# [Pw_forum] why are there two Fermi energies?

Lorenzo Paulatto Lorenzo.Paulatto at impmc.upmc.fr
Thu Apr 21 11:00:49 CEST 2011

```On Thu, 21 Apr 2011 01:35:39 +0200, Eduardo Ariel Menendez Proupin
<eariel99 at gmail.com> 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     6.3821    6.1598 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
> Phone: (56)(2)9787439
> URL: http://fisica.ciencias.uchile.cl/~emenendez

--
Lorenzo Paulatto (IdR)
IMPMC - CNRS UMR 7590 & Université 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/

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