnetization, with pw.x version 4.2.1. However, despite reporting different > Fermi levels, the total energy and magnetization are equal. Also are equal KS > energies, at least around the Fermi levels. Yes, I know there have been some changes in the last versions. I think Paolo can be more helpful here. HTH GS > > Thanks, > > Eduardo Menendez > Departamento de Fisica > Facultad de Ciencias > Universidad de Chile > Phone: (56)(2)9787439 > URL: http://fisica.ciencias.uchile.cl/~emenendez > ___ > Pw_forum mailing list > Pw_forum at pwscf.org > http://www.democritos.it/mailman/listinfo/pw_forum ? Gabriele Sclauzero, EPFL SB ITP CSEA PH H2 462, Station 3, CH-1015 Lausanne -- next part -- An HTML attachment was scrubbed... URL: http://www.democritos.it/pipermail/pw_forum/attachments/20110421/63369d32/attachment.htm
[Pw_forum] why are there two Fermi energies?
On Thu, 21 Apr 2011 01:35:39 +0200, Eduardo Ariel Menendez Proupin wrote: > Why are there two Fermi energies in certain spin-polarized calculations ? > > input starting_magnetization(1) = 0.0, > starting_magnetization(2) = 0.5, > output the Fermi energy is 6.1598 ev >!total energy =-502.92538790 Ry > > input tot_magnetization = 1 > output the spin up/dw Fermi energies are 6.38216.1598 ev > !total energy =-502.92538790 Ry > > What is the meaning of the spin up Fermi level in the second case? Dear Eduardo, if you force the system to have a certain magnetization (i.e. setting tot_magnetization) you are actually asking to occupy the "up" spin orbital more then the "down" spin ones, i.e. you have more up electrons then down electrons. This is achieved by filling the up orbitals up to a higher energy than the down orbitals, by setting two distinct Fermi energies. On the other hand, if you only set starting magnetization, you get the computational ground state, where up and down orbitals are be filled up to the same level; what changes is the KS eigenvalues. hth, lorenzo > > This numbers are for a 64 atoms Si unit cell with one Si replaced by Al, > and > only one k-point, but the same happens with more k-points. I also used > Fermi > smearing with a very low smearing. > There is a difference if I set the starting magnetization or the total > magnetization, with pw.x version 4.2.1. However, despite reporting > different > Fermi levels, the total energy and magnetization are equal. Also are > equal > KS energies, at least around the Fermi levels. > > Thanks, > > Eduardo Menendez > Departamento de Fisica > Facultad de Ciencias > Universidad de Chile > Phone: (56)(2)9787439 > URL: http://fisica.ciencias.uchile.cl/~emenendez -- Lorenzo Paulatto (IdR) IMPMC - CNRS UMR 7590 & Universit? P&M Curie T23-C23/24-4e16 - 4 place Jussieu - 75252 Paris Cedex5 phone: +33 (0)144 27 5211 www: http://www-int.impmc.upmc.fr/~paulatto/
[Pw_forum] why are there two Fermi energies?
Hi, Let me clarify that I found no difference between version 4.2.1 and others. I have used only 4.2.1. I suspected that the Fermi level was a way to control the occupations. However, using different fermi levels will produce different charge densities because the occupation numbers will be different. If both types of calculations produce the same energy, then the ground state is degenerate, but the one with two Fermi energies seems incompatible with thermodynamics. I used Fermi smearing, by the way. I am committed to teaching duties today. Thanks for your answers, and I will come back tomorrow, or maybe late today, and I will look at the occupations using verbosity = .true. Mathematically it seems logical that to control the number of electron (one degree of freedom) one needs one parameter, which is the Fermi level. To control an additional degree of freedom, the magnetization, one needs an additional parameter, then it is reasonable to use two Fermi levels or an equivalent set of two parameters. For example, one could define a single Fermi level and apply a shift to the spin down eigenvalues. This needs a physical interpretation, as well as having to Fermi levels. Moreover, reversing the reasoning, I wonder why or how one gets the same number of electrons and magnetization using only one parameter (Fermi level) in the case of not using tot_magnetization. Is it a hazard or is there a trick that bias the calculation to the integer magnetization? Best regards -- Eduardo Menendez Departamento de Fisica Facultad de Ciencias Universidad de Chile Phone: (56)(2)9787439 URL: http://fisica.ciencias.uchile.cl/~emenendez -- next part -- An HTML attachment was scrubbed... URL: http://www.democritos.it/pipermail/pw_forum/attachments/20110421/a7025c46/attachment.htm
[Pw_forum] why are there two Fermi energies?
Hi, Why are there two Fermi energies in certain spin-polarized calculations ? input starting_magnetization(1) = 0.0, starting_magnetization(2) = 0.5, output the Fermi energy is 6.1598 ev !total energy =-502.92538790 Ry input tot_magnetization = 1 output the spin up/dw Fermi energies are 6.38216.1598 ev !total energy =-502.92538790 Ry What is the meaning of the spin up Fermi level in the second case? This numbers are for a 64 atoms Si unit cell with one Si replaced by Al, and only one k-point, but the same happens with more k-points. I also used Fermi smearing with a very low smearing. There is a difference if I set the starting magnetization or the total magnetization, with pw.x version 4.2.1. However, despite reporting different Fermi levels, the total energy and magnetization are equal. Also are equal KS energies, at least around the Fermi levels. Thanks, Eduardo Menendez Departamento de Fisica Facultad de Ciencias Universidad de Chile Phone: (56)(2)9787439 URL: http://fisica.ciencias.uchile.cl/~emenendez -- next part -- An HTML attachment was scrubbed... URL: http://www.democritos.it/pipermail/pw_forum/attachments/20110420/33eb2c6f/attachment.htm
